Agents and Implications of Landscape Pattern: Working Models for Landscape Ecology [1st ed. 2023] 3031402537, 9783031402531

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Dean L Urban

Agents and Implications of Landscape Pattern Working Models for Landscape Ecology

Agents and Implications of Landscape Pattern

Dean L Urban

Agents and Implications of Landscape Pattern Working Models for Landscape Ecology

Dean L Urban Nicholas School of the Environment Duke University Durham, NC, USA

ISBN 978-3-031-40253-1 ISBN 978-3-031-40254-8 https://doi.org/10.1007/978-3-031-40254-8

(eBook)

© Springer Nature Switzerland AG 2023 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland Paper in this product is recyclable.

Foreword

Be it enacted. . . That the tract of land in the Territories of Montana and Wyoming, lying near the headwaters of the Yellowstone River, and described as follows, to wit, commencing at the junction of Gardiner’s river with the Yellowstone river, and running east to the meridian passing ten miles to the eastward of the most eastern point of Yellowstone lake; thence south along said meridian to the parallel of latitude passing ten miles south of the most southern point of Yellowstone lake; thence west along said parallel to the meridian passing fifteen miles west of the most western point of Madison lake; thence north along said meridian to the latitude of the junction of Yellowstone and Gardiner’s rivers; thence east to the place of beginning, is hereby reserved and withdrawn from settlement, occupancy, or sale under the laws of the United States, and dedicated and set apart as a public park or pleasuring-ground for the benefit and enjoyment of the people.

On March 1, 1872, President Grant signed the Yellowstone National Park Protection Act that created the world’s first national park. Although it is a stretch to assert this to be the birthdate for land conservation in general, it most certainly is a signature moment in its history. But this opening paragraph to the Act also belies some of the challenges that would plague conservationists and land managers over the next 150 years. The park’s dedicated goal was unambiguously anthropocentric, but ambiguous about the particular benefits and joys it should provide, and to which people it should provide them. Its central focus was protection from outside forces rather than conservation of its innards. And, most relevant to the central theme of this book, it defines the park’s geographic boundaries, an 892,000 ha rectangle, with no reference to the domains of the myriad processes (physical, biological, and anthropological) that determine and sustain the features that inspired its conservation. Forty-four years and over a dozen national parks later, Congress finally saw fit to create a federal agency, the National Park Service, dedicated explicitly to park conservation. The 1916 Park Service Organic Act also clarified the National Parks’ reason for being, to wit: the conservation of “the scenery and the natural and historic objects and the wild life therein and to provide for the enjoyment of the same in such manner and by such means as will leave them unimpaired for the enjoyment of future generations.” Now, the focus was to be on the innards. People v

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remain important but only insofar as they leave those innards unimpaired for their children. But the phrase “natural and historic objects” turned out the be very troublesome. It reflected the prevailing view that, absent of human disturbance, nature consisted of static climax ecosystems and that parks were akin to museums dedicated to the curation of “vignettes of primitive America.” This book is about space and time. Judging from the national park system management prior to about 1970, one might conclude that these dimensions existed solely to ensure that things did not all happen at a single place or moment. Park boundaries could be and were defined by political expediency (e.g., be sure to include portions of the Wyoming, Montana, and Idaho territories) or convenience (e.g., rivers are convenient boundaries even though they bisect watershed ecosystems). Landscape disturbance and change were to be avoided. I pick on national parks management not because it was unique. On the contrary, on the full spectrum from parks and conservation preserves to lands dedicated to wood fiber production, agriculture, or urban development, such land management was typical during that time. There were of course a few individuals and organizations that, early on, advocated for management that recognized the importance of spatial scale and temporal dynamics. But it was not until the early 1970s, a century after Yellowstone National Park’s creation, that explicit consideration of spatial variation and change became the norm in land management. In this book, Dean Urban describes methods for depicting and quantifying spatial and temporal relationships within and among ecosystems that facilitated this transition. Just as important, he provides guidance on the application of these tools to management challenges on landscapes across the full spectrum of human influence. Dean asserts that models that depict our best understanding of how the world works are, first and foremost, the foundation of landscape ecology and necessary prerequisites for land management; necessary but not sufficient. Dean makes clear that models must always be treated as provisional hypotheses, subject to change or replacement as we learn and our understanding of the world changes. This implies that management like science must always include the means to learn new things. Land managers were certainly motivated by models from the very beginning. That the primeval world was dominated by stable climax ecosystems and that disturbed ecosystems inevitably succeeded to such climaxes were axiomatic assumptions of these models. But it is no exaggeration to say that these long-ago assumptions were faith-based rather than data-based. They represented the world the way we wanted it to be. Like a pendulum or an ideal gas, ecosystems left to themselves always trended toward stability. Worse, there was no accommodation for acquiring new knowledge much less adapting models and management to it. It was only toward the middle of the twentieth century that ecologists began to consider the possibility that ecological systems looked and behaved differently depending on spatial and temporal scales. Populations and communities of organisms that seemed to be stable at large over large expanses of space and time appeared less so over smaller domains. It was becoming hard to deny that disturbances such as fire, wind, and disease, as well as the change they generated, were inevitable, natural, and (lord forbid) essential ecosystem processes. The spatial and temporal domains of these processes also varied widely.

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The incongruity between the scales of these processes and the boundaries of land management units was also becoming painfully obvious. Yellowstone is an exemplar of that pain. Its linear boundaries bear little relationship to the movement of its iconic ungulates, elk, bison, pronghorn, and the like. The fires of 1988 revealed that 892,000 ha is too small an area to capture the disturbance and change necessary to sustain all of the landscape elements for which the park was dedicated. The reintroduction of gray wolves in the 1990s confirmed our suspicions about the importance of food chain diversity and complexity to ecosystem sustainability. It also taught us about the spatial and temporal variability in that diversity and complexity. Together, these lessons made clear that the timeframes of electoral cycles and park management plans are antithetical to those of the processes that sustain this landscape. The phrase “ecosystem management” is now embedded in the planning document of every federal land management agency. It is no accident that this management concept co-evolved with the field of landscape ecology. The elements of ecosystem management map out wonderfully on the organization and lessons of this book. • Scientists and managers should always be humble about the extent of their understanding. Models are essential but only helpful insofar as they represent our best data-based understanding of ecosystem elements and processes. They must be viewed as provisional and adaptable to changes in that understanding. • Diversity and complexity are essential to sustainable management. They are not, however, static properties of ecosystems and landscapes; they vary widely across domains of time and space and management must accommodate that variation. • Spatial and temporal management scales for a landscape should be defined by the myriad processes necessary to sustain it. Alas, these scales vary widely among those processes; there is no single ideal spatial scale for landscape management. • It follows that the boundaries of management units are inevitably arbitrary with regard to some processes, and managers must collaborate with others beyond those boundaries. • There are now eight billion of us on this planet. Human actions are an inescapable feature of all landscapes. I am especially pleased that Dean has acknowledged this reality throughout his book. Professor and Dean Emeritus, Nicholas School of the Environment, Duke University, Durham, NC, USA

Norman L. Christensen

Preface

Landscape ecology is a maturing discipline that might be envisioned as the intersection of a variety of fields concerned with natural, semi-natural, and cultural landscapes. Substantial contributions from ecology are obvious, but so are linkages to geography, history, and social sciences invested in human activities on or perceptions of landscapes. This rich smörgåsbord of intellectual content and personal perspective clearly enriches the discipline, but it also can be a bit daunting. Imagine the hellish Venn diagram that might arise from any effort to fully chart this space! For many years, I have taught a graduate-level course in Landscape Ecology. My course has always targeted students whose interests are in pursuing careers in the business of doing landscape ecology. For all of those years, I have been frustrated by the lack of a single text that might bring together all of the pieces for my students. Finally, I decided to just write that text. As several good friends (and friendly reviewers of earlier versions of these chapters) have pointed out, this is a ridiculous premise for a book. The topics developed in every single chapter (outlined below) already have spawned many, many books; to hope to synthesize these is a fool’s errand. And yet, here we are. In trying to create something useful, I have adopted a few conventions. First, I have tried to focus on core ideas that are “need to know” for management applications. This means that I have forced myself to not include every new or tantalizing idea, every shiny object to appear on the horizon. Many of the core ideas, indeed, are quite venerable and I take some comfort in that. I also have taken a somewhat tactical approach in citations to original work. In each chapter, I have tried to highlight thought leaders on that topic, referencing their seminal contributions. In doing this, I necessarily omit a huge number of new and relevant papers. By the time this book comes to press, many of the citations will be outdated . . . but a quick search by name for the thought-leaders—or people who have cited them—will find the newer stuff.

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In all of this, I have tried to convey my own excitement about the core ideas in landscape ecology. I was a graduate student when landscape ecology emerged as a discipline in the United States, and I have relished the gift of watching a discipline invent itself in real time. I hope you will enjoy this perspective as well.

The Role of Models in Landscape Ecology and in This Book In a sense, the approach taken in this book is to develop a model of how landscapes work, and then to explore this model from various perspectives. Because models play such a central role in the book, I must digress a bit here to make clear the role that models play in landscape ecology in general and in this book in particular. Model is a fuzzy term and there are as many perspectives on models as there are modelers. Models range from conceptual diagrams or narrative descriptions of how we think a system works, to extremely detailed and complicated simulators of real systems. But regardless of the format or level of detail, models are used for a few common purposes: (1) to organize our thinking about a system; (2) to communicate this understanding efficiently and effectively; (3) to make obvious the implications of the structure and functional linkages of the system; (4) to suggest implications of system behavior that might not yet have been appreciated; and (5) to make formal predictions (forecasts) about the future state of the system given an explicit scenario. These applications reflect the maturation of any particular model, from working hypothesis to predictive tool. In most of this book, I emphasize the earlier stages of modeling, especially conceptual models. These are used principally to illustrate concepts that would be unwieldy if conveyed in purely narrative form. In a few instances, I turn to more realistic models—conceptual models that are calibrated empirically for a given landscape. This two-level approach to models is fundamental to this book, and (I believe!) to landscape ecology. My approach to landscape ecology is to present a general model of how landscapes work . . . with the explicit expectation that precisely how each landscape works will be unique and particular to that time and place. Steward Pickett and his colleagues (whose work we will feature in Chap. 9) call these model templates: generic and sometimes high-level abstractions that become real only when they are implemented with details (and data) for a particular system. The net result is an approach where I argue that the same general model(s) apply to every landscape, but each landscape turns out to be unique depending on its particulars. While this might seem frustrating initially (nothing holds in general!), I find it reassuring that this approach allows one to embrace a new study area by considering, in turn, a conceptual construct and list of “likely suspects” that might explain how the system works. Thus, my model template is to provide a set of explanatory principles (model templates), with illustrations of how these might play out in different systems. The following chapters collectively provide a conceptual foundation of how landscapes function along with a reasonably rich vocabulary and models for working with landscapes. This forms the basis for a semester’s course in Landscape Ecology (indeed, this is my class). Much of this material is illustrated with examples from

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particularly well documented case studies, including (perhaps unavoidably) some of my own work. Readers will naturally be inclined to substitute their own examples for the ones in this book. Indeed, when I teach this class I invite my students to “adopt” a landscape for the duration of the course, and we do reflective exercises throughout the semester wherein students apply or extend the concepts from the illustrations in the book to their adopted landscapes. I invite readers of this book to adopt the general model templates as provided, and to adapt these to your own landscapes. This exercise reinforces the general models while making them real, personal, and useful. There is a lot of ecology in this book. This course would be suitable for advanced undergraduates, or for graduates in a variety of disciplines in ecology and natural resource management. Researchers and practitioners, likewise, should find this a compact synthesis of a lot of wide-ranging material. The material might be challenging in places, as no reader is likely to have deep experience with all of this material. But that was my aim: to collect all of this in one place. I hope you find the synthesis and packaging useful.

Organization of This Book This book is organized into two main parts, reflecting the dominant paradigm in landscape ecology: pattern and process. Landscape ecology holds that ecological processes generate spatial heterogeneity and pattern, and that this pattern reciprocally constrains processes that occur on landscapes. This book’s two main parts focus first on agents that generate pattern on landscapes, and then on how ecological processes respond to pattern. Because the interaction is reciprocal, this is an artificial separation and we need to be a bit careful in reconciling this “chicken or egg” problem. The first three chapters explore the primary agents of landscape pattern: the physical template of landscapes as manifested in biophysical gradients, especially temperature and moisture (Chap. 1); biological processes that generate broadscale vegetation pattern such as what we see along montane or topographic gradients (Chap. 2); and disturbance regimes (Chap. 3). Because each of these agents interacts with the others, they are first layered onto each other and then their interactions are emphasized (at the end of Chap. 3). These first chapters will have broached, quite naturally, issues of spatial and temporal scaling, and we digress at this point to delve more explicitly into the crucial topics of scale (Chap. 4) and spatial pattern (Chap. 5). In the latter, we focus especially on the logical and empirical basis from which we make inferences about the relationships between pattern and process. In the next three chapters, we look at the implications of pattern for populations (Chap. 6), communities and biodiversity (Chap. 7), and ecosystem processes (Chap. 8). In each case, the importance of spatial heterogeneity and local interactions mediated by dispersal or other fluxes will lead to higher-level, emergent behaviors: of metapopulations, metacommunities, and meta-ecosystems.

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The final two chapters apply this perspective to two critical, emerging areas. In Chap. 9, we look at urban landscapes. In Chap. 10, we turn to global climate change and issues of adaptation and resilience. In both cases, we apply the conceptual models of previous chapters to these new frontiers. Durham, NC, USA

Dean L Urban

Acknowledgments

Landscape ecology originated as a small world of highly interactive colleagues, and I am deeply grateful to several friends who have shared their courses over the years. It is not coincidental that our course syllabuses (and our books!) have much in common. I especially thank David Mladenoff, Monica Turner, and Bob Gardner, with whom I “co-taught” courses for many years early on. This has been an evolving effort over a long time, and I am grateful especially for the sequence of amazing graduate students who have helped craft this book as students and as teaching assistants in my classroom. I especially appreciate their willingness to intervene when I was standing too close to the material. Regina Barnhill, B Design Studio, generated the consistent graphic scheme for all of the figures, from reproducing old figures from journal articles to creating new schematics and illustrations. I truly appreciate her talent, patience, and good humor. Each of the chapters here has been vetted by friends (I hope they are still friends!). Nate Stephenson helped with the first several chapters, which feature our work together in Sequoia National Park in the Sierra Nevada of California. Other reviewers include Peter White (Chap. 3), Indy Burke (Chaps. 4 and 8), Kevin McGarigal (Chap. 5), Lenore Fahrig (Chap. 5), Brenna Forester (Chaps. 6 and 7), Rob Fletcher (Chap. 6), Marie-Josee Fortin (Chap. 7), Emily Bernhardt (Chaps. 8 and 9), Rob McDonald (Chap. 9), Steward Pickett (Chap. 9), Pat Comer (Chap. 10), and Mark Anderson (Chap. 10). Many of the chapters evolved substantially in the wake of their reviews and I can only hope that I have not disappointed too much in this. (Shortcomings are my own, of course.) Andy Bunn taught his advanced undergraduate course for a few years using early drafts of the first half of this book (I cringe a bit at the thought of those early versions). Nicki Cagle reviewed and edited the entire thing, and I am grateful for her unerring instincts in making this a more accessible and much friendlier book.

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Norm Christensen also reviewed the entire beast and offered sometimes painful but always useful high-level advice on what I was trying to do with this book. His friendship over many decades has been a pure joy. Durham, NC, USA

Dean L Urban

Contents

1

2

The Physical Template of Landscapes . . . . . . . . . . . . . . . . . . . . . . . 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Gradient Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.1 Gradient Complexes . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 The Water Balance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.1 A Simple Model: PET = AET + Deficit . . . . . . . . . . . 1.4 Estimating Elements of the Template . . . . . . . . . . . . . . . . . . . . 1.4.1 Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4.2 Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4.3 Precipitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4.4 Soils . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5 Case Study: The Sierra Nevada . . . . . . . . . . . . . . . . . . . . . . . . 1.5.1 The Physical Template of the Sierra Nevada, California . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.6 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Biotic Processes as Agents of Pattern . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 The “Pattern and Process” Paradigm . . . . . . . . . . . . . . . . . . . . . 2.3 Coupling of Demographic Processes . . . . . . . . . . . . . . . . . . . . 2.4 Interaction with the Physical Template . . . . . . . . . . . . . . . . . . . 2.4.1 Coupling Demography and the Physical Template . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.2 Competition Along Environmental Gradients . . . . . . . . 2.4.3 Illustration: Gradient Response in the Sierra Nevada . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.4 The Unit Pattern Revisited . . . . . . . . . . . . . . . . . . . . .

1 1 2 3 5 5 9 9 11 15 16 21 21 26 26 29 29 30 33 34 35 36 40 43

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2.5

Dispersal as an Agent of Pattern . . . . . . . . . . . . . . . . . . . . . . . . 2.5.1 Interactions Between Dispersal and Gradient Response . . . . . . . . . . . . . . . . . . . . . . . . 2.6 Animals, Pests, and Pathogens . . . . . . . . . . . . . . . . . . . . . . . . . 2.6.1 Animals, Pests, and Pathogens as Subtle Agents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6.2 Animals as Dramatic Agents . . . . . . . . . . . . . . . . . . . . 2.7 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Disturbances and Disturbance Regimes . . . . . . . . . . . . . . . . . . . . . . 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.1 Context and Definitions . . . . . . . . . . . . . . . . . . . . . . . 3.2 Perspectives and Lessons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 Are Disturbances “Part of the System”? . . . . . . . . . . . . 3.2.2 Interactions, Synergies, and Indirect Effects . . . . . . . . . 3.2.3 Disturbances and Positive Feedback . . . . . . . . . . . . . . 3.2.4 Overlapping Disturbances and Legacies . . . . . . . . . . . . 3.2.5 Heterogeneity in Disturbance and Response . . . . . . . . . 3.3 Disaggregating Disturbance Toward Generality . . . . . . . . . . . . . 3.3.1 A Not-Too-General Model . . . . . . . . . . . . . . . . . . . . . 3.3.2 The Fire Regime in the Sierra Nevada . . . . . . . . . . . . . 3.4 Characteristic Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Humans and Disturbance Regimes . . . . . . . . . . . . . . . . . . . . . . 3.5.1 Human Impacts on Natural Disturbances . . . . . . . . . . . 3.5.2 Novel Disturbance Regimes . . . . . . . . . . . . . . . . . . . . 3.5.3 Human Perception and Landscape Change . . . . . . . . . . 3.6 Agents of Pattern: Reprise . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.7 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

55 55 55 58 58 59 60 62 63 65 65 66 70 73 73 75 75 76 78 79

4

Scale and Scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 The Importance of Scale in Ecology . . . . . . . . . . . . . . . . . . . . . 4.2.1 Observational Scale as a Filter on Nature . . . . . . . . . . . 4.2.2 Characteristic Scaling . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.3 Sampling Grain and Extent, and Statistical Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Scaling Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.1 Scaling Techniques for Geostatistical Data . . . . . . . . . . 4.3.2 Illustration: Scaling of the Sierran Physical Template . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 Tactical Scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.1 Tactical Targeting of Sampling Scale(s) . . . . . . . . . . . . 4.4.2 Avoid or Embrace Space? . . . . . . . . . . . . . . . . . . . . . . 4.5 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

85 85 86 87 95

45 48 48 49 51 51

95 98 99 107 109 110 110 113 114

Contents

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Inferences on Landscape Pattern . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Patchiness and Patches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.1 Patch Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Landscape Pattern Metrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.1 Levels of Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.2 Components of Pattern . . . . . . . . . . . . . . . . . . . . . . . . 5.3.3 Correlation and Redundancy . . . . . . . . . . . . . . . . . . . . 5.3.4 Alternative Framings for Landscape Pattern . . . . . . . . . 5.4 Interpreting Landscape Metrics . . . . . . . . . . . . . . . . . . . . . . . . 5.4.1 Neutral Models and Neutral Landscapes . . . . . . . . . . . 5.4.2 Neutral Templates for Landscape Processes . . . . . . . . . 5.4.3 Extending Neutral Models: Agents of Pattern, Revisited . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5 Explanatory Models and Inferences . . . . . . . . . . . . . . . . . . . . . 5.5.1 Approaches to Inferences on Pattern . . . . . . . . . . . . . . 5.5.2 Illustrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5.3 Inferences on Pattern: Area Versus Configuration . . . . . 5.5.4 Inferences on Pattern: The State of the Art . . . . . . . . . . 5.6 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.6.1 Homage to John Curtis . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

117 117 118 119 121 121 122 126 127 129 129 132

Implications of Pattern: Metapopulations . . . . . . . . . . . . . . . . . . . . 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Metapopulations in Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.1 The Levins Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.2 The Spreading-of-Risk Model . . . . . . . . . . . . . . . . . . . 6.2.3 The Source-Sink Model . . . . . . . . . . . . . . . . . . . . . . . 6.2.4 The Incidence Function Model . . . . . . . . . . . . . . . . . . 6.2.5 Commonalities Among Metapopulation Models . . . . . . 6.2.6 Characteristic Behaviors of (Model) Metapopulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3 Metapopulations in Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.1 Are There Real Metapopulations in Nature? The Evidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.2 Macroscopic Approaches to Metapopulations . . . . . . . . 6.4 Network Models of Metapopulations . . . . . . . . . . . . . . . . . . . . 6.4.1 Graphs and Metapopulations . . . . . . . . . . . . . . . . . . . . 6.5 Metapopulations and Connectivity Conservation . . . . . . . . . . . . 6.5.1 Structural and Functional Connectivity . . . . . . . . . . . . 6.5.2 Metapopulations and Landscape Genetics . . . . . . . . . . 6.6 A Model Template for Applications . . . . . . . . . . . . . . . . . . . . . 6.7 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

153 153 154 154 155 155 156 157

133 135 135 138 141 144 145 145 146

158 163 164 165 167 170 173 173 176 179 180 181

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Contents

Communities and Patterns of Biodiversity . . . . . . . . . . . . . . . . . . . . 7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 Island Biogeography and Landscapes . . . . . . . . . . . . . . . . . . . . 7.2.1 Area and Isolation Effects . . . . . . . . . . . . . . . . . . . . . . 7.2.2 Island Biogeographic Theory and the SLOSS Debate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.3 A Diversity of Diversities . . . . . . . . . . . . . . . . . . . . . . 7.3 Perspectives on Metacommunities . . . . . . . . . . . . . . . . . . . . . . 7.3.1 A General Framing . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3.2 Inferences and Limits to Inference . . . . . . . . . . . . . . . . 7.4 Approaches and Lines of Evidence . . . . . . . . . . . . . . . . . . . . . . 7.4.1 The Incidence Matrix and Community Assembly . . . . . 7.4.2 Metacommunity Models: Variations on a Theme . . . . . 7.4.3 Species Distribution Models . . . . . . . . . . . . . . . . . . . . 7.4.4 Multivariate Approaches to Partitioning Beta Diversity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.4.5 Lines of Evidence and Complementary Analyses . . . . . 7.5 Illustration: Sierran Forests . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.5.1 The Perspective of Ordination and Gradient Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.5.2 Partitioning Beta Diversity . . . . . . . . . . . . . . . . . . . . . 7.6 Managing Metacommunities . . . . . . . . . . . . . . . . . . . . . . . . . . 7.7 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

191 191 192 193

211 213 215 217 218

Implications of Pattern for Ecosystems . . . . . . . . . . . . . . . . . . . . . . 8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2 Spatial Heterogeneity and Ecosystems . . . . . . . . . . . . . . . . . . . 8.2.1 Spatial Heterogeneity in the Physical Template . . . . . . 8.2.2 Lateral Fluxes on Landscapes . . . . . . . . . . . . . . . . . . . 8.2.3 Landform and Landscape Processes . . . . . . . . . . . . . . . 8.2.4 Ecosystem Processes and Positive Feedbacks . . . . . . . . 8.2.5 Ecosystems Are both Fast and Slow . . . . . . . . . . . . . . 8.3 Ecosystems and Landscape Legacies . . . . . . . . . . . . . . . . . . . . 8.4 Patch Juxtaposition and Edge Effects . . . . . . . . . . . . . . . . . . . . 8.4.1 Edge Effects, Revisited . . . . . . . . . . . . . . . . . . . . . . . . 8.5 Ecosystems and Meta-ecosystems . . . . . . . . . . . . . . . . . . . . . . 8.5.1 Couplings Between Systems . . . . . . . . . . . . . . . . . . . . 8.5.2 Meta-ecosystems, Revisited . . . . . . . . . . . . . . . . . . . . 8.5.3 Implications of Meta-ecosystem Structure . . . . . . . . . . 8.6 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

225 225 226 227 228 230 232 233 234 237 237 242 244 247 249 250 251

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Contents

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Urban Landscapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2 Social-Environmental Systems . . . . . . . . . . . . . . . . . . . . . . . . . 9.2.1 Approaches to Studying Cities . . . . . . . . . . . . . . . . . . 9.3 Agents and Implications of Pattern . . . . . . . . . . . . . . . . . . . . . . 9.3.1 Agents of Pattern . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.3.2 Scale and Pattern . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.3.3 Implications of Pattern . . . . . . . . . . . . . . . . . . . . . . . . 9.3.4 Revisiting the Agents-and-Implications Framing . . . . . . 9.4 Urban Landscapes as Laboratories . . . . . . . . . . . . . . . . . . . . . . 9.4.1 The Urban Stream Syndrome . . . . . . . . . . . . . . . . . . . 9.4.2 Cities as Mesocosms for Global Change . . . . . . . . . . . 9.5 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

255 255 256 258 259 259 263 265 270 270 271 276 279 279

10

Climate Change: Adapting for Resilience . . . . . . . . . . . . . . . . . . . . 10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2 Framing Adaptation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2.1 Components of Climate Change . . . . . . . . . . . . . . . . . 10.2.2 The Perspective of Risk Management . . . . . . . . . . . . . 10.2.3 Options for Response and Adaptation . . . . . . . . . . . . . 10.2.4 Resilience Planning: The Tasks at Hand . . . . . . . . . . . 10.3 Approaches to Adaptation Planning . . . . . . . . . . . . . . . . . . . . . 10.3.1 Levels of Activity and Currency of Assessments . . . . . 10.3.2 Elements of Adaptation . . . . . . . . . . . . . . . . . . . . . . . 10.3.3 A Template for Applications . . . . . . . . . . . . . . . . . . . . 10.4 Illustrations of Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.4.1 NatureServe’s Habitat Climate-Change Vulnerability Index . . . . . . . . . . . . . . . . . . . . . . . . . . 10.4.2 Species Range Shifts Implied by Climate Change . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.4.3 The Nature Conservancy’s Resilient Landscapes Initiative . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.4.4 The Adaptation for Conservation Targets Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.4.5 Complementarity of Approaches . . . . . . . . . . . . . . . . . 10.5 Collateral Benefits and Leverage . . . . . . . . . . . . . . . . . . . . . . . 10.5.1 Adaptation Planning and Conservation Practice . . . . . . 10.5.2 Collateral Benefits . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.5.3 Adaptation and Mitigation . . . . . . . . . . . . . . . . . . . . . 10.6 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

287 287 288 288 290 293 295 296 297 298 301 302 302 304 306 309 311 312 312 313 314 314 315

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323

Chapter 1

The Physical Template of Landscapes

1.1

Introduction

Landscapes are shaped fundamentally by the interaction of climate and landform. These interactions generate gradients in temperature, radiation, soil moisture, and soil fertility. Other surficial processes, especially erosional and depositional processes along hillslopes, modify or amplify these gradients. These gradients constrain all biophysical and ecological processes on landscapes. Thus, a consideration of landscape patterns logically begins with the physical template. In this chapter, we focus on landscape-scale variation in temperature, radiation, precipitation, and drainage. These are influenced by elevation and topographic position to generate spatial heterogeneity in temperature and soil moisture. The approach here is first to understand the conceptual basis for these gradients, but further, to consider methods for interpolating these variables empirically over entire landscapes. We will explore a variety of models of each of these factors, including general conceptual models as well as more detailed biophysical simulators. In particular, we consider a variety of macroscopic proxies for temperature and moisture, focusing on indices that can be computed in a geographic information system (GIS) using readily available geospatial data. A case study based on gradient patterns in the Sierra Nevada of California, motivated by issues of global climate change, helps illustrate these concepts and models. Montane landscapes are a particularly apt focus for this chapter as they exemplify a central challenge in landscape ecology: the study areas are vast and heterogeneous and the data sparse; and thus we depend on models for interpolating what little data we might have. We will spend some effort on empirical proxies for elements of the physical template because we will use these later in applications such as habitat classification or species distribution models. In particular, the task of forecasting changes in species distribution in response to climate change (see Chap. 10) will demand that

© Springer Nature Switzerland AG 2023 D. L. Urban, Agents and Implications of Landscape Pattern, https://doi.org/10.1007/978-3-031-40254-8_1

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1 The Physical Template of Landscapes

we understand how the biophysical environment is patterned and at what scales (see Chap. 4), and how species respond to the physical template in a competitive milieu (see Chap. 2).

1.2

Gradient Analysis

Gradient analysis, a long tradition in community ecology, emphasizes the relationships between species distributions and biophysical gradients (Whittaker 1967; ter Braak and Prentice 1988; Austin and Smith 1989; McCune and Grace 2002). Much of this work is based on ordination, a family of multivariate statistical tools (Curtis and McIntosh 1951; Bray and Curtis 1957; Whittaker 1978; Gauch 1982; Beals 1984; Pielou 1984; Jongman et al. 1995; McCune and Grace 2002; Legendre and Legendre 2012). While the details of these techniques vary considerably, all ordinations are similar in that they attempt to condense high-dimensional ecological data into a low-dimensional summary that emphasizes the main trends. For example, in many studies, the ecological data represent very many species tallied at very many sample locations, along with many environmental factors measured at the same locations. The aim is to identify the main trends in community composition and to relate these to the environmental factors. A striking consensus of gradient analysis is that vegetation patterns can usually be condensed into a very few dimensions (Fig. 1.1). One main trend is related to temperature, and a second common trend is related to soil moisture. This pattern is repeated in many, many examples (e.g., Whittaker 1956, 1960, 1967; see reviews by Stephenson 1990, 1998). To be precise, Fig. 1.1 is a direct ordination: Whittaker subjectively chose those axes to summarize those forests. He also selected the proximate variables—elevation and topographic position—used to quantify species position along the axes. Two points should be noted in the ordination diagram. First, the axes usually are not measured directly; they are interpreted in terms of proxy variables such as elevation (temperature) or topographic position (e.g., from mesic cove to xeric ridge, or from mesic northerly to xeric southerly exposures). Second, in many such direct ordination diagrams, the vegetation zones or ecotones are arrayed on a slight diagonal in the ordination space. That is, vegetation types occur at higher elevations on more southerly or xeric exposures, and at lower elevations on more northerly or protected exposures. In other words, more southerly exposures are effectively equivalent to lower-elevation sites, while more northerly exposures are effectively higher elevations: the two axes interact. This is because temperature and moisture are expressed on both ordination axes; these factors are influenced by elevation and also by local topographic position. Our concern here is to develop a fuller understanding of how these gradients develop, with the eventual aim being to model them statistically from geospatial data. That is, we would like to be able to interpolate temperature and relative soil moisture over landscapes, ideally in a geographic information system (GIS) (e.g.,

1.2

Gradient Analysis

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Fig. 1.1 Example of a direct ordination of plant community pattern, for serpentine soils in the Siskiyou Mountains of Oregon and California, summarizing temperature and moisture as the dominant trends. Compositional details have been omitted, to emphasize the axes. (Redrawn with permission of John Wiley & Sons, from Whittaker (1960); permission conveyed through Copyright Clearance Center, Inc.)

Lookingbill and Urban 2003, 2004, 2005). This capacity will provide a first approximation of the physical template of landscapes. This working model of the physical template will provide the foundation not only for the next several chapters but also for many of the applied tasks of landscape ecology.

1.2.1

Gradient Complexes

Before delving into the details of modeling environmental gradients, it is worth underscoring one essential feature of most gradients: There are many environmental factors that covary along gradients such as elevation. For example, temperature, precipitation, radiation, soil pH and soil chemistry, soil texture, and soil depth all tend to vary with elevation in mountain systems. Ecologists often use the term gradient complex to connote this suite of interacting factors. Indeed, one aim of ordination is to condense all of these factors into a single, readily interpretable

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1 The Physical Template of Landscapes

construct. We will see more of this in the montane case study developed as an illustration here (Sect. 1.4 below, and in the next few chapters). But gradient complexes are common, probably the rule for landscapes. Absent a strong elevation gradient, landscapes still exhibit a gradient complex over hillslopes (see Fig. 1.6, below). At this level, the proximate factors contributing to the gradient are radiation loading (a function of slope and aspect), local topography (as this affects hillslope processes), and soils. In the case of river and stream ecosystems, a gradient complex is explicit in the river continuum concept (Vannote et al. 1980). The river continuum refers to the complex of physical and biological factors that covary along a stream from its source to its mouth. Physical factors include water flow, temperature, and chemistry (e.g., dissolved oxygen and solutes), as well as bottom conditions (sediment type and amount). Biological factors include communities of microbes, algae, invertebrates, fish, and the structure of food webs. The river continuum differs somewhat from terrestrial gradients because in streams, inputs into and productivity within the system at one point flow further downstream, physically connecting the system longitudinally. Stream systems are further complicated by the alternating sequences of pools, riffles, and straight runs of water; these habitats differ in their own physical and biological factors and these also vary along the stream from its source to mouth. For example, a pool might be more similar to another pool farther downstream than it is to a riffle immediately adjacent to it. Thus, the river continuum can be a complex gradient complex! Gradient complexes are characteristic of coastal marine systems where a host of physical and biological factors vary with distance from shore. On the shoreward side, many factors (e.g., wave energy, drought stress from exposure) vary with distance above the waterline. On the ocean side, water depth, chemistry, and biota all vary as one proceeds into deeper water offshore. In the ocean, these gradients are expressed in terms of depth profiles of temperature, salinity, light, and biota: gradients are explicitly three-dimensional. This gradient is a nice analog of terrestrial elevation gradients, in that the marine gradient is essentially the interaction of bathymetry and ocean currents as compared to the interaction of landform and climate on land. Similar gradients, although perhaps less profound, are observed at the shorelines of freshwater lakes and ponds; seasonal snowfields in alpine systems exhibit their own gradient complexes as they melt. Forest ecologists are familiar with edge effects, in which a suite of biophysical and biological factors vary with increasing distance from the nonforest edge (and see Chap. 8, Sect. 8.3). In short, gradient complexes are the rule on landscapes. The essential feature of gradient complexes is that a suite of factors covary in a systematic way. This lends itself readily to abstraction and summary (e.g., the “elevation gradient”) but this abstraction also can mask the interplay of all the constituent factors. The correlations can also make it challenging to tease out the particular influence of individual factors (to which we return in Chap. 9, Sect. 9.4.1). No wonder that ecologists interested in gradients have come to depend on

1.3

The Water Balance

5

multivariate analytic methods to deal with this complexity (Gauch 1982; Pielou 1984; Jongman et al. 1995; McCune and Grace 2002; Legendre and Legendre 2012)!

1.3

The Water Balance

Stephenson (1990, 1998) has argued that the water balance provides a powerful framework for interpreting terrestrial vegetation distribution at spatial scales ranging from hillslopes to the globe. The climatic water balance is simply water supply minus water demand; a positive water balance implies available water, while a negative balance implies deficit (drought). Water demand typically is modeled in terms of potential evapotranspiration (i.e., surface evaporation plus transpiration from plants), while supply is provided as precipitation. This framework is beguilingly simple (only two terms!) but can result in rather complicated interactions. First, note that water deficit (drought) can be the result of either too much demand or too little supply; Stephenson cautions that these conditions might have very different ecological implications (we will return to this later). More to the point here, many factors can contribute to either supply or demand, and so understanding the water balance requires delving into these various factors. Importantly, the climatic water balance ignores the crucial role of water storage in the soil. Here, we delve into a more useful version of the water balance, one that includes the storage term. This exercise will lead to a more nuanced appreciation of the gross patterns typically revealed in ordinations. This model of the water balance is the first of several models that we will encounter in this book, models that are symptomatic of landscapes. The water balance in general is a simple concept (again, just two terms!) but because of the way the terms interact, the water balance plays out differently in every single case. Indeed, the water balance for any given landscape plays out differently at every location depending on topographic position or soil type, and in every year depending on the weather. A full appreciation of the water balance requires an understanding of the general model as well as the range of behaviors this admits in particular cases.

1.3.1

A Simple Model: PET = AET + Deficit

The water balance begins with two terms, supply and demand, but these terms unpack to reveal how complicated the model can become for any real landscape. Supply Water supply is all water available at a site, which includes new inputs as well as storage in the soil (we will ignore storage in the vegetation itself). Inputs include precipitation as well as topographic drainage from upslope positions. Precipitation might be either liquid or frozen (rain or snow) with the practical

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1 The Physical Template of Landscapes

implication that snow’s input to a site is time-lagged, deferred until spring snowmelt. The timing of snowmelt depends on temperature, typically modeled in terms of a cumulative heat sum. (A common heat sum is degree-days, a tally of degrees above freezing, per day: 3 days at 3 °C yields 9 degree-days.) Drainage inputs depend not only on slope but also on the infiltration capacity of the land cover and the permeability of the soil (which itself depends on soil texture, structure, and water content). Water storage in the soil depends on its water-holding capacity and depth. Waterholding capacity varies with soil texture (finer-textured clays hold more water than coarser sands) and soil organic matter (SOM). Both of these vary with depth: there is more clay deeper in the soil, while organic matter is more concentrated near the top of the soil profile. So total water-holding capacity must be integrated over soil depth. Soil water storage increases or decreases seasonally depending on the balance of evaporative demand and water supply. Thus, the term supply unfolds to include precipitation, temperature as this affects the partitioning of total precipitation into rain or snow and also the timing of snowmelt, topography and land cover as this affects drainage, and soil texture and organic matter as these vary over the depth of the soil profile to determine storage capacity. Demand The demand terms are similarly nested. Demand is essentially potential evapotranspiration (PET). PET depends on temperature, radiation, and the water content of the air (we will ignore, for now, further complications such as wind speed). Temperature varies with elevation (higher elevations are cooler) and topographic exposure, with the topographic effect largely mediated by radiation load (higher, hence hotter, on south-facing slopes in the northern hemisphere). Cold-air pooling in topographic depressions and valley bottoms can also have a substantial effect on local temperature. Radiation increases with elevation unless cloud cover— which also increases with elevation in the mountains—compensates for this. Air moisture content, typically modeled as vapor pressure deficit (VPD), also influences evaporative demand. (Vapor pressure is a measure of actual water content in the air, and vapor pressure deficit refers to the difference between actual water content and the maximum amount that air could hold at a given temperature. By comparison, the actual water content in the air, divided by the possible maximum at that temperature, is relative humidity—a more familiar measure of air moisture content.) Air moisture content also affects temperature, and so factors that affect air moisture (such as proximity to water bodies) also can affect the water balance via temperature. Thus, the term demand also unfolds to reveal a more complicated pattern over landscapes. This is a relatively simple approximation of the water balance, and yet this already reveals two important lessons. First, this can get complicated: there are many factors that can come into play (Fig. 1.2) and most of these terms interact (e.g., temperature affects many of these terms, and sometimes in opposite directions). Second, it should be intuitive that many of these factors will affect the water balance at different spatial scales. Elevation affects temperature (and hence, also soil moisture) over distances of hundreds of meters, while soil texture might vary over

1.3

The Water Balance

7

Slope, Aspect Cold Air Pooling

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Fig. 1.2 Factors affecting the climatic water balance, arrayed in terms of demand (left side) and supply terms (right side), with factors farther from the center being less directly tied to the water balance. Colors emphasize factors of varying character (brown: terrain and soils; blue: water; etc.). Abbreviations: VPD vapor pressure deficit, AWC available water content, SOM soil organic matter

distances of centimeters. This means that an empirical model that incorporates these terms will generate a rich pattern in the physical template, with spatial heterogeneity over multiple scales. We will return to this scaling lesson later, in Chap. 4. It is important to understand the terms of the water balance and how they relate to one another. Potential evapotranspiration (PET) is essentially energy; indeed, dividing PET by the latent heat of water (the amount of energy required to evaporate water) converts this into terms of energy. AET is actual evapotranspiration, which is that portion of demand (PET) that can be met by available water. Available water (AW) is the sum of water supply (rain plus snowmelt plus lateral flow from adjacent upslope positions) and storage in the soil. Water deficit (D) accrues when PET is greater than AW (i.e., AET is the lesser of PET or AW). If available water is greater than PET, there is a water surplus (S) that typically would recharge dry soils, with further excess water draining away through runoff or deep percolation. And so, equivalently: PET = AET þ D; D = PET - AET; AW = AET þ S:

ð1:1Þ

Over the course of a year, the water balance typically varies substantially. In a temperate climate with evenly distributed precipitation, PET traces a unimodal curve driven largely by monthly temperature and radiation. That pattern results in an early spring water surplus, followed by a period when PET = AET, and then perhaps a period of deficit when AW is less than PET; after this, PET decreases and water surplus recharges the soil, after which the surplus is lost to drainage (Fig. 1.3, left: Erie, Pennsylvania). The nuances emerge depending on how the terms vary seasonally (Fig. 1.3, right). For example, in a colder environment (Moosonee, Ontario), AET is energy-limited and if water supply is high, there could be a water surplus all year. In Flagstaff, Arizona, PET is quite high and available water limits AET. In Portland, Oregon, lower AET and seasonal deficits accrue because of the asynchronous timing of

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Fig. 1.3 Left: The water balance as a seasonal interaction of demand (PET; red line) and supply (blue line), for Erie, Pennsylvania. Surplus (S, solid blue fill) occurs when supply is higher than demand (Jan–May), once the soil has been recharged (R, blue diagonals, Sept–Dec). Deficit occurs when demand is higher than available water (red fill, June–Sept). Right: Water balances in contrasting climates: Moosonee, Ontario (top); Flagstaff, Arizona (middle), and Portland, Oregon (bottom). (Redrawn with permission of University of Chicago Press, from Stephenson (1990); permission conveyed through Copyright Clearance Center, Inc.)

demand (energy) and supply (precipitation is concentrated in the winter). In short, AET is defined by the interaction of available energy, available water, and the timing of each of these. To underscore this crucial point, the water balance applies everywhere and it plays out differently at every location, at any time. This is a specific instance of our more general premise: all landscapes work the same but each is unique.

1.4

Estimating Elements of the Template

9

Most of the terms of the water balance can be measured (but perhaps not easily!) or, more typically, modeled using semi-empirical approximations. We turn to this in the next section. We also will consider some ways to approximate these factors using readily available geospatial data. The goal, ultimately, will be to develop approaches that can interpolate temperature and relative moisture over heterogeneous landscapes.

1.4

Estimating Elements of the Template

This exercise of “expanding terms” of the water balance serves as a general illustration of how one might unpack a gradient complex into its constituent parts. The exercise also invites a more practical consideration of how one might estimate these terms over a larger study area—a landscape—using geospatial data that are likely to be available at these scales. In each case, we will begin with physical models and consider how these might be implemented in applications. Subsequently, we consider some simple approximations based on terrain-based proxies (Wilson and Gallant 2000). We begin with the main driving variables (temperature, radiation, precipitation, soils) and then combine these to illustrate their interaction in the water balance. We also will consider additional surficial processes that contribute to the physical template of landscapes.

1.4.1

Temperature

Temperature is perhaps the most straightforward variable to interpolate over a landscape. In part, this is because the main source of local variability is elevation, and the relationship between temperature and elevation is essentially linear. To a rough approximation, ideal gas laws allow us to estimate temperature via a linear lapse rate that defines the decrease (lapse) in temperature with increasing elevation. (This same principle applies to latitudinal variation in temperature, but this is rather larger in spatial extent than most landscape applications.) For dry air, the standard (adiabatic) lapse rate is about 10 °C per 1000 m altitude gain in the atmosphere. Along mountainsides, near-ground lapse rates tend to be around 5–6 °C per 1000 m elevation gain. Lapse rates depend on air moisture content (moist-air lapse rates are lower) and other factors, so even limited local data can often provide more accurate estimates of actual environmental lapse rates. For example, lapse rates in the Sierra Nevada of California vary seasonally due to humidity in this Mediterranean climate (Urban et al. 2000), and temperature varies as a function of distance to the coast in the Pacific Northwest of the United States due to the moderating maritime effect (Urban et al. 1993).

10

1

The Physical Template of Landscapes

This regional variation invites a regionalized approach to lapse rates, and Daly et al. (1994) have provided one solution to this.1 Daly’s approach has been to define regional slope facets as areas of relatively consistent topographic influence; lapse rates are then computed within each facet. For example, this approach might compute different lapse rates for the windward as compared to leeward slopes of mountain ranges, to capture the rain-shadow effect of the mountains as this affects air moisture content and hence temperature lapse rates. The spatial resolution of this approach depends on the density of meteorological stations or other available data: there must be sufficient data within a facet to estimate a lapse rate reasonably. Beyond Lapse Rates At more local landscape scales, temperature estimates can be refined by fitting regressions to temperature data collected strategically over contrasting topographic positions. Increasingly, low-cost data-loggers provide an enabling technology for such applications. Lookingbill and Urban (2003) deployed data-loggers in a stratified design to estimate the effects of elevation, slope and aspect, and local effects associated with stream channels. Their regressions provided much better spatial resolution to temperature estimates compared to lapse rates based on elevation alone. In particular, slope aspect had a significant impact on maximum daily temperature (afternoon highs) via radiative heat loading, while minimum temperatures (overnight lows) were more strongly associated with cold air drainage and distance to streams. Similarly, Fridley (2009) developed a distributed model of temperature for the Great Smoky Mountains National Park (Tennessee and North Carolina, USA). He was able to model fine-scale patterns in temperature that were substantially different than regional (synoptic) temperatures and those estimated from lapse rates. While convective heat loss due to winds would depend on consistent wind exposure, such temperature effects could also be captured by data-loggers distributed over topography. At higher temporal resolution, canopy cover has an additional effect on diurnal temperature swings: the amplitude of min/max differences is reduced in closedcanopy forests compared to open space (Running et al. 1987; Davis et al. 2019). The increasing availability (and decreasing cost) of data-logging devices and highresolution land cover data is making it much easier to generate high-resolution, ecologically relevant estimates of temperature gradients at the landscape scale. In short, temperature is a rather well-behaved variable that can be approximated at various levels of spatial resolution, from simple lapse rates to much more highly resolved interpolations, based on available data. A word of caution, however: geospatial climate datasets are increasingly available as surfaces interpolated from coarser-resolution digital elevation data, sometimes downscaled from coarseresolution climate data (actual or as output from general circulation models). In rugged terrain, these interpolations miss most of the fine-grained variation in

1

Daly’s group continues to provide interpolated climate data of various kinds for much or all of the United States (see https://prism.oregonstate.edu/).

1.4

Estimating Elements of the Template

11

temperature driven by topographic influences, resulting in what can be highly inaccurate and misleading estimates. End-users should evaluate these data products carefully.

1.4.1.1

Geospatial Proxies for Temperature

Given linear lapse rates for temperature on elevation, a digital elevation model is a perfect analog for temperature: these differ only by a constant (the lapse rate itself). This can be useful for some applications, but the lack of information about the effect of radiation loading or other features (e.g., distance to water) can render this proxy rather coarse and a bit unsatisfying. Because temperature data are increasingly accessible (via meteorological stations or inexpensive data-loggers), models that adjust temperature for topography or other features are increasingly common.

1.4.2

Radiation

Our interest in radiation is because of its contribution to the energy that drives potential evapotranspiration either directly, or indirectly via its effect on temperature. This is shortwave radiation from the sun, and includes visible light as well as some near-infrared (IR) and ultraviolet (UV) radiation. Thus, we are not concerned here with radiation as connoted by “available light” and referring strictly to photosynthetically active radiation (PAR) as this affects plant growth. Available light is influenced by many local factors, especially shading by a forest canopy, and is not considered here. The Geometry of Solar Radiation Spatial and temporal variation in radiation depends on the geometry of two dynamics: the earth’s orbit around the sun, driving seasonal patterns; and the earth’s rotation about its axis, driving diurnal patterns (Bonan 2008). Solar angles frame this geometry. Seasonal patterns arise from the angle between the sun and the earth’s surface, or solar declination angle. Solar declination depends on the day of the year as well as latitude (Fig. 1.4a). At the summer solstice, the longest day of the year in the northern hemisphere, the sun is directly overhead at the Tropic of Cancer (23.5 oN) and the sun never sets above the Arctic Circle (66.5 oN). In the southern hemisphere, the sun is at its lowest at the Tropic of Capricorn and the sun never rises beyond the Antarctic Circle. At the winter solstice, these patterns are reversed. At the spring and fall equinoxes, the declination angle is such that there are 12 h of day and 12 of nights at the equator. Solar altitude angle is the angle between the sun’s position in the sky relative to the horizon. This angle is the complement of solar zenith angle, which is the angle between the sun and a line perpendicular to the earth’s surface; that is, zenith angle is 90° minus altitude angle. These angles depend in part on solar declination, hence time of year. But they also vary diurnally. Solar altitude angle is 0 at sunrise and

12

1

(a )

The Physical Template of Landscapes

(b) Sunset Azimuth Declination (23.5° at solstice)

N

Sunrise

(c)

(d)

Direct Beam

Diffuse Sky

Fig. 1.4 Geometric models of radiation. (a) Calendar day and latitude affect solar declination. (b) Azimuth and topography influence the time at which the sun emerges above the horizon (sunrise) and the time it dips below the horizon (sunset). The effects of topography on (c) direct-beam insolation and (d) diffuse-sky radiation. With direct beam radiation, deviations of the slope from perpendicular to the solar path essentially dilute the beam. With diffuse-sky radiation, a slope effectively obscures part of the visible sky, which is modeled as a hemispherical dome. (Redrawn with permission of Cambridge University Press, from Bonan (2008))

sunset, and reaches its maximum at solar noon (Fig. 1.4b). As the sun traces its path across the arc of the sky, it defines its solar azimuth angle, the angle between the sun and due south (though typically expressed as degrees from true north). On flat ground, the geometry of solar radiation depends only on latitude, day of year, and time of day. But surface topography can have substantial local effects on radiation. For this purpose, radiation is often partitioned into its two components, direct-beam and diffuse-sky. Direct-beam radiation is that impinging on a surface as an uninterrupted beam from the sun. The intensity of this component depends on local slope angle relative to a line perpendicular to solar altitude angle (Fig. 1.4c). As slope angle deviates from this perpendicular, the beam is spread over a larger surface area, essentially diluting the radiation (a flashlight beam is a perfect physical model for this). Diffuse-sky radiation is scattered radiation that impinges to the surface from all directions in the sky. In this, the sky is modeled as a bowl (a hemisphere) and the amount of diffuse radiation impinging to a surface depends on how much of the sky is visible from that point—which, in turn, depends on slope angle (Fig. 1.4d). Local topography also affects daylength, by altering the time of sunrise and sunset; a familiar instance is when the sun sets behind the mountains long before it is truly night.

1.4

Estimating Elements of the Template

13

Estimates of radiation loadings at landscape scales fall into one of two general approaches. The first approach entails simulating actual radiation from biophysical principles. The second entails relatively simple approximations of relative radiation, typically not scaled to any actual units used to measure radiation and often based solely on topography. Biophysical Models Biophysical approaches to estimating radiation vary, but most share a few key elements (Bonan 1989; Nikolov and Zeller 1992; Bonan 2008). First, solar declination is computed based on calendar day and site latitude, and these terms are used to compute solar altitude (or zenith) and azimuth angles. These angles are used to estimate radiation to the edge of the earth’s atmosphere, and then this radiation is attenuated to a horizontal plane at the earth’s surface (which depends on atmospheric thickness, cloudiness, etc.). Finally, the local effects of topography are estimated. This might entail tracking the sun’s path across the sky, from sunrise to sunset and tallying daylength as well as solar altitude. These estimates are then integrated to daily or monthly time steps. Local slope is then used to adjust directbeam and diffuse-sky components of the radiation. Bonan (1989) and Nikolov and Zeller (1992) used these geometric models to build simulation models that could estimate solar radiation to a topographic position specified in terms of latitude, slope, and aspect. The model of Nikolov and Zeller, based on that of Bonan, successfully simulated monthly radiation values measured at meteorological stations distributed across much of the northern hemisphere. We will return to this model later in this chapter, where it is applied to landscapes of the Sierra Nevada in California. Fu and Rich (2002) developed an approach to radiation modeling based on modeling the view of the sky as if via hemispherical photography. In this, the sky is modeled as a hemisphere and obstructions to this block parts of the view. Initially applied to estimates of canopy closure from hemispherical photos taken beneath a forest canopy, this approach has been implemented in the radiation model available in the Arc-GIS package (ESRI, Redlands, CA). In the model, the estimate is developed in four steps: 1. A viewshed of the sky is estimated from a point on the ground; in mixed terrain, this view might be partially obstructed by nearby peaks or other features. 2. The viewshed is then overlaid with a map of direct-beam radiation, estimated by ray-tracing based on solar geometry. This provides an estimate of direct-beam radiation. 3. The sky viewshed is overlaid on a sky map of diffuse radiation, estimated over eight zenith angles and 16 azimuth angles. This provides an estimate of diffusesky radiation. 4. Total radiation is the sum of the direct and diffuse components. This approach can be computationally demanding for a large raster landscape, but advances in computing power make this less of an issue. The accuracy of the approach does depend on details about the location, such as the proportion of total radiation that is direct as compared to diffuse (which depends on cloudiness etc.).

14

1.4.2.1

1

The Physical Template of Landscapes

Geospatial Proxies for Radiation

The main effect in radiation modeling is to capture the simple reality that southfacing slopes in the northern hemisphere capture more radiation than northern exposures (the reverse is true in the southern hemisphere). Thus, estimates of “southness” are reasonable first approximations. Such estimates must account for the awkward geometry that slope azimuth has a circular distribution (i.e., north = 0 = 360°, and south = 180°). For correlation-based analyses, azimuth must be transformed into a form that can be used in linear models. The simplest approach is to take the absolute value of azimuth, or by common convention, the absolute value of (180 – azimuth). This accounts for the variation in radiation load, but not the effect of radiation load on temperature. Because of the time lag between radiation loading and actual temperature increase, the aspect corresponding to maximum temperature effect is displaced somewhat from true south, more toward a southwesterly exposure (225 degrees). A simple way to index this effect is to transform aspect to be biased toward southwestern exposures: TA = - 1  ðcosðA - 45ÞÞ

ð1:2Þ

where A is the slope aspect in degrees (modified from Beers et al. 1966). This formula realigns the index and rescales it (by multiplying by -1) so that southwestfacing slopes take on a maximum value of 1.0, while northeast-facing slopes assume a minimum value of -1. McCune and Keon (2002) used a slightly different normalization to create their heat index, but it is based on the same cosine term as Beers et al. (1966) and Eq. 1.2. This estimate can be refined further by multiplying TA by slope angle, which increases the radiation index on steep slopes facing the sun while decreasing the index for steep northeastern slopes; using the sine of slope angle ensures that the index still varies on [-1,1] (Pierce et al. 2005). McCune (2007) discusses other variations on this theme. The increasing availability of geographic information systems and geospatial terrain data (digital elevation models, or DEMs) provides for some simple but useful extensions of these estimates. Analytic hillshading in a GIS amounts to “‘shining a light” at a DEM and estimating the relative brightness of each grid cell. By incorporating topographic interference, it is possible to model relative radiation loading while also respecting larger-scale influences of landforms between a focal point and the line-of-sight path to the sun. This general approach can be extended arbitrarily. For example, Pierce et al. (2005) used analytic hillshading in a GIS, setting the altitude angle of the light source based on solar altitude angle for particular days during the growing season; they then integrated relative radiation loadings over the growing season. In short, methods for estimating radiation range from quite simple models based on slope aspect to rather complicated models that incorporate solar geometry, topography, and corrections for atmospheric effects (Fig. 1.5). Which approach is appropriate will depend on the application, of course, but for landscapes any useful estimate must attend to the influences of topography on relative radiation loads.

1.4

Estimating Elements of the Template

15

Fig. 1.5 An estimate of relative radiation load for a watershed in western North Carolina, Coweeta Hydrologic Laboratory. The index is -cos(aspect-45°) (Eq. 1.2), based on a 30-m DEM, and colored on a rainbow palette so that cool colors are shady and hot colors are sunny. The view is from the east, looking up into the watershed, so ‘hot’ aspects are facing south/southwest

1.4.3

Precipitation

Temperature is relatively well-behaved as a variable, in that it can be draped over landscapes using a little data and rather simple statistical models. By contrast, precipitation is much less well behaved. Part of this stems from the factors that influence the distribution of precipitation, and part stems from the nature of the data (i.e., what is measured in rain gauges). Precipitation is complicated by the airmass dynamics that generate it. Rainfall can come through frontal systems or in convective events. Frontal systems can be quite large and slow-moving (and consequently, comparatively well behaved statistically). By contrast, convective systems tend to be quite patchy and often rapidly moving, and so more difficult to predict locally. (One solution to this latter issue is to assume that convective events “average out” over a large region, over time.) Precipitation is also influenced by topography, through orographic lifting. In this, an airmass rises upslope as it reaches a mountain, until the moisture content of the air increases so much with decreasing temperature that it rains. Consequently, the air moisture content on the leeward side is depleted, generating a rain shadow. Due to orographic lifting, precipitation typically shows an increase with elevation in montane regions. This means that lapse rates can be fitted to data gathered at various elevations. Because of rain-shadow effects, the precipitation pattern on the

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1 The Physical Template of Landscapes

windward slope of a mountain would naturally be different than on the leeward side. A complication emerges, however, in that the lift often degrades at some (high) elevation, with the result that the lapse rate fails at some point. Stephenson (1988) suggested a piecewise regression approach to sidestep this problem. In fact, precipitation data at higher elevations might be too noisy to fit a lapse rate, which raises the second complicating issue. Precipitation data at high elevations is often in the form of snow, and snow is often not well measured by rain gauges. Stephenson (1988) has detailed the bias in precipitation data resulting from this under-sampling. It is difficult to model precipitation at large scales from biophysical principles, and so there has been a growing interest in using remotely sensed precipitation data to construct better statistical models. This approach takes advantage of the availability of radar-based data products such as NEXRAD (Smith et al. 1996, Young et al. 2000; and see https://www.ncdc.noaa.gov/data-access/radar-data/nexradproducts). Since rain and snow play different roles in the water balance, temperature enters into modeling the form of precipitation at the landscape scale, that is, in determining whether precipitation falls as rain or snow. This transition is typically a sigmoidal function of temperature, with the transition occurring near (but not necessarily exactly at) 0 °C. As a final consideration, many applications require information on the event size distribution of precipitation. This matters when precipitation comes in infrequent but large storms (and so with high potential for flooding or erosion), as compared to smaller events. This distribution can be estimated from historical data (with the caveat that historical patterns will likely not hold under future climates).

1.4.4

Soils

The climatic water balance, estimated in terms of evaporative demand and precipitation, is intended for coarse-resolution estimates of available moisture and so emphasizes supply and demand but does not include water storage, which is considered to be a local and transient influence on available water. But for many systems, seasonal variation in either supply or demand can be a defining aspect of the water balance, and so it is appropriate to consider the effects of water storage in the soil (Stephenson 1990). In the temperate zone, temperature varies seasonally (by definition!), and in regions where precipitation also varies seasonally this interaction can have a profound impact on available water. Mediterranean systems are a clear example of this: the precipitation falls in the winter—a period of low demand, while demand peaks in the summer—a period of low supply. In such systems, the water balance depends largely on spatiotemporal patterns of water storage. Water storage in the soil depends on the water-holding capacity of the soil, typically indexed in terms of field capacity (FC, the water content at which water drains from the soil gravitationally) and wilting point (WP, the content at which

1.4

Estimating Elements of the Template

17 Erosional

Depositional

More clay More OM More water

Water Table

Shallower on steeper slope (deeper on flat tops and bottoms)

Coarser Less OM Less water

Fig. 1.6 Schematic illustration of the catena model of hillslope processes. Gravity mediates a shift from erosional processes near the top, to depositional processes near the bottom of the hillslope

plants can no longer extract water from the soil particles). FC and WP depend on soil texture (relative proportions of sand, silt, and clay): clays have higher FC and WP, but WP is proportionately higher for clays than for coarser-textured soils. Available water-holding capacity (AWC) is FC–WP. Both FC and WP also increase with the organic matter content of the soil. Texture and organic matter both vary with depth: soils become more clayey at depth while organic matter is concentrated in the upper 30 cm or so. Thus, AWC for a soil profile is AWC per layer of the horizon, integrated over the soil horizon (or, more appropriately, the rooting zone of plants). Empirically, these hydraulic parameters can be estimated by regression, given data on soil texture and organic matter content (e.g., Cosby et al. 1984). Much of the variability in soils over landscapes can be interpreted in terms of the hillslope model (Brady 1990). A catena is a hillslope unit subject to the same soilforming regime of parent material, climate, biota, terrain, and time. In a catena, hillslope processes mediated by gravity drive a shift from erosional processes nearer the top of the hill, to depositional processes nearer the bottom (Fig. 1.6). As a result, soils nearer the top tend to have coarser texture (less clay, more silt and sand) and less organic matter (hence, lower water-holding capacity), while soils nearer the bottom have more clay and organic matter and are often deeper as well (hence, higher water-holding capacity). The water table itself shows a trend along the hillslope, rising nearer the surface at the bottom of the slope. While this simple schematic ignores many complexities of soil systems, it still serves as a sufficiently powerful organizing framework that many proxies based on the catena model have been used for hydrologic and ecological applications (Moore et al. 1991, and see Sect. 1.6 below). Until recently, modeling soil factors at the landscape scale has been confounded by a lack of detailed soils data at this scale. This situation is improving as more data are being digitized and made available at national or global scales. For example, in

18

1 The Physical Template of Landscapes

the United States, digital soils data are available via the State Soil Geographic (STATSGO) soils database at coarse (1:250,000) resolution and the Soil Survey Geographic (SSURGO) data at higher (1:24,000) resolution (see http://websoilsurvey.nrcs.usda.gov). These databases include a large number of soil attributes associated with each map unit. Some caution must be exercised in using digital soils data in landscape-scale models. In many instances, these data are interpolated from rather sparse ground samples, often using air photos as a guide to the delineation of map units. This introduces several issues related to data quality and interpretation. The spatial precision and accuracy of the data might be rather low, and with artificially abrupt transitions between typal values assigned to map units. Thus, mapped soil properties change abruptly as map units change, unlike the continuous gradients expected on the ground. Some soil properties are simply difficult to estimate, even with a rather dense field sites. For example, mapped soil depths might be highly uncertain not only because of sparse field samples but also because the field sites (soil pits) were dug to a standard but arbitrary maximum depth. It should also be emphasized that soil units are mapped as regions with internally consistent soil-forming regimes. This means that a long hillslope might be mapped as a single unit, even though many soil characteristics would naturally vary substantially along that hillslope. These caveats aside, soils are clearly a crucial component of the water balance and other edaphic properties such as soil chemistry and organic matter content play an important role in soil fertility and ecosystem productivity. As better soils data become available in digital format, our ability to incorporate these factors into landscape-scale models will improve as well, providing a much richer depiction of the physical template of landscapes.

1.4.4.1

Geospatial Proxies for Hillslope Processes and Hydrology

The catena model emphasizes hillslope processes and this invites further consideration of how hillslopes—or terrain more generally—govern hydrology and the movement or routing of water. Hydrologists rely heavily on terrain shape in modeling hydrologic flows (Moore et al. 1991). Two key aspects of this are flow direction and flow accumulation. Flow direction indexes the direction “downhill” from any point on a landscape. This can be done at varying levels of precision, ranging from choosing the direction of steepest downhill slope based on either four (D4) or eight (D8) neighboring cells in a raster grid of elevation, to more sophisticated models that partition flow over the neighboring cells. Flow accumulation is a tally of the upslope contributing area that would drain to (or through) any given point on a landscape. For a DEM as a raster grid, this calculation uses flow direction as a guide, and tallies all of the cells that are hydrologically uphill from a given point. This tally is then converted to units of area. A map of flow accumulation provides an easy visualization of the drainage pattern for a watershed (Fig. 1.7). Indeed, one can delineate streams by applying a

1.4

Estimating Elements of the Template

19

Fig. 1.7 Flow accumulation for the Coweeta Hydrologic Laboratory in western North Carolina. Each 30-m cell tallies the upslope area that would flow through that cell (darker blues are higher values). Tallies in this image are in number of 30-m cells. Thresholding this map to a minimum accumulation area would delineate streams

minimum area threshold to flow accumulation: specifying a small threshold (e.g., 1–10 ha) would include many smaller headwater streams, while using a larger threshold would retain only the larger stream reaches. Flow accumulation can be combined with other terrain-based variables to generate more hydrologically nuanced indices. One such index is the topographic convergence index (TCI; Beven and Kirkby 1979, Moore et al. 1991): TCI = ln

A tan β

ð1:3Þ

where A is upslope contributing area (i.e., flow accumulation) and the denominator is the tangent of local slope angle β. TCI thus takes on high values at low-slope positions with very high A and on flatter slopes that would tend to collect water; it takes on lower values for lower contributing area or for steep slopes that would tend to have faster runoff. A raster map of TCI highlights the topographically wetter positions on a landscape as compared to excessively drained slopes or drier hilltops (Fig. 1.8). TCI clearly illustrates the pattern of drainage in the watershed: the blue-violet values effectively delineate the streambeds and riparian zones. The image also nicely illustrates the concept of the variable source area in hydrology. Under drier

20

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The Physical Template of Landscapes

Fig. 1.8 Topographic convergence index for Coweeta Hydrologic Laboratory in western North Carolina. Image is colored on a rainbow scale (violet is highest values; red, lowest). Values are multiplied by 10 so they can be stored efficiently as integers

conditions, only the highest values of TCI would be expected to contribute to surface flow (i.e., to be wet). Under wetter conditions, the source area expands upslope from the stream channel so that areas that have slightly lower values of TCI would also be wet. Thus, the image can be used to visualize the temporal dynamics of topographic moisture content. TCI thus presents itself as a useful proxy for topographic moisture. It should be emphasized that proxies for the various elements of the water balance do not and cannot capture the full richness of the water balance, which changes in response to individual precipitation events, short-term variation in evaporative demand, seasonal patterns in supply and demand, and longer-term variation in climate. In a field study at Coweeta (the watershed used here to illustrate proxies), Yeakley et al. (1998) measured soil moisture along a hillslope gradient, and correlated moisture to indices of water-holding capacity (based on texture and soil organic matter) and topographic convergence (as TCI). They found the relative contribution of topography and storage varied over the course of wetting and drying cycles: TCI was more important during dry-down while storage was more important during wetting. Biophysical proxies can help us understand (and even model) the water balance; they are simple but useful handles for the complexities of real systems.

1.5

Case Study: The Sierra Nevada

1.5

21

Case Study: The Sierra Nevada

In the previous section, we considered a range of empirical and semi-empirical approaches for interpolating the terms of the water balance over landscape scales. This was a logical next step from the initial presentation of the water balance as a general but somewhat abstract model. Here, we assemble these terms into more integrated models of temperature and soil moisture as these are distributed over landscapes. This case study illustrates the local implementation of a general model, using site-specific data and with decisions driven by the application. While there are many models that have been used to address applications such as this, we will delve into an extended example from the Sierra Nevada in California. We will revisit this example in each of the next two chapters, layering biotic processes (forest dynamics) and disturbance (fire) onto the physical template illustrated here. We also will come back to this model system in Chap. 4 (on scale and scaling) and in Chap. 7 (on patterns in biodiversity).

1.5.1

The Physical Template of the Sierra Nevada, California

Urban et al. (2000) built on previous work by Stephenson (1988, 1998) to model the elevation gradient in the southern Sierra Nevada of California. This work, motivated by concerns over the implications of climate change for Sequoia-Kings Canyon and Yosemite National Parks (Graber et al. 1993), aimed to account for patterns in temperature and soil moisture as these vary over a steep (~4000 m) elevation gradient. Urban et al. developed a forest gap model (Botkin et al. 1972; Shugart 1984; Urban et al. 1991) to simulate a slope facet as point on the landscape defined by its elevation, slope, aspect, and soils. For now, we focus on the physical template as simulated in their model. Temperatures (average daily minimum and maximum for each month) were regressed as lapse rates on elevation, using data from a few meteorological stations within the study area. Radiation was modeled using geometric models developed by Bonan (1989) as extended by Nikolov and Zeller (1992). In this approach, direct-beam and diffuse sky components were estimated as a function of elevation, slope, and aspect. These calculations were computed for the single day of each month for which that day’s radiation is equal to the monthly average (Bonan 1989); radiation was integrated hourly from sunrise to sunset for each day. Temperatures were then modified to reflect radiation loads on slopes relative to a horizontal surface (Running et al. 1987). Precipitation (mean monthly total) was regressed as lapse rates using piecewise regression, with the result that the lapse rate was truncated above 2000 m. The same meteorological station data were used to estimate the size distribution of precipitation events, and the fraction falling as rain versus snow as a function of mean daily temperature for each month.

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The Physical Template of Landscapes

Fig. 1.9 Components of the soil water balance as simulated for landscapes of the Sierra Nevada in California (Urban et al. 2000). Circled values are inputs (temperature and precipitation interpolated, soils estimated from field data); other terms are computed by the model at a daily timestep

The model incorporates a soil moisture model that operates at a daily time-step to generate precipitation, summarizing the water balance by month and then integrating soil moisture over the growing season (Fig. 1.9). Potential evapotranspiration (PET) is estimated using the Priestley–Taylor approximation, which uses temperature, radiation, and an empirical adjustment for vapor pressure deficit based on the difference between daily maximum and minimum temperature (Bonan 1989). Precipitation is generated randomly at a daily time-step, based on long-term records from the study area. Temperature is then used to determine whether this falls as snow or rain. Snow is accumulated over the winter and melted in the spring as a function of a cumulative heat sum (degree-days above freezing). Canopy leaf area (LAI) determines a fraction of precipitation that is intercepted (and which then relieves some PET demand) and the fraction that reaches the ground. LAI also determines how much of the PET is met through transpiration as compared to surface evaporation. An open canopy results in more surface evaporation while a closed canopy forces transpiration from the soil column. Each soil layer is defined by its depth and water-holding capacity at field capacity and wilting point, with these capacities estimated by regression (Cosby et al. 1984). Surface evaporation is drawn from the litter layer and top 10 cm of the mineral soil, while transpiration is drawn from the soil layers in proportion to their fine root distribution (itself modeled as a triangular function of soil depth, after Bonan 1989). A running water balance is tallied over a multi-layered soil, using a simple tipping-bucket logic: Each day, precipitation (if by chance it occurs) is added to the top of the soil after removing any interception loss. If the evaporative demand can be met by stored water plus new inputs (i.e., rain or snowmelt), this is withdrawn and storage in the layer is updated accordingly. Excess water flows to the next layer.

1.5

Case Study: The Sierra Nevada

23

Water (cm)

150

100

50

0 500

PET Total Ppt Snow

1500

2500

3500

Elevation (m)

Fig. 1.10 Trends in water supply (total precipitation, snow) and demand (potential evapotranspiration, PET) in relation to elevation, as simulated for the Sierra Nevada. Each point is the 100-yr average for a single topographic setting specified in terms of elevation, slope, and aspect. (Redrawn with permission of Springer Nature, from Urban et al. (2000); permission conveyed through Copyright Clearance Center, Inc.)

If water is insufficient (below wilting point), a “drought-day” is accumulated for that layer and that day. This running balance is simulated for the entire year, and then soil water status is summarized as the number of drought-days, per layer, integrated over the growing season. Urban et al. (2000) virtually “sampled” their study area by stratifying model simulations over the empirical distribution of elevation, slope, and aspect as represented by the study area, based on a digital elevation model of the Park. Because soils data are very limited for the Park, they generated a series of representative soil types of similar textures (mostly sandy loams) and varying mostly in depth (ranges based on field measurements). They then simulated a shallow (50 cm), “average” (100 cm), and deeper (150 cm) soil for each of the sampled topographic settings, yielding a total of 1500 parameter combinations (elevation, slope, aspect, and soil type). To illustrate how the soil water balance varies over this montane landscape, the model simulations were run for 100 years and summary statistics were extracted for each topographic setting. The main trends underscore the importance of the steep elevation gradient in this system (Fig. 1.10). With increasing elevation, evaporative demand decreases because of decreasing temperature, although there is still considerable variability in this due to slope and aspect as these affect radiation load; this is visible as the scatter in estimates of PET at any given elevation (Fig. 1.10, red dots).

24

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The Physical Template of Landscapes

240

Drought-Days

180

120

60

0 500

Entire profile Topsoil (20 cm)

1500

2500

3500

Elevation (m)

Fig. 1.11 Trends in growing-season drought index for topsoil (30 cm, open circles) and entire soil profile (solid symbols) as simulated along an elevation gradient in the Sierra Nevada of California. (Redrawn with permission of Springer Nature, from Urban et al. (2000); permission conveyed through Copyright Clearance Center, Inc.)

Note that this variability decreases at high elevations, where it is so cold that PET is very low on slopes of any aspect. At the same time, water supply increases with increasing elevation, as total precipitation and, more importantly, as snow (blue and cyan symbols, respectively, in Fig. 1.10). Water supply does not show appreciable variability at any given elevation, as precipitation was modeled as a function of elevation only. This figure summarizes the expected trends in the supply and demand terms of the water balance, while emphasizing the nonlinear relationship of snow to elevation, a function of temperature. Summary statistics for drought-days from these simulations show a similar trend with elevation (Fig. 1.11). The drought index for the whole soil profile (dark blue symbols) shows a strong and slightly nonlinear trend, with drought-days decreasing dramatically at mid-elevations, corresponding to the availability of snowpack that can help meet evaporative demand into the summer. The drought index integrated over the top 30 cm of the soil (the topsoil) shows a somewhat different pattern, especially at lower elevations. This implies that tree seedlings or plants with shallow roots experience a different soil moisture regime than larger trees or plants that can mine deeper soil water reserves. Interestingly, these two trends cross at low elevations, at a point where winter precipitation falls mostly as rain (because of warmer temperatures). This winter rain is not stored into the summer as snow is at higher elevations, and so the low-elevation topsoil is actually drier in the summer than that at higher elevations. While not the focus of this study, it is intriguing that this

1.5

Case Study: The Sierra Nevada

25

Fig. 1.12 Contrasts in the supply and demand terms of the water balance, as simulated for mid-elevation sites in the Sierra Nevada of California. Light symbols form a background context of 1500 simulations over a range of elevations and topographic positions; dark connected symbols trace an elevation gradient from 1500–3500 m for a 1-m soil on flat ground. AET is PET met by available water supply; deficit is PET-AET. (Redrawn with permission of Springer Nature, from Urban et al. (2000); permission conveyed through Copyright Clearance Center, Inc.)

elevation seems to correspond to the transition zone from woody vegetation (oak savanna) to low-elevation grasslands. Urban et al. (2000) used their simulation model to explore a suggestion by Stephenson (1988, 1990, 1998) that vegetation can distinguish “different kinds of dry.” That is, a water deficit can be due to too much demand or not enough supply; and these distinctions can matter to vegetation. Exploring this, Urban et al. simulated changes in supply by contrasting a shallower and deeper soil, and changes in demand by contrasting south- and north-facing slopes; the reference case was a 1-m soil on flat ground at 2000 m elevation. Consistent with Stephenson’s argument, they found that changes in water supply versus demand had nearly orthogonal implications for the water balance (i.e., the supply and demand trends are nearly perpendicular in Fig. 1.12). At the reference setting, the dominant tree species is white fir (Abies concolor). Intriguingly, vegetation data for this landscape (Stephenson 1988, 1998) suggest that sites that are drier due to higher evaporative demand tend to support Ponderosa pine (Pinus ponderosa), while sites that are dry due to lower available water (or water supply) tend to support Jeffrey pine (P. jeffreyii). This invites a consideration of the biological and ecological reasons for this community-level response. We turn to biotic mechanisms of pattern formation in the next chapter.

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1.6

1

The Physical Template of Landscapes

Summary and Conclusions

The physical template of landscapes is the result of climate as it interacts with landform. This interaction governs landscape-scale patterns in temperature, soil moisture, and other edaphic factors. The principal climate variables (temperature, radiation, and precipitation) and soils exhibit considerable spatial heterogeneity over landscapes, and this pattern can be modeled in a variety of ways ranging from biophysical models to simple proxies based on digital terrain data. Semi-empirical models, in which sparse data are interpolated geospatially, are especially promising for landscape-scale applications. The host of factors that covary along elevation or topographic gradients invite the notion of gradient complexes, suites of variables that are correlated because of mutual causation or biophysical interactions. A working understanding of the physical template of landscapes requires some appreciation of these nuances. To be sure, there are other aspects of surficial processes that are important agents of landscape patterns. In particular, the erosive power of water and wind shape landforms in profound and often dramatic ways. But the more subtle influences discussed here should provide a solid foundation for understanding the physical template of landscapes. A working understanding of the biophysical relationships underlying the physical template also will be crucial to our ability to anticipate the possible consequences of climate change on landscape-scale patterns in temperature and moisture, and the implications of such changes in the physical template for populations, communities, and ecosystem processes. This understanding will be enriched by a fuller appreciation of the interactions among the physical template, biotic processes, and disturbance regimes. We turn to biotic processes in the following chapter.

References Austin, M.P., and T.M. Smith. 1989. A new model for the continuum concept. Vegetatio 83: 35–47. Beals, E.W. 1984. Bray-Curtis ordination: An effective strategy for analysis of multivariate ecological data. Advances in Ecological Research 14: 1–55. Beers, T.W., P.E. Press, and L.C. Wensel. 1966. Aspect transformation in site productivity research. Journal of Forestry 64: 691–692. Beven, K.J., and M.J. Kirkby. 1979. A physically-based, variable contributing area model of basin hydrology. Hydrological Sciences Bulletin 24: 43–69. Bonan, G.B. 1989. A computer model of the solar radiation, soil moisture, and soil thermal regimes in boreal forests. Ecological Modelling 45: 275–306. Bonan, G. 2008. Ecological climatology: Concepts and applications. 2nd ed. Cambridge: Cambridge Univ. Press. Botkin, D.B., J.F. Janak, and J.R. Wallis. 1972. Some ecological consequences of a computer model of forest growth. Journal of Ecology 60: 849–873. Brady, N.C. 1990. The nature and properties of soils. 10th ed. New York: Macmillan. Bray, J.R., and J.T. Curtis. 1957. An ordination of the upland forest communities of southern Wisconsin. Ecological Monographs 27: 325–349.

References

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Cosby, B.J., G.M. Hornberger, R.B. Clapp, and T.R. Ginn. 1984. A statistical analysis of the relationship of soil moisture characteristics to the physical properties of soils. Water Resources Research 20: 682–690. Curtis, J.T., and R.P. McIntosh. 1951. An upland forest continuum in the prairie-forest border region of Wisconsin. Ecology 32: 476–496. Daly, C., R.P. Neilson, and D.L. Phillips. 1994. A digital topographic model for distributing precipitation over mountainous terrain. Journal of Applied Meteorology 33: 140–158. Davis, K., S.Z. Dobrowski, Z.A. Holden, P.E. Higuera, and J.T. Abatzoglou. 2019. Microclimate buffering in forests of the future: The role of the local water balance. Ecography 42: 1–11. Fridley, J.D. 2009. Downscaling climate over complex terrain: High fine-scale ( than the 75th percentile in basal area) was compared to that observed in more open stands (< the lower quartile). From this (dashed orange lines in Fig. 2.10), it can be seen that, at the elevation of the ecotone, pines outgrow white fir in open stands while firs outgrow pines in denser stands. This is because fir is very shade tolerant. White fir’s growth rate is uncorrelated with basal area and positively but weakly correlated with elevation. What this implies is that in denser stands, white fir’s ability to displace pine is even greater than in stands of average stature, while pine should have the competitive advantage in more open stands. This is completely consistent with what has been observed in the study area: Fire suppression over the past several decades has allowed white fir (which very firesensitive while small due to its thin bark) to encroach into or grow more densely at lower elevations at the expense of pine. The increase in density (and height) of firs increases shade in the understory and, in turn, interferes with the successful regeneration and growth of pines. Thus, the observed recent encroachment and increasing density of white fir to lower elevations, at the expense of Ponderosa pine, can be interpreted in terms of shifting patterns of competitive advantage mediated by a combination of drought tolerance, shade tolerance, and fire suppression. This interaction adds a layer to the gradient model, invoking disturbance to the explanation. We will turn to disturbances as agents of pattern in the next chapter. But the main message from this Sierran case study is that the mechanisms and outcomes of the general model posed by Smith and Huston (1989) can be observed in real systems, in a way that depends on the particulars of that system.

2.5

Dispersal as an Agent of Pattern

2.4.4

43

The Unit Pattern Revisited

We began this chapter considering demographic processes in the absence of any heterogeneity in the physical template of landscapes, and then explored the implications of a heterogeneous physical template (here, as environmental gradients). This combination has emerged previously. One significant instance, from an historical perspective, is Whittaker’s (1953) notion of climax pattern as a model for the plant community. A direct result of his work in gradient analysis (Sect. 1.2), this model amounts to a locally adaptive version of Watt’s unit pattern: at each location on the landscape, physical conditions determine the “winner” of succession, and this winner is contingent on local site conditions in the sense of the simulation results of Smith and Huston (1989). This conceptual model is essentially Watt’s model modified to admit a locally defined endpoint (late-successional dominant), so that the overall pattern is a mosaic of sites, each undergoing its own temporal dynamics toward a successional endpoint defined by local site conditions. In the simulation framework of Smith and Huston, this would mean that each gradient position (i.e., the rows of the matrix in Fig. 2.8) would be its own unit pattern. This conceptual model is substantially richer than Watt’s model, but it also is the perfectly logical extension of Watt’s model to a heterogeneous physical template. (Indeed, to give due credit, Watt addressed this issue as well in his 1947 address, and his early work described different successional sequences or seres on different sites.) This general model has emerged in other guises. For example, Tilman’s (1982, 1987, 1988) work in (mostly grassland) plant communities emphasized the role of competition for soil resources (especially nitrogen) as a basis for local patterns of biodiversity. In this, the species best adapted (most competitive) under a given resource level will “win” locally; local patterns in biodiversity thus depend on local spatial heterogeneity in resource levels. This model is essentially Whittaker’s climax pattern applied to grassland communities competing for nitrogen. Again, Grime’s (1979) emphasis on plant strategies underscores the fundamental importance of trade-offs in life-history traits that confer differing competitive advantage (or tolerance) under various biophysical settings. Thus, in high-resource settings a competitive species wins, but only so long as resources persist. In resource-poor settings, tolerant species persist. Ruderal species behave similarly, but they track resources in time rather than space—though the mechanism is essentially the same. This model, then, is an invocation of biotic processes as an agent of pattern—but especially, demographic processes interacting with the physical template.

2.5

Dispersal as an Agent of Pattern

Dispersal is a pure demographic process and as such might have been considered after our initial exploration of the implications of birth and death processes as agents of pattern. But dispersal also can interact with the physical template, and so it is

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Biotic Processes as Agents of Pattern

logical to defer its consideration to this point. Arguably, too, much of what we suspect of dispersal as an agent of pattern is somewhat challenging to demonstrate empirically. The field data needed to show these effects are logistically difficult, so we more often tend to measure the result of dispersal rather than the process of dispersal (again, invoking Watt’s pattern–process paradigm to get at process via pattern). And so it is appropriate to tack this on as an additional consideration to what we have already considered. Clearly, dispersal can be a pattern generator. Decades of model-based explorations in population ecology have amply demonstrated this (e.g., Skellam 1951; Okubo and Levin 2001). A simple simulation model can show the logical implication of local dispersal as a population process. One such model is a cellular automaton. In an automaton, the world is a gridded space and the actions at a given cell depend only on the state of that cell and its neighboring cells. In a simple case, each cell is either occupied (shaded) or not, and dispersal acts as the movement from occupied to adjacent and unoccupied cells. If dispersal is constrained to be local, this process acts to “clump” population pattern over time. In the example shown (Fig. 2.11), dispersal is localized to a four-cell neighborhood (cardinal neighbors only) and unsuccessful dispersal (i.e., dispersal to an occupied cell) results in mortality. Alternative assumptions about the size of the neighborhood can influence the timing or intensity of clumping but not the qualitative eventuality of clumping. Similarly, invoking density-dependence in dispersal can complicate the patterns (e.g., to generate traveling waves in population density, Malanson and Rodriguez 2018) but do not alter the fundamental result that dispersal can generate profound spatial heterogeneity even on a perfectly homogeneous physical template.

Fig. 2.11 Dispersal-mediated in a population simulated on a homogeneous physical template. The model is a cellular automaton invoking local dispersal with stochastic birth and death. Left: initial pattern of spatial randomness. Right: pattern after 1000 time-steps, illustrating the clumping effect of local dispersal

2.5

Dispersal as an Agent of Pattern

2.5.1

45

Interactions Between Dispersal and Gradient Response

Of particular interest here is the potential for dispersal as a process to interact with other demographic processes to either amplify or (perhaps) weaken spatial patterns generated by other agents. Another simulation model will serve to illustrate this potential. The model, METAFOR, is a cellular automaton, a cell-based simulator for applications geared to large forested landscapes. It is, in fact, a model-of-a-model (a meta-model, Urban et al. 1999) based on the forest gap model we have already examined (Urban et al. 2000; Urban 2005). This illustration is developed for the southern Sierra Nevada of California. Each cell is identified by its environmental settings (temperature, soil moisture as an elevation gradient), and a cell can be occupied by a given species or it can be unoccupied (i.e., a gap). The physical template is interpolated over the digital landscape using regressions based on more detailed simulations with the gap model (i.e., as shown in Fig. 1.6). Tree demographic rates and tolerances are similarly based on the gap model (Fig. 2.9). The modeled dynamics are rather simple: at each time step, a cell can either persist (and age) in its current cover state (species) or become empty as a result of mortality. An empty cell is recolonized probabilistically based on species response to local site conditions and (optionally) local dispersal implemented as a neighborhood automaton. With neighborhood effects enabled, the likelihood of which species colonizes an empty site depends on its relative abundance in the immediate neighborhood (i.e., the eight neighbor cells surrounding the empty cell). There are only three species in this illustration. “White fir” (species are somewhat simplified caricatures) is the competitive dominant, achieving its best growth on mid-elevation sites. The growth rate of this species declines at lower elevations because of drought, and at higher elevations because of cold temperature. “Ponderosa pine” has a lower maximum growth rate than “white fir” but higher drought tolerance, while “lodgepole pine” has growth rates even slower than “Ponderosa pine” and very low drought tolerance; “lodgepole pine,” does, however, perform better at low temperatures than either “white fir” or “Ponderosa pine.” The species as parameterized are thus consistent with the conceptual model of Smith and Huston (1989). To illustrate the potential for interactions between dispersal, demographic processes, and the physical template, a set of model experiments was devised. In the experimental design, the landscape was simulated either as a gradient (an elevation gradient in temperature and soil moisture, consistent with the results of Urban et al. 2000) or uniformly average (mid-elevation) conditions. These cases are crossed with simulations that invoke neighborhood effects in dispersal or none (i.e., all species are eligible to colonize any empty site). This design yields four simulated landscape patterns, each initiated from a random distribution of species (Fig. 2.12). In the case where there is no gradient and no local dispersal effects (Fig. 2.12, top left), the resultant pattern essentially reflects the relative growth rates of the species: “white fir” is most abundant, followed by “Ponderosa pine” and then “lodgepole

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Neighborhoods

No Gradient

No Neighborhoods

Gradient

Fig. 2.12 Interactions between the physical template, biotic responses (including competition), and local dispersal (see text). Simulated species are white fir (green), Ponderosa pine (orange), and lodgepole pine (cyan). (Reproduced from Urban 2005)

2

pine.” The species are “speckled” randomly throughout the grid. On an environmental gradient, the result is similar but with some sorting of the species along the elevation gradient (Fig. 2.12, bottom left); the pattern, nonetheless, is still quite speckled over the gradient. With local dispersal and no gradient (Fig. 2.12, top right), the species tend to clump locally, although the clumps are essentially randomly distributed over the landscape. In this case, competition also gives an advantage to the faster-growing species, with the result that “lodgepole pine” is nearly extirpated from the landscape. This is a form of mass effect (Shmida and Ellner 1984), in which competitive advantage confers a numerical advantage locally, which in turn confers an advantage in establishment that amplifies over time even though the competitive advantage is slight. When local dispersal is added to an environmental gradient (Fig. 2.12, bottom right), the resulting pattern is amplified: species are locally clumped, and each species tends to be concentrated toward the region of the gradient where its competitive position places it: “white fir” dominates the middle elevations, “Ponderosa pine” is displaced downhill, and “lodgepole pine” is displaced uphill. This pattern is strongly reinforced by a local mass effect, in which competitive advantage related to environmental sorting is amplified over time by a numerical advantage locally, a positive feedback. Patterns of relative abundance of each species underscore these spatial patterns and the positive feedback effect of dispersal (Fig. 2.13). In this figure, species abundance was tallied over each row of the simulated grid for the gradient cases; abundances were simply averaged for the cases with no gradient. The result of local dispersal without a gradient (top right in the figure) has a substantial impact on “lodgepole pine,” again as a consequence of local mass effects. And again, the interaction of gradient sorting and local mass effects mediated by dispersal (bottom right) has a profound impact on species abundances over the gradient, essentially displacing each species from regions where it is not competitive while amplifying its

2.5

Dispersal as an Agent of Pattern

47

Abundance (%)

80 60 40 20

Abundance (%)

0 60 40 20 0 2000 2250 2500

2000 2250 2500

Elevation (m)

Elevation (m)

Fig. 2.13 Patterns of relative abundance as mediated by the interaction of gradients and biotic processes, corresponding to the spatial patterns in Fig. 2.9. Data are tallies of species abundance averaged over rows of the grids, rotated here so that the elevation gradient runs left to right (right is high elevation). Species are color-coded as in Fig. 2.12. (Reproduced from Urban 2005)

abundance where it has a competitive advantage. The intensity and timing of the dispersal amplification vary with the size of the local neighborhood (i.e., dispersal distance) and the relative demographic rates of the species, but the qualitative result depends only on the existence of competitive inequalities and local dispersal. Indeed, competitive inequalities and local dispersal are sufficient and necessary to generate these qualitative patterns. The addition of dispersal to species response to the physical template clearly can have a strong effect on vegetation pattern. In the cases shown, this is because local dispersal reinforces the advantage of species already established at a site. This presumes that the dispersal range of the species is short relative to the environmental gradient (in the simulations shown here, dispersal was limited to a single cell’s distance). Alternatively, we might consider a case where species dispersal range is long, relative to the environmental gradient. In this case, a species established on local site might disperse to sites quite far away, and thus dilute or negate the environmental sorting by the physical template. This invites a consideration of the spatial scale of the physical template, relative to the spatial scale of biotic processes such as dispersal. We will turn to scaling considerations in Chap. 4. This illustration also raises the question of the relative importance of environmental sorting as compared to dispersal in governing local patterns of biodiversity. We return to this fundamental and somewhat vexing issue in Chap. 7.

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2

Biotic Processes as Agents of Pattern

Animals, Pests, and Pathogens

The discussion so far has focused entirely on plants, and how plant communities interact with the physical template. This focus is justified by the reality that much of what we see when we look at landscapes is vegetation pattern and landform. In many instances, animals add a layer to landscape pattern in that they respond in turn to vegetation pattern, essentially tracking the pattern of availability of habitat. We will turn to this in some detail when we consider metapopulations and community-level response to landscape pattern—which in many cases will attend animal response to vegetation (habitat) pattern, especially in cases where the habitat is spatially patchy. But animals can have direct effects on landscape pattern. Mechanisms include herbivory (via grazing and browsing), seed predation, and secondary seed dispersal. In each case, the effects might be rather subtle, or the influences can be quite dramatic. Some animals, so-called ecosystem engineers, can also have direct and profound impacts on landscape pattern; beavers and very large animals (bison, elephants) are examples. Invertebrates—Wilson’s (1987) “little things that run the world”— have an enormous effect on ecosystems, although these impacts are not often as directly visible as the actions of larger beasts except during pest outbreaks.

2.6.1

Animals, Pests, and Pathogens as Subtle Agents

Animals can have substantial impacts on vegetation via herbivory and seed predation (Schowalter et al. 1986; Huntly 1991). In many instances, these impacts are not obvious to us from a distance—they do not affect landscape pattern—even though estimated losses to herbivory might be substantial. Other mechanisms also can have subtle but important influences on vegetation. One example is the classic JanzenConnell model of seed predation (Janzen 1970; Connell 1971). In this model, seed dispersal declines steeply with increasing distance from the source tree; at the same time, seed predation rates are highest close to the source tree (in response to seed density). As a result, seed survival to establishment is highest farther from the source, beyond the reach of intense seed predation. A mechanism such as this might have a profound influence on species dispersion within plant communities, but this is more subtle than actions that affect the way landscapes look from a distance. Similarly, meso-fauna (medium-sized animals) can be important in many systems in mediating seed dispersal by ingesting fruits and then depositing seeds after they pass through the gut. As with herbivory, these influences might have important influences on community structure and species composition, but these effects fall somewhat short of altering landscape pattern itself. Pests and pathogens can have substantial effects on tree mortality. Das et al. (2016) analyzed causes of mortality from mapped forest stands in the Sierra Nevada, tallying mortality from 200,668 tree-years of field measurements. Causes of

2.6

Animals, Pests, and Pathogens

49

mortality varied by species and tree size, but overall, 58% of deaths were caused by biotic agents (pests and pathogens, including fungal pathogens). Half of all trees had only one mortality factor (of six tallied), and 90% of trees had only one or two contributing factors. Suppression was the next most common factor, involved in 51% of tree deaths (mostly of smaller trees), followed by mechanical damage (25%). Their data were collected over a 13-year period during which there were no pest or pathogen outbreaks, nor any severe drought. Thus, most of the mortality events that we tend to think of as “background” or random were caused by biotic agents. There can be a spatial signal in this, either because the agents respond to gradients (especially elevation) or due to contagious spread of pathogens. Again, these are mortality events of individual trees, and while they would have an important influence on local species composition and community structure, this would not typically be considered a substantial effect on landscape pattern in a larger sense. Still, as data like these are not commonly collected, we almost certainly underestimate the importance of these biotic agents (Das et al. 2011, 2016; Stephenson et al. 2019). By contrast, the influences of pests can be quite dramatic when these erupt into broadscale infestations. At these levels, the results clearly can be seen to affect landscape pattern. The spread of pine bark beetles is an illustration now familiar on many landscapes in the western United States. Beetle infestations respond to the physical template as well as to inter-annual variation in weather: cold winter temperatures typically keep populations in check while warmer summer temperatures favor population growth. The beetle infestations also interact with other agents of pattern, with other stressors such as drought resulting in reduced tree resistance to the attacks, and beetle-killed trees interacting with other disturbances (especially fire). We will revisit these interactions in Chap. 3. And we will return again to biotic agents in Chap. 10, when we consider the likelihood that climate change will increase the prevalence and outbreak potential of pests whose populations respond directly to temperature.

2.6.2

Animals as Dramatic Agents

Animals are more directly agents of pattern in the case of large herbivores in grazing systems throughout the world. The Serengeti of Africa is an iconic example (e.g., McNaughton 1985), although similar systems occur elsewhere (Frank et al. 1988). In these systems, large grazers and browsers affect landscape pattern by controlling vegetation. Grazing responds to the physical template as it governs forage availability in space (i.e., along topographic gradients) and in time (following seasonal patterns in precipitation). In many such systems, the biotic agents of pattern also interact with disturbance regimes (often, fire).

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Animals can have a direct impact on landscape pattern through the activities of so-called ecosystem engineers (Jones et al. 1997). Beavers (Wright et al. 2018) and elephants (Poulsen et al. 2018) are familiar examples. In each case, habitat modifications have impacts that propagate to other species. In many instances, the effects of animals on vegetation and ecosystems have been illustrated nicely (although usually inadvertently!) through the actions of humans. In the case of tropical meso-fauna and seed predation, this has been revealed by observing the impacts of local hunting pressure and the trophic cascades resulting from the removal of key species (e.g., Terborgh and Estes 2010). In the case of the Yellowstone ecosystem, the trophic cascade was mediated by the removal of a key top predator, the gray wolf (Canis lupus) (Ripple and Beschta 2012). Wolves were extirpated from this system around 1920, resulting in an increase in elk (Cervus elaphus) populations, which in turn caused drastic reductions in aspen (Populus tremuloides), cottonwoods (Populus spp), and willows (Salix spp) due to increased browsing pressure. The wolf was reintroduced in 1995–96, and in the wake of that reintroduction the elk populations have declined somewhat and, more importantly, altered their movement and behavior (Fortin et al. 2005); the vegetation has regrown in places (Fig. 2.14). At the same time, populations of beaver (Castor canadensis) and bison (Bison bison) have also increased, in response to the greater availability of forage, and grizzly bears (Ursa arctos) have benefited from an increase in berryproducing shrubs. (Ripple et al. 2014). We will return to interactions among agents of pattern in the next chapter, and to the legacy effects of past actions in Chap. 8.

Fig. 2.14 Comparison photographs from Yellowstone in 1997 and 2010. Wolves were reintroduced in 1995–96. Vegetation on the right has regrown following depression of elk populations. (Used with permission from Elsevier, from Ripple and Beschta (2012) (their panel B, from 2001, is omitted here) Images courtesy W. Ripple)

References

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51

Summary and Conclusions

We began this chapter by considering the implications of the simplest demographic processes—birth and death—and discovered that biotic processes can generate rich patterns at the community level. Couplings among these processes, again, as simple couplings of death and regeneration mode, generated still richer patterns. Overlaying these processes onto the physical template, invoked as a simple gradient, revealed a much more complicated pattern mediated by relative competitive advantages under particular combinations of above- and below-ground resources—advantages dictated by trade-offs in life-history traits. Finally, we added dispersal as a process that can interact with competition and local abundances to amplify patterns of species abundance locally. One unavoidable conclusion from this sequence of increasingly complicated models is that we are not likely to be able to make clean inferences about generating processes from observations of the patterns resulting from these processes. This is despite the fact that the simplest scenario, manifest as the pattern-process paradigm, is the logical basis for making exactly such inferences. In particular, the combination of Watt’s conceptual model with the competition-mediated gradient response model illustrated by Smith and Huston (1989) provide us with two very fundamental rules for interpreting landscape pattern. First, what we observe on a landscape is likely the result of demographic processes or other events that occurred in the past (Watt’s “anomalous events”), and so all landscape pattern is contingent in historical legacies. Second, what we observe in community pattern is contingent on relationships among the species actually present, interacting with local environmental gradients. So, likewise, species response to environmental change (such as climate change) will depend on historical legacies as well as the contingencies of current conditions. This complicates our simple model of landscape pattern, but in a healthy way that respects the interaction of biological processes with the physical template of landscapes, as well as the role of history. In the next chapter, we will further enrich this model by adding disturbances and disturbance regimes as another layer in the model, the third agent of landscape pattern. Disturbances, of course, come in various sizes and at varying frequencies. This complication, in turn, will yield to an approach that parses landscape pattern as a function of characteristic scaling (Chap. 4).

References Bormann, F.H., and G.E. Likens. 1979. Pattern and process in a forested ecosystem. New York: Springer. Botkin, D.B. 1993. Forest dynamics: An ecological model. Oxford: Oxford University Press. Clark, J.S., A.E. Gelfand, C.W. Woodall, and K. Zhu. 2014. More than the sum of the parts: Forest climate response from joint species distribution models. Ecological Applications 24: 990–999.

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Clark, J.S., D. Nemergut, B. Seyednasrollah, P.J. Turner, and S. Zhang. 2017. Generalized joint attribute modeling for biodiversity analysis: Median-zero, multivariate, and multifarious data. Ecological Monographs 87: 34–56. Clark, J.S., C.L. Scher, and M. Swift. 2020. The emergent interactions that govern biodiversity change. PNAS 117: 17074–17083. Connell, J.H. 1971. On the role of natural enemies in preventing competitive exclusion in some marine animals and in rain forest trees. In Dynamics of populations, ed. P.J. den Boer and G.R. Gradwell, 298–312. Wageningen: Center for Agricultural Publishing and Documentation. Connell, J.H., and R.O. Slatyer. 1977. Mechanisms of succession in natural communities and their role in community stability and organization. The American Naturalist 111: 1119–1144. Das, A., J. Battles, N.L. Stephenson, and P.J. van Mantgem. 2011. The contribution of competition to tree mortality in old-growth coniferous forests. Forest Ecology and Management 261: 1203–1213. Das, A.J., N.L. Stephenson, and K.P. Davis. 2016. Why do trees die? Characterizing the drivers of background tree mortality. Ecology 97: 2616–1627. Drury, W.H., and I.C.T. Nisbet. 1973. Succession. Journal of the Arnold Arboretum 54: 331–368. Fortin, D., H.L. Beyer, M.S. Boyce, D.W. Smith, T. Duchesne, and J.S. Mao. 2005. Wolves influence elk movements: Behavior shapes a trophic cascade in Yellow-stone National Park. Ecology 86: 1320–1330. Frank, D.A., S.J. McNaughton, and B.F. Tracy. 1988. The ecology of the Earth’s grazing ecosystems. BioScience 48: 513–521. Grime, J.P. 1974. Vegetation classification by reference to strategies. Nature 250: 26–31. ———. 1977. Evidence for the existence of three primary strategies in plants and its relevance to ecological and evolutionary theory. The American Naturalist 111: 1169–1194. ———. 1979. Plant strategies and vegetation processes. New York: Wiley. Huntly, N. 1991. Herbivores and the dynamics of communities and ecosystems. Annual Review of Ecological Systems 22: 477–503. Huston, M.A., and T.M. Smith. 1987. Plant succession: Life history and competition. The American Naturalist 130: 168–198. Janzen, D.H. 1970. Herbivores and the number of tree species in tropical forests. The American Naturalist 104: 501–508. Jones, C.G., J.H. Lawton, and M. Shachak. 1997. Positive and negative effects of organisms as physical ecosystem engineers. Ecology 78: 1946–1957. Malanson, G.P., and N. Rodriguez. 2018. Traveling waves and spatial patterns from dispersal on homogeneous and gradient habitats. Ecological Complexity 33: 57–65. McNaughton, S.J. 1985. Ecology of a grazing ecosystem: The Serengeti. Ecological Monographs 55: 259–294. Okubo, A., and S.A. Levin. 2001. Diffusion and ecological problems: Modern perspectives. New York: Springer. Pollock, L.J., R. Tingley, W.K. Morris, N. Golding, R.B. O’Hara, K.M. Parris, P.A. Vesk, and M.A. McArthy. 2014. Understanding co-occurrence by modelling spe cies simultaneously with a joint species distribution model (JSDM). Methods in Ecology and Evolution 5: 397–406. Poulsen, J.R., C. Rosin, A. Meier, E. Mills, C.L. Nunez, S.E. Koerner, E. Blanchard, J. Callejas, S. Moore, and M. Sowers. 2018. Ecological consequences of forest elephant declines in Afrotropical forests. Conservation Biology 32: 559–567. Ripple, W.J., and R.L. Beschta. 2012. Trophic cascades in Yellowstone: The first 15 years after wolf reintroduction. Biological Conservation 145: 205–213. Ripple, W.J., R.L. Beschta, J.K. Fortin, and C.T. Robbins. 2014. Trophic cascades from wolves to grizzly Bears in Yellowstone. The Journal of Animal Ecology 14: 223–233. Schowalter, T.D., W.W. Hargrove, and D.A. Crossley Jr. 1986. Herbivory in forested ecosystems. Annual Review of Entomology 31: 177–196. Shmida, A., and S. Ellner. 1984. Coexistence of plant species with similar niches. Vegetatio 58: 29–55.

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Shugart, H.H. 1984. A theory of forest dynamics. New York: Springer-Verlag. ———. 1987. Dynamic ecosystem consequences of tree birth and death patterns. BioScience 37: 596–602. Shugart, H.H., and D.L. Urban. 1989. Factors affecting the relative abundance of forest tree species. In Toward a more exact ecology. Jubilee symposium of the British ecological society, ed. P.J. Grubb, 249–273. Oxford: Blackwell. Skellam, J.G. 1951. Random dispersal in theoretical populations. Biometrika 38: 196–218. Smith, T., and M. Huston. 1989. A theory of the spatial and temporal dynamics of plant communities. Vegetatio 83: 49–69. Smith, T.M., and D.L. Urban. 1988. Scale and resolution of forest structural pattern. Vegetatio 74: 143–150. Stephenson, N.L., A.J. Das, N.J. Ampersee, B.M. Bulaon, and J.L. Yee. 2019. Which trees die during drought? The key roles of insect host-tree selection. Journal of Ecology 107: 2383–2401. Terborgh, J., and J.A. Estes, eds. 2010. Trophic cascades: Predators, prey, and the changing dynamics of nature. Washington: Island Press. Tilman, D. 1982. Resource competition and community structure. Princeton: Princeton University Press. ———. 1987. Secondary succession and the pattern of plant dominance along experimental nitrogen gradients. Ecological Monographs 57: 189–214. ———. 1988. Plant strategies and the dynamics and structure of plant communities. Princeton: Princeton University Press. Urban, D.L. 2005. Modeling ecological processes across scales. Ecology 86: 1996–2006. Urban, D.L., and D.O. Wallin. 2002. Introduction to Markov models. In Learning landscape ecology: A practical guide to concepts and techniques, ed. S.E. Gergel and M.G. Turner, 35–48. New York: Springer-Verlag. Urban, D.L., M.F. Acevedo, and S.L. Garman. 1999. Scaling fine-scale processes to large-scale patterns using models derived from models: Meta-models. In Spatial modeling of forest landscape change: approaches and applications, ed. D. Mladenoff and W. Baker, 70–98. Cambridge: Cambridge University Press. Urban, D.L., C. Miller, N.L. Stephenson, and P.N. Halpin. 2000. Forest pattern in Sierran landscapes: The physical template. Landscape Ecology 15: 603–620. Usher, M.B. 1992. Statistical models of succession. In Plant succession: Theory and prediction, ed. D.C. Glenn-Lewin, R.K. Peet, and T.T. Veblen, 215–248. London: Chapman and Hall. Warton, D.I., F.G. Blanchet, R.B. O’Hara, O. Ovaskainen, S. Taskinen, S.C. Walker, and F.K.C. Hui. 2015. So many variables: Joint modeling in community ecology. Trends in Ecology & Evolution 30: 766–779. Watt, A.S. 1924. On the ecology of British beechwoods with special reference to their regeneration. II. The development and structure of beech communities on the Sussex Downs. Journal of Ecology 12: 145–204. ———. 1925. On the ecology of British beechwoods with special reference to their regeneration. Part II, sections II and III. The development and structure of beech communities on the Sussex Downs. Journal of Ecology 13: 27–73. ———. 1947. Pattern and process in the plant community. Journal of Ecology 35: 1–22. Whittaker, R.H. 1953. A consideration of climax theory: The climax as a population and pattern. Ecological Monographs 23: 41–78. Wilson, E.O. 1987. The little things that run the world (the importance and conservation of invertebrates). Conservation Biology 1: 344–346. Wright, J.P., C.G. Jones, and A.S. Flecker. 2018. An ecosystem engineer, the beaver, increases species richness at the landscape scale. Oecologia 132: 96–101.

Chapter 3

Disturbances and Disturbance Regimes

3.1

Introduction

Disturbance regimes interact with the physical template and biotic processes, generating landscape pattern that cannot simply be reduced to any of the agents of pattern by themselves. Natural disturbances such as fire, floods, and hurricanes are highly visible agents of landscape pattern and, consequently, disturbance is a topic with considerable human interest. In this chapter, we begin by reviewing key definitions and our current understanding of disturbance dynamics and then focus on how disturbance regimes interact with biophysical gradients and biotic processes as agents of pattern. The interplay between climate, elevation, biotic process, and fire regimes in many forest systems provides a rich illustration of the complexities of these interactions. As disturbance events tend to occur with characteristic timing and sizes, disturbance regimes naturally broach issues of spatial and temporal scale—to which we turn in the next chapter. Here, the consideration of natural scaling relative to the perspective of human life spans helps encourage a perspective that focuses on the landscape itself instead of the observers of the landscape.

3.1.1

Context and Definitions

The topic of disturbance occupies a special place in ecology because disturbance events directly affect people—including people who study disturbance. Not surprisingly, there is appreciable semantic baggage attached to the term, which can sometimes confuse discussion. Our perceptions of disturbance also have evolved substantially over the past several decades, apace with notions of ecological dynamics in general (Sousa 1984; Pickett and White 1985; Turner 1987, 2010; White and Jentsch 2001; Peters et al. 2011; Jentsch and White 2019; Gaiser et al. 2020).

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Disturbance is also a complicated issue because it overlaps with or contributes to other (most?) areas of ecology and also with human systems. Much of disturbance theory is about post-disturbance succession and ecosystem recovery, and so overlaps with community and ecosystems ecology (reviewed by Pulsford et al. 2016). We have already considered succession as a process (Sect. 2.4.2) closely aligned with gradient response. We will revisit disturbance and ecosystem processes in Chap. 8, in terms of the spatial heterogeneity that disturbances create and the lasting legacies of landscape history. Disturbances also feature in discussions of system resilience and the emergence of tipping points or surprises (Ratajczak et al. 2017). We will return to resilience in Chap. 10. In human systems, or coupled social-environmental systems (Pickett et al. 2001, 2011; and see Chap. 9), disturbances are challenging because humans are both agents (causing) and subjects of (responding to) disturbance (Grimm et al. 2017; Gaiser et al. 2020). We will delve into social-environmental systems in Chap. 9, on urban landscapes; but we will review some ways that humans modify disturbance regimes later in this chapter. There is an enormous literature on disturbance ecology. White and Jentsch (2001), Peters et al. (2011), Jentsch and White (2019), and Gaiser et al. (2020) provide extensive reviews. Our narrow interest here is in the role of disturbance as an agent of landscape pattern. We will bring in disturbance ecology more generally only when we need it to understand disturbance as a pattern generator.

3.1.1.1

Definitions

Some definitions are in order. These are not to codify any particular phrases, but to be as precise as possible in the following discussion. Here we adopt the definition of Pickett and White (1985: 7), that disturbance is “any relatively discrete event in space and time, that disrupts ecosystem, community, or population structure and changes resources, substrate, or the physical environment.” The two key terms in this definition are discrete—which distinguishes a disturbance event from a chronic stress such as heavy metal contamination or seasonal anoxia, and disrupts—which requires that a disturbance have a measurable impact on system properties or processes. The discreteness element of this definition is problematic, of course, in that many chronic stressors (sometimes termed press disturbances) can change into disturbances (pulses) rather suddenly, such as when chronic heat stress becomes a heat wave, or a low-level pest infestation erupts into an outbreak. Chronic stress also can lead to structural changes in the system (e.g., when vegetation dies). And an event that seems prolonged from our perspective as humans might be rather abrupt, for example, for a tree that lives many hundreds of years. Thus, this general definition—still adopted by many (Turner 2010; Gaiser et al. 2020)—often requires further specification to be useful in applications. Pickett and Cadenasso (2021) suggest a distinction of terms that can help reconcile these definitions. They use disturbance to refer to a structural change to a system (as in the original definition, above), and stress to refer to a functional

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change (e.g., in ecosystem metabolism). This distinction makes it easier to think about chronic stresses that do not change a system structurally, but it also admits such changes when they do happen. Disturbances and disturbance regimes are characterized by several attributes. Disturbance intensity refers to the event itself: fire temperature, wind speed, and water depth. The units of measure depend on the disturbance. Disturbance severity refers to the impact of the event on the system: percent mortality, or other estimates of damage. Spatially, disturbances have a size or magnitude, measured in units of area. A particular landscape is likely to witness disturbances that vary in size, and a disturbance regime tends to have a characteristic distribution of event magnitudes (e.g., fire sizes). Disturbances often have particular spatial associations; for example, fires, floods, and windstorms all respond to topography, although in different ways. Some disturbances (e.g., fire, disease, or pests) are spatially structured by an explicitly contagious process, while others (e.g., floods, wind) are structured by dependencies on or interactions with topographic settings (e.g., wind routing, fires spreading uphill). Understanding the spatial structure of disturbance regimes is key to any effort to forecast disturbances or to manage landscapes prone to disturbance. Temporally, disturbances often have a characteristic frequency (events per unit time), the inverse of which is recurrence interval (time between events). Frequency is sometimes interpreted as a likelihood. For example, fires with a 20-year recurrence interval have a frequency of 0.05; one might expect such a fire with a 5% chance in any given year—if there is no temporal structure to the regime. This is often not the case: if a fire removes a lot of the fuel in a system, we might not expect another fire right away and so the likelihood of fire is not constant over time but highly variable. By contrast, we might expect a “100-year flood” with a 1% chance in any given year—even in two sequential years—because the “100 years” refers only to the long-term distribution of flood depths and properly connotes a “1 in 100” flood intensity (floods, of course, also are somewhat structured in time because the weather is structured in time: precipitation has inherent periodicities). There can be a fair bit of confusion about the meaning, for example, of a “100year flood” in part because of the definition itself (it is about statistical likelihood, not recurrence interval) and partly because the statistics themselves are based on historical records and not the present, much less the near-term future. The spatial and temporal aspects of disturbances interact, yielding more integrative descriptors. Return time for a disturbance is the time from an initial event until we might expect another event to occur at the same point on the landscape (to be clear: frequency and recurrence interval refer to the events, while return time refers to a location). This depends not only on disturbance frequency but also on spatial associations such as topography. In the case of fire, return time also reflects any lag needed to rebuild fuel loads before another fire can occur. A related term sometimes used in fire ecology, rotation period, refers to the time it would take to disturb a given reference area (park or management unit); this depends on disturbance frequency, spatial associations, and magnitude. Note that for a real fire system, over a rotation period, some points might be burned repeatedly while some points might not be burned at all; the term is an expression in the aggregate.

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Finally, a disturbance is a single event; a disturbance regime is a collection of events, over time, with their characteristic frequencies and magnitudes. Sometimes it will be useful to qualify these terms: for example, a fire regime is a collection of fires, and a landscape subject to fire—a fire system—is a particularly well-studied case (e.g., McKenzie 2019; McLauchlan et al. 2020). But that same landscape also might have a disturbance regime that includes other types of events beyond fires (e.g., droughts, pest outbreaks). Other disturbance terms have been defined (and argued over!) but these will suffice for the discussion that follows.

3.2

Perspectives and Lessons

There is an enormous literature on disturbance ecology, and we could easily get lost in the topic. Here we visit a few samples. These examples are selected to illustrate key concepts related to disturbance.

3.2.1

Are Disturbances “Part of the System”?

Richness

Abundance

Allen and Wyleto (1983) used a study of prairie fires to ask an important question: Are disturbances “inside” or “outside” the system? Their answer: either, depending on the ecological question (Fig. 3.1). If the question of interest is about post-fire succession, then a fire is an event that initiates succession. The organizing variable is “time since fire.”. The interesting dynamics after the fire can be isolated from the fire itself, and the fire can be considered extrinsic to the system. In this case, the successional dynamics play out largely as we might expect as a gradient in time (recall Sect. 2.4.2) and the fire itself can be separated from the study system; it is outside the system.

Time Since Fire

Fire Frequency

Fig. 3.1 Two perspectives on the position of fire in a system. Left: the dynamic of interest is postfire succession and the initiating fire can be separated from the study. Right: fire frequency implies a pattern of species richness and fire is integral to the study system. (After Allen and Wyleto 1983)

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Alternatively, one might be interested in how fire frequency influences species richness in this system. We might expect that, at high fire frequency, only species that establish immediately after a fire would be supported, hence low diversity. At very low fire frequency, long fire intervals would allow late-successional species to come into dominance, and again lower diversity would result. At intermediate frequencies, a mix of early-, mid-, and late-successional species could persist, yielding higher diversity. This expression of the intermediate disturbance hypothesis (Connell 1978; Huston 1979; but see Fox 2013) requires the interplay of disturbances and biotic process for its explanation; fire is part of this system. This choice to study disturbances as events as compared to a disturbance regime that integrates events over space and time echoes Watt’s (1947) conceptual model of the plant community (Sect. 2.2). His hierarchical model can thus be applied quite generally (O’Neill et al. 1986; Urban et al. 1987).

3.2.2

Interactions, Synergies, and Indirect Effects

Knight (1987) provided an in-depth discussion of fire regimes in the Rocky Mountains of the western United States. His graphical model (not shown here) highlighted through its sheer busyness the complicated nature of these systems: many factors interact and in many different ways. The basic model might well be revised substantially in the wake of research since that time (e.g., Romme 1982; Turner and Romme 1994; Turner 2010), but this still serves as a useful heuristic. It is instructive to explore these interactions and feedbacks in a slightly different format. In this, each component of the system can be identified as a node, a point (the dots in Fig. 3.2); these include soil moisture, insects, lightning, and other nouns in Knight’s original diagram. Each arrow between two nodes can also be extracted as a separate link. In this instance, the arrows in Fig. 3.2 represent causal links, verbs. The nodes and links together define a directed graph (Harary 1969), also known as a path model or causal chain. Graph theory is much invested in the topology of these models (i.e., the pattern of links among nodes). In particular, graph-drawing algorithms are designed to depict graphs with minimal overlap among links. In this exercise, the data were encoded as a list of pairwise directed links such as “from soils to drought” and the resulting graph was drawn using the default “plot” command in the package for social network analysis in the R analytic environment (Butts 2019; R Core Team 2019). In drawing a graph of Knight’s model (an incomplete version, but adequate for our purpose here), this rendering orders the nodes to separate biological features from physical features (Fig. 3.2). In doing so, the diagram also provides a means to follow causal pathways that affect the fire regime, simply by connecting the dots. Some of these are rather simple and straightforward, such as the effect of stand age on fuel load. In the diagram, this is the path age → fuel load → fire. Some connections are even more direct: wind → fire. Other pathways are more complicated, involving intermediate factors that propagate effects through the system. An

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Disturbances and Disturbance Regimes Soils

Species Drought

Topo Fuel Moisture

Parasites

Fuel Load

Lightning Wind Openness

Age Suppression

Fire

Fig. 3.2 Knight’s (1987) model redrawn as a graph of ecosystem features (nodes) and causal links between pairs of these (arrows). Rendering the graph distinguishes biophysical features (upper right) from factors governed by biological processes (lower left). Causal pathways can be traced along nodes to see their impact on fire (flammability in Knight’s model)

example might be the path topo → soils → drought → species → parasites → (canopy) openness → wind → fuel moisture → fire. Importantly, this depiction emphasizes the reality that some factors or landscape features play multiple roles in the fire regime while also providing a means to trace the possible implications of changes to the system (e.g., warmer winters). Put another way, the graph-based depiction of interaction pathways provides a perspective that portrays the system in terms of causes and effects. To be clear: the information both Knight’s original (and very busy) diagram and Fig. 3.2 is essentially the same; what differs is the ease with which paths can be traced in the graph model. We return to interaction pathways and causal chains in Chap. 10, where we consider means of anticipating climate-change impacts for complicated systems like this one.

3.2.3

Disturbances and Positive Feedback

Over huge expanses of the circumboreal zone, boreal forest systems exhibit a complicated interplay of climate, forest process, and disturbances (e.g., Bonan

3.2

Perspectives and Lessons

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et al. 1992; Shugart et al. 1991). One well-studied disturbance regime is insect outbreaks, especially the spruce budworm (e.g., Holling 1973; Ludwig et al. 1978). In this system, the budworms can persist for decades at low levels of infestation, representing a chronic stress on trees locally; healthy trees are resistant to low densities of insects. In response to a climate trigger, the insects begin to multiply rapidly, and soon reach densities at which even healthy trees succumb. The infestation escalates into an eruption over a huge spatial extent. This represents a positive feedback via which a local dynamic “escapes” to a larger scale, and becomes a disturbance in the strict sense of having acute attack and significant disruption (recall Sect. 3.1.1). This is one of the seminal illustrations of positive feedback in ecosystems. The effects of fire on the physical template of boreal forests are complicated by the role of permafrost, which can act as an impervious layer in the soil and which can thus play a crucial role in the soil moisture regime (Fig. 3.3). Melting the permafrost allows soil moisture to leak away, leading to drought and increased chance of fire (and greater intensity of fire, when fires occur). Forest development acts as a moderator on fire, as the mossy ground layer under the forest canopy insulates the ground. Fire removes this insulation but, significantly, also chars the ground and changes the surface albedo: the dark fire scars absorb more radiation and warm the ground. This warming can reduce permafrost, decrease soil moisture, and further increase the likelihood and intensity of fires: another positive feedback. On a larger scale, the fate of boreal systems (especially the relative cover of ice, snow, and forest) has taken on a more urgent focus in the area of feedback between ecosystems and the climate system itself. As these systems warm, frozen soil thaws and the peat in these soils is decomposed to release CO2 into the atmosphere. Adding more greenhouse gases to the atmosphere, of course, will result in further warming,

Insect Outbreak

Forest Structure

Fire

Cloudiness Nutrient Availability Slope/ Aspect

Solar Radiation

Soil Temperature Permafrost Soil Physical Properites

Air Temperature

Forest Floor Organic Layer

Soil Moisture

Elevation Precipitation

Fig. 3.3 Environmental processes controlling landscape pattern in boreal forests. (Redrawn with permission of Annual Reviews Inc., from Bonan and Shugart (1989); permission conveyed through Copyright Clearance Center, Inc.)

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creating a positive feedback to accelerate climate warming (Bonan et al. 1992; Payette et al. 2004; Camill 2005). As the land area involved is immense, this feedback has drastic and global implications and thus is a focus of heightened activity in research as well as policy in global climate change (witness the Intergovernmental Panel on Climate Change’s 2019 special report: https://www.ipcc.ch/ srocc/). Boreal systems thus illustrate a range of complex feedback that play out from local to global scales, including older, seminal studies as well as very recent activity in the area of ecological complexity, resilience, and tipping points. These small-scale stressors or perturbations that “escape” to very large scales are often called cross-scale interactions (Peters et al. 2004). Well-documented examples involve the local pattern of erosion characteristic of some arid and semi-arid systems, fire systems, pest eruptions, and vegetation die-offs (e.g., Peters et al. 2004; Allen 2007; Peters et al. 2007; Raffa et al. 2008; Peters et al. 2011). In general, it seems that many of these cross-scale “escapes” are generated or augmented by positive feedback. We return to positive feedback in Chap. 8.

3.2.4

Overlapping Disturbances and Legacies

Reiners and Lang (1979) detailed the disturbance regime of the White Mountains of the New Hampshire (USA). They recognized first- and second-order patterns on the landscape. First-order patterns were in response to elevation and wind exposure, and included overall trends in species composition and canopy height with elevation. Overlaid onto this were second-order patterns, including four distinct kinds of disturbance patches: fir waves, glades, strips, and canopy gaps. These disturbances vary in magnitude (patch size) and arise from various physical and biological processes (some poorly understood still). Overlaid onto this are patches from more acute disturbances, hurricanes, and avalanches. Reiners and Lang (1979) cast these dynamic patterns as a logical extension of Watt’s conceptual model of the plant community, although the model becomes a bit more complicated. Because disturbances overlap in time as well as in space (e.g., due to similar topographic associations), it is generally difficult to infer very much about the disturbance history of a given site based on field observations alone. A landscape is, in fact, a well-used canvas—a palimpsest1—on which new patterns are continually superimposed, while the ghost patterns of previous events persist. Many (most?) landscapes are subject to multiple disturbances, and many of these are the result of human activities. For example, Tuttle and White (2016), see also White et al. 2018) overlaid Whittaker’s (1956) mapping of the vegetation of the Great Smoky Mountains with human-mediated pests and disturbance legacies: a logging history predating the Park’s establishment, the balsam woolly adelgid at

1

I am grateful to Frank Davis, UC-Santa Barbara, for sharing this perfect metaphor.

3.2

Perspectives and Lessons

63

B Hath balds

A Spruce-fir

Beech

Balsam woolly adelgid 1970s

Beech Bark Disease 1990s

Fire suppression 1930s

Chestnut blight 1930s

ade Hem 200 lock w 0s oolly

Pine-hardwoods

Submesic to subxeric Hardwoods, often dominated by oaks

Rich hardwood coves Acidic hemlock coves

lgid

Northern hardwoods Hemlock

Fig. 3.4 Landscape legacies of prior land use and various pests, overlaid onto vegetation pattern in Great Smoky Mountains National Park. Vegetation pattern is simplified from Whittaker (1956), and legacies and disturbances are redrawn from an original by P.S. White and J. Tuttle

high elevations, the hemlock adelgid in lower-elevation cove forests, the chestnut blight over much of the mid-elevations, and feral hogs throughout; the list goes on (Fig. 3.4). We will return to the issue of landscape legacies in Chap. 8.

3.2.5

Heterogeneity in Disturbance and Response

Fire systems provide an important lesson on the causes and consequences of pattern. With fire systems, it is often tempting to simplify these into either surface- (ground-) or crown-fire systems. The simplification is that surface fires are small and frequent, with low intensity and severity; crown-fires, by contrast, are large and intense but infrequent. There is some truth in this generalization, but it belies the profound amount of variation in fire regimes. Indeed, many fire systems support mixedseverity regimes comprised of a mix of event sizes and frequencies (e.g., Perry et al. 2011). The lesson from fire systems characterized by large, infrequent disturbances is about the profound level of spatial heterogeneity: variability in pre-fire conditions, variability in fire intensity and severity, and variability in post-fire regeneration and ecosystem processes. The Yellowstone ecosystem has been instrumental in our understanding of this heterogeneity, and Monica Turner with her colleagues has

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Fig. 3.5 Spatial heterogeneity in the 1988 Yellowstone fire. (Reproduced with permission of John Wiley & Sons, from Turner (2010); permission conveyed through Copyright Clearance Center, Inc. Photo courtesy M.G. Turner)

been a lead architect of that understanding. Turner summarized this in her MacArthur Award address (Turner 2010 and many references therein). Among the lessons learned is the appreciation that even very large disturbances are not homogenizing; rather, they create a multi-scaled mosaic of spatial heterogeneity. For illustration, within the nearly 250,000-ha fire perimeter of the 1988 Yellowstone fire, 28% of the area was unburned, 16% lightly burned (surface fire), 25% moderately burned (partial crown fire), and 31% was crown fire (Turner et al. 1994, Fig. 3.5). All of the moderately burned sites and 50% of the severely burned sites with within 200 m of a “green” (unburned or lightly burned) forest edge: the resulting mosaic is highly heterogeneous and interspersed. Similarly, spatial heterogeneity in burn intensity creates variation in soil properties and nutrient dynamics that then result in profound variation in post-fire plant establishment and succession. Much of this variability in post-fire recovery is mediated by biological legacies surviving the disturbance (Foster et al. 1998; Franklin et al. 2000; Johnstone et al. 2016). Such legacies include surviving trees (which then act as seed trees), seed banks in the soil, serotinous cones (cones that require the heat of a fire to open and release seeds), and persistent roots and rhizomes. These remnants facilitate system recovery, and because they are spatially heterogeneous they impart more spatial heterogeneity in system response.

3.3

Disaggregating Disturbance Toward Generality

65

The lessons from Yellowstone apply more generally to other systems (e.g., Fraterrigo and Rusak 2008), but it was Yellowstone that taught us that large, infrequent disturbances are not homogenizing catastrophes but rather, profound agents of pattern at many scales.

3.3

Disaggregating Disturbance Toward Generality

Disturbance ecology has long resisted easy generalizations (Jentsch and White 2019). Peters et al. (2011) argued for a different approach to generalization, by disaggregating the simple model of a disturbance event and system response into a more granular model that provides a template for more consistent applications across various types of disturbances.

3.3.1

A Not-Too-General Model

The key to the Peters et al. (2011) model is that some detail is retained in terms of how a disturbance acts and what its impacts are on the system. In their model (Fig. 3.6), a disturbance is specified not only by type but also in terms of the specific mechanisms by which the disturbance perturbs the system (Fig. 3.6, left panel). They noted that most disturbances act via multiple mechanisms (e.g., a hurricane includes wind, an acute storm surge, and prolonged inundation) and that some mechanisms are shared by multiple disturbance types (e.g., windstorms and floods might both include abrasion). How these mechanisms play out depends on the state of the system (e.g., wind damage varies with vegetation height and routing by topography). A disturbance has measurable impacts on the systems (Fig. 3.6, middle panel), consistent with the adoption of Pickett and White’s (1985) definition. A disturbance often results in biophysical legacies, and the combination of direct effects and legacies redefines the state of the system. The system then recovers, to some extent, to the event via processes such as succession, although the system might also be reconfigured in ways that differ from its previous state (Fig. 3.6, right panel). This new state then can influence the way that future disturbance events behave. Peters et al. argued that a level of detail such as this is necessary for meaningful comparisons of disturbances across events of different types (fires, floods) and in different ecosystems (forests, grasslands). Peters et al. (2011) used this model to generalize across a wide range of disturbances documented at the US Long-term Ecological Research (LTER) sites representing a variety of ecosystem types. As we shall see in Chap. 9, this model can also be applied readily to coupled natural and human systems in urban landscapes. This is another example of a model template that is generic in itself but that becomes real when implemented for a particular landscape. We will attempt to illustrate this in the next section.

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Fig. 3.6 A general conceptual model of disturbance, in which the event is disaggregated into specific mechanisms (e.g., abrasion, wind, inundation), impacts to the system (including legacies), and system response (recovery, succession, reorganization). The changes to the system might then influence the actions and impacts of subsequent disturbances. In the figure, boxes represent measurable attributes of the system and ovals are processes. (Redrawn from Peters et al. 2011; Grimm et al. 2017)

3.3.2

The Fire Regime in the Sierra Nevada

We return to the Sierran case study from previous chapters, but now with an aim of exploring the fire regime from the perspective of disturbance mechanisms, impacts on the system, and how the forest responds. In this, we also emphasize the interactions among fire, forest process, and the physical template. Anticipating the implications of changing climate for this fire-driven landscape was a central goal of the Sierran project (Stephenson and Parsons 1993). This required a basic understanding of how fire interacts with climate and forest processes as these are distributed over the landscape. Miller and Urban (1999a) extended the forest simulation model described in Chaps. 1 and 2, to embrace the interactions with fire explicitly. Their model of the climate-forest-fire system (Fig. 3.7) emphasizes climate as a direct constraint on fuel moisture as well as an indirect constraint of forest process to generate fuel load (the mass and density of burnable material including litter, woody debris, and live vegetation). The model, again, is implemented as a grid of tree-size plots, with the gridded stands distributed over the landscape as a stratified sample of slope facets (elevation, slope, aspect) and soil types. At the stand level, the model generates substantial

3.3

Disaggregating Disturbance Toward Generality

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Ignition

FIRE Crown scorch

INTENSITY

Fig. 3.7 Schematic of the climate-forest-fire model system for the Sierra Nevada of California. (Redrawn with permission from Elsevier, from Miller and Urban (1999a); permission conveyed through Copyright Clearance Center, Inc.)

spatial variability in fuel load, because litterfall depends on the sizes and species of trees on each plot. And, because the forest canopy influences the interception of precipitation, soil water drawdown via transpiration, and surface evaporation by radiation reaching the forest floor, there is also considerable fine-scale spatial variability in fuel moisture. As a result, there is also substantial variability in flammability and fire intensity. Flammability depends on fuel characteristics as well as moisture levels and is calculated using established models. Over the extent of the elevation gradient, the model generates realistic patterns in forest productivity (as basal area), litter depth, and fuel load. The trend in forest productivity is a direct reflection of growing conditions, as defined by the average temperature and soil moisture as these vary with elevation: maximum productivity is at middle elevations, while lower elevations are too dry and higher elevations are too cold to achieve high productivity. Fuel load, in turn, reflects productivity in that a certain percentage of live tissue is converted to litter each year. Litter depth depends partly on productivity and decomposition rates but it also depends on the bulk density or packing ratio of fine litter (leaves and needles), which varies among species. Firs, for example, generate comparatively dense litter because their small needles fall off the leaf rachis; lower-elevation pines drop longer and more loosely packed needles. Also at low elevations, annual grasses are a substantial part of the ground layer and these generate loosely packed litter. Thus, the density of litter increases dramatically from the lower-elevation pine zone into the higher mixed conifer zone characterized by firs (Miller and Urban 1999a).

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Fig. 3.8 Trends between elevation and fire as simulated for the Sequoia National Park. Left: fire recurrence interval and elevation. Open circles are simulated; solid symbols, data from the Park’s monitoring program. Right: the relationship between fire frequency and fire magnitude. In this panel, simulations (solid symbols) overestimate fire size because all burnable cells are burned if connected; field data (open circles) underestimate fire size because not all trees record a fire as a scar (Swetnam 1993). (Reproduced with permission of Elsevier, from Miller and Urban (1999a); permission conveyed through Copyright Clearance Cetner, Inc.)

In the model, fires are ignited randomly at some cell in the gridded stand. If that cell is burnable a fire starts, and the fire may spread to adjacent cells if they too are burnable (this is implemented as a cellular automaton, based on 8-neighbor cells). The connectivity of the fuelbed depends on fuel moisture. Under wet conditions, fuels on many grid cells are too wet to burn and so fire spread is retarded and fires tend to be smaller. By contrast, under dry conditions, most cells are burnable and the fuelbed is highly connected, so fires tend to spread and be larger. The model generates a trend of increasingly longer fire recurrence intervals with increasing elevation, with a dramatic increase above the mixed-conifer zone at roughly 2500 m (Fig. 3.8). Along this gradient, fire frequency is inversely related to fire magnitude, with more frequent fires tending to be smaller and larger fires less frequent. The biophysical and ecological reasons behind these trends provide a timely reminder of the complicated interactions among the physical template, forest process, and disturbance. The burnability of the fuelbed depends on fuel load and moisture. The interaction between fuel load, moisture, and connectivity plays out over the elevation gradient. At low elevations, fuels are generally dry but fuel loads are often quite low, and so fires are fuel-limited. Fires might occur but they tend to be small. In an anomalously wet year, high production of grasses under the pines generates higher fuel loads at the lower elevations. The following year, when these fuels dry, there are often larger fires on these sites. By contrast, fuels at high elevations are typically sufficient to support a fire, but they are not often dry enough to burn; and so, fire is moisture-limited at the higher elevations. In an anomalously dry year, these fuels dry sufficiently to burn, and large fires occur at higher elevations.

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This relationship among climate, forest process, and fire underscores the sensitivity of this fire system to climate and the tight coupling among these components. Summarizing the effects of climate variation: average climate drives average fuel load and moisture as these vary with elevation, and this in turn constrains average fire behavior. But fire behavior also depends on the inter-annual variability in climate and this, in turn, is different at lower as compared to high elevations: anomalous wet years are important at low elevations while anomalous dry years matter at high elevations. This same general pattern seems to play out in many landscapes across the southwestern United States (Swetnam and Betancourt 1990; Swetnam 1993). McKenzie (2019) has emphasized the distinction between flammability-limited and fuel-limited systems in the western mountains of the United States. From a management perspective, we can have some influence over fuel-limited systems but we have less control over flammability-limited systems where flammability depends on fuel moisture and the weather. It is perhaps frustrating (and also perhaps symptomatic of this topic!) that this presentation of the Sierran fire regime has not specifically addressed the general terms advocated by Peters et al. (Fig. 3.6). To this end, it will be helpful to reinterpret some of the foregoing discussion in these more general terms. For example, fire mortality stems from more than one mechanism. Some trees (especially small ones or those with thin bark) are killed outright by fire, via temperature effects on the growing tissue. Other trees suffer crown scorch and drop their lower branches; these trees, with less photosynthetically active tissues after the fire, might succumb in subsequent years due to loss of vigor. In real systems (but not in this model), fires also include effects mediated by falling trees and other idiosyncratic events. In terms of fire impacts on the system, a fire directly reduces fuels by consuming them, but also can generate some additional fuels in the short term via lagged mortality. The reduction in the forest-floor fuelbed, in particular, has a legacy effect on seedling establishment: some species require bare mineral soil to germinate. This, in turn, has a direct effect on post-fire recovery and succession. Residual trees, fuel loads, and fuel moisture (as influenced by changes in evapotranspiration affected by changes in leaf area profiles) have a direct effect on the likelihood of future fires in this system. This specific illustration has some very general implications. In applications concerned with the impacts of climate change on fire systems, it is crucial to go beyond correlations between fire regime statistics and elevation. We need to understand the physical template as an interaction between climate and landform, how biotic processes overlay onto this, and how disturbances interact with both the physical template and biotic processes. Miller and Urban (1999b) underscored this last point by using this model to explore how this system might respond to anthropogenic climatic change. They drove the model with climate-change scenarios provided by general circulation models. They found two modes of ecosystem response. Some responses were the direct effects of climate change on fuel moisture (e.g., from increased evaporative demand, decreased precipitation, or reduced snowpack from increased temperatures). But they also identified indirect impacts on the fire regime mediated by the forest process. For example, a slow change in species composition along the

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Climatic Change

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Fig. 3.9 Schematic of climate change impacts on the fire regime, as simulated for Sequoia National Park in the Sierra Nevada. Direct climate impacts (left arrow) are mediated largely through fuel moisture. Indirect effects (right arrow) are mediated through species effects on fuel characteristics, with species composition itself influenced by soil moisture but over longer time-scales than fuel moisture dynamics. (Redrawn with permission from Springer Nature, from Miller and Urban (1999b); permission conveyed through Copyright Clearance Center, Inc.)

elevation gradient also produced a slow change in fuel bulk density via changes in litterfall, and this change was reflected in fire behavior. Somewhat surprisingly, their simulations suggested that the indirect effects might be nearly as substantial as the direct effects of climate (Fig. 3.9). This is complicated, of course, because climate change might develop over decades while the changes mediated by forest process might play out over much longer time scales. The interactions between climate change and disturbance regimes will be challenging to forecast (Millar et al. 2007). We will return to this issue in Chap. 10. In this illustration, an important feature of the interactions among the physical template, plant processes, and disturbances is the emergence of characteristic temporal scaling (e.g., fire frequencies) and spatial scaling (e.g., fire sizes). This invites a consideration of the natural scaling of disturbance regimes.

3.4

Characteristic Dynamics

Turner et al. (1993) posed a general framework in which to explore the characteristic dynamics of disturbance-driven landscapes. One dimension is spatial, which they indexed in terms of the size of disturbance relative to the size of the reference

3.4

Characteristic Dynamics

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Disturbance Interval / Recovery Interval

landscape (e.g., study area, management unit, park). The second dimension is temporal, indexed in terms of the disturbance recurrence interval relative to the recovery time of the system (i.e., its succession rate). Any landscape can be plotted into this framework, an intuitive mapping of spatial and temporal scaling. Turner et al. (1993) used a simple simulation model to explore the temporal dynamics of ecosystems subject to disturbances of varying size and frequency. They summarized the natural variability of the system in terms of variance in biomass measured over time. (Similar approaches have been developed more specifically for forests: see Shugart and West 1981; Urban et al. 1987). Turner et al.’s (1993) simulations produce a contour plot that depicts the natural variability of ecosystems in terms of the scaling of its disturbance regime (Fig. 3.10). In the figure, the labeled domains A–F exhibit a trend of increasing natural variability. In domain A, disturbances are very small and infrequent, and the system would exhibit low variability over time—even appearing to be at equilibrium. Systems in domain C would show high but well-bounded variability, a “sawtooth” cycle of biomass loss and recovery (sometimes called quasi-equilibrium). In domain F, the variability is so high that the system would appear nonequilibrium or even chaotic over time. This framework is particularly useful for exploring alternative vantage points on the natural scaling of landscapes. For example, consider the same ecosystem but from differing perspectives of spatial extent. Thus, treefall gaps are highly disturbing at a small spatial scale (100 m2), locating this system in domain F (gap dynamics, indeed, are a classic example of high but bounded variability, Shugart 1984). By

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Fig. 3.10 Characteristic domains of the natural variability of landscapes, in terms of spatial and temporal scaling of disturbances. (Redrawn with permission from Springer Nature, from Turner et al. (1993); permission conveyed through Copyright Clearance Center, Inc.)

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Fig. 3.11 Rescaling of disturbance regimes. Left: scaling of rather frequent, low-intensity fires as compared to infrequent, high-intensity fires in Yellowstone. Right: rescaling of the fire regime in shrub-steppe ecosystems following the introduction of cheatgrass. (Redrawn with permission from Springer Nature, from Turner et al. (1993); permission conveyed through Copyright Clearance Center, Inc.)

contrast, a treefall gap at the scale of a large watershed or park is not disturbing at all, placing this system in domain A. This approach allows us to view Watt’s (1947), Sect. 2.2) hierarchical concept of gap dynamics in an explicitly scaled framework. Similarly, we might consider how changes in disturbance magnitude might affect system dynamics (Turner et al. 1993). The Yellowstone fire of 1988 was very large relative to the Greater Yellowstone Ecosystem area; and over a temporal window of a few decades centered on 1988, this system would appear chaotic. Over a similar temporal window but a few decades earlier, smaller fires recurred regularly but with a much less dramatic impact on the system, in part, because the climate was cooler and wetter; this would locate this system in the lower left corner of the figure. But fires such as that of 1988 have occurred regularly in the Yellowstone area over the past thousand years or more, recurring every 300 years or so (Romme 1982; see also Christensen et al. 1989; Romme and Despain 1989 for post-1988 perspectives). This regime and temporal window would place the system near domain E in this framework. Thus, the Yellowstone ecosystem experiences a mixed fire regime at different temporal scales (Fig. 3.11, left panel). Returning to the spatial domain, this exercise can be recast to ask questions such as, is Yellowstone National Park large enough to sustain a natural fire regime? The answer, it should be obvious, will depend on the spatial and temporal window through which the system is referenced. In this instance, the Park is large enough to contain the smaller fires that characterize the system, but the entire Greater Yellowstone Ecosystem (the Park plus the surrounding National Forests and other areas managed as a unit) is not large enough when fires like those of 1988 happen. Thus, this framework provides an intuitive depiction of the sort of dynamics one might expect of a system, from a particular spatial and temporal perspective. That is, what is the natural range of variability we might expect to observe? This is crucial to management, because while posing an expectation of normalcy, it also provides a

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yardstick by which we might measure deviations from natural variability (Landres et al. 1999; Parsons et al. 1999; Keane et al. 2009). A key to the adaptive management of ecosystems is knowing what to expect of the system (Christensen et al. 1996). A reciprocal perspective on this same spatial rescaling would be to use disturbance dynamics to posit an area that would be sufficient to stabilize those dynamics. This would be the exact equivalent of Watt’s unit pattern (Sect. 2.2), in this case representing the system and all of its successional stages at a steady state. This would be, as Watt implied, the minimum critical size of a Park representing that system (Pickett and Thompson 1978; Lovejoy and Oren 1981). Finally, using this framework, consider how human activities might rescale disturbance regimes. One example is the introduction of the invasive cheatgrass (Bromus), a diffuse sod-forming annual grass, to the sagebrush steppes of the Great Basin of the American West (Turner et al. 1993). Before cheatgrass, fires were infrequent and small, because the bare soil between shrubs prevented fire spread. But cheatgrass not only provided more fuel, it also provided a highly connected fuelbed; so now large fires burn frequently. This has rescaled the characteristic dynamics from domain A to F, dramatically changing the system (Fig. 3.11, right panel). We turn to other human impacts on disturbance regimes in the following section.

3.5

Humans and Disturbance Regimes

Few landscapes are untouched by humans, and so it is natural to consider how human activities affect disturbance regimes. This happens in two ways. First, human activities often rescale natural disturbances by modifying the magnitude or timing of disturbances. Second, humans have introduced novel disturbance agents to some landscapes. We will consider each of these in turn.

3.5.1

Human Impacts on Natural Disturbances

Humans modify natural disturbances in a variety of ways. We modify the spatial and temporal dynamics of disturbances, either directly or indirectly. As disturbances tend to generate substantial patchiness, the result of human interventions is to reduce this heterogeneity. A familiar example is fire suppression and its unintended consequences. In a sense, the goal of fire suppression is to deny the spatiotemporal variability generated by fire by preventing large fires. The consequence of this is higher build-up of fuels and eventual increases in fire magnitude and intensity when fires do burn (Covington and Moore 1994; Arno et al. 2000; Allen et al. 2002; Bekker and Taylor 2010). At the scale of individual fires, fire management tends to reduce the natural variability in fire intensity; prescribed fires tend to be smaller and cooler, and burn more uniformly than natural fires. This has implications for post-fire

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vegetation response and biodiversity (Miller and Urban 1999c). For example, Rocca (2009) showed experimentally that fine-scale variation in fire intensity had measurable impacts on ground-layer plant diversity. Koontz et al. (2020) used fire history data from the Sierra Nevada to show that fine-scale structural heterogeneity reduced fire severity by decreasing fuelbed connectivity; by inference, the homogenization of forest structure through fire suppression reduced forest resilience to fire. At very large scales, humans also modify spatial dynamics of fire systems. Over much of the western United States, the history of forest clearing and land use following European settlement has resulted in landscapes that are now more heavily forested and rather similar in terms of stand ages. This has apparently synchronized large regions of the west in terms of forest vulnerability to contagious disturbances (pests, fire). More generally, humans tend to homogenize forests structurally and simplify them in terms of biodiversity. In the upper midwest of the United States, human land uses have homogenized forests in terms of structure and composition (Schulte et al. 2007; Hanberry et al. 2012). In the case of species composition, this trend has often favored mixed mesophytic tree species at the expense of other (often fire-adapted) species; this trend is termed mesophication (Nowacki and Abrams 2008). In riverine systems, human interventions to regulate flow levels have dramatically modified the natural range of hydrologic variability (Poff et al. 1997; Vitousek et al. 1997; Poff 2002; Criss and Shock 2001), with implications for ecological responses (Poff and Zimmerman 2010). A goal was to reduce extremes (floods and droughts); and an unintended consequence in some cases has been larger floods instead. Disastrous floods that have recently occurred in the midwestern United States illustrate the consequences of building infrastructure to control 30-year floods when larger floods occur predictably over long time spans. Indeed, looking forward under climate change, historical flood frequencies would seem a poor guide to future flood management. In each of these cases, the result of human intervention is to rescale disturbance events in space and time, by altering disturbance magnitude and frequency. Humans also rescale disturbance regimes by artificially and arbitrarily bounding natural systems. For example, arbitrarily bounding a park and surrounding it with other land uses (development, agriculture) often renders the park too small to incorporate its disturbance regime and alters the characteristic dynamics of the system; Yellowstone, as discussed above, is a good illustration. Of course, in the longer term, humans influence many other disturbance regimes indirectly through our effect on the climate. This means that we might expect changes in wind storms, extreme and acute droughts, avalanches, and other climate-mediated events. We will return to this issue in Chap. 10.

3.5

Humans and Disturbance Regimes

3.5.2

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Novel Disturbance Regimes

Humans introduce novel disturbances through land use practices such as forestry and agriculture. In the case of forestry, the size of the harvest and rotation length (the time between harvests) provide a characteristic magnitude and frequency. In the case of agriculture, this happens only in swidden systems in which a patch of forest is cleared, farmed for a period, then abandoned. In most agricultural landscapes, the clearing is essentially permanent, although crop rotation might impose a sort of patch dynamics. Similarly, development creates a novel patch structure on a landscape, but as development is rarely abandoned or reversed, this does not really conform to our usual sense of an event with a post-disturbance recovery. (In fact, some land use change has been reversed over much of the eastern United States, following broadscale abandonment of agriculture and ensuing reforestation since the early to mid-1900s.) Humans have had a profound effect on natural landscapes by introducing non-native species, especially alien diseases, pests, and invasive plants. In the southeastern United States, these would include the chestnut blight, gypsy moth, woolly adelgids, emerald ash borer, . . . the list goes on and on, and every region has its list. These species reshape vegetation and sometimes landscapes by influencing biotic processes, altering disturbance regimes, and sometimes modifying the physical template (e.g., by modifying nutrient cycles). We will return to disturbances in human-dominated landscapes in Chap. 9.

3.5.3

Human Perception and Landscape Change

The characteristic spatiotemporal scaling of many disturbance regimes suggests that some landscapes might be in a sort of steady-state with respect to their disturbance regimes. This would be exactly equivalent to Watt’s unit pattern, but generalized to all disturbances and landscapes. While it is possible that such landscapes might actually exist, our perceptions of landscape dynamics are conditioned very much by our own life spans and how much change we can observe over that time scale. Sprugel (1991) provided an insightful essay on how our perceptions of the nature of landscape change are shaped by the timescales that shape our lives. He explored examples of “primeval” landscapes, those we tend to envision as ancient and unchanging. His examples included the iconic savannas of Africa, the “Big Woods” of the upper Midwest in the United States, lodgepole pine forests in the Rocky Mountain west, and old-growth forests of the Pacific Northwest. The real stories behind his examples are telling. Most of Africa’s iconic savannas came into being as a result of the introduction of the rinderpest at the beginning of the 1900s. The pest killed most of the native herbivores, which released the expansion of trees. There were other complications (especially with fire), but once the native herbivores developed a resistance they

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effectively reduced tree regeneration; the system returned to grassland but with a few scattered trees that are relics from a transient dynamic caused by an introduced pest. The Big Woods of the North American Midwest were apparently old-growth mesic forests when Europeans settled the region. Almost all have been cleared for agriculture or other land uses. But these ancient forests are underlain by prairie soils. Their establishment can be traced to the Little Ice Age (~300 years ago), when the region was substantially cooler and wetter. Released from agriculture, these sites do not regrow as mesic forests similar to the Big Woods; they regrow as very different forests appropriate to the current climate. The Big Woods were a fluke, a relic from a climate anomaly. When the Greater Yellowstone Ecosystem experienced the dramatic fire of 1988, there was considerable discussion of its “unnatural” magnitude. But Romme’s (1982) detailed reconstruction of the system’s fire history makes it clear that this system experiences fires like those of 1988 rather regularly, a cycle synchronized by the resonance of episodic droughts and the typical life span of the dominant tree species (and hence, fuel accumulation). That is, such fires occur repeatedly over long time scales, but we as observers have not been around long enough to have seen one before. Romme and Despain (1989) suggested that it might have been nearly 300 years since Yellowstone had as flammable a mix of forest stands as it had in 1988. Finally, Sprugel looked into the age structure of the ancient old-growth forests of the Pacific Northwest. Somewhat remarkably, very few stands exist that are much older than about 600 years. Fire history suggests that much of the region burned during widespread and intense fires of the Medieval Warm Period (~950–1250 AD). The dominant species in this system, Douglas-fir (Pseudotsuga menziesii), has a maximum life span that is much longer than the age of the forests that developed after those epic fires. That is, these ancient forests are still successional, in transition. Sprugel used these examples to make the point that every landscape is unique in space and time, as each landscape bears witness to its history (much of which is unobserved by us) (Fig. 3.12). While this perspective would seem to question the usefulness of the idea of characteristic scaling, it is quite consistent with Watt’s notion of the unit pattern and the usefulness of that construct . . . even if (as Watt noted) it was unlikely to be true of very many real landscapes. Instead, what we see in Sprugel’s examples is the long-term persistence of anomalies propagating through the system—just as Watt suggested.

3.6

Agents of Pattern: Reprise

Much of this discussion has focused on montane forest ecosystems. In part, this not only reflects the relative popularity of these systems as study systems, but it also reflects how appropriate these systems are for studying the interactions of climate with land-form and how biotic processes and disturbance regimes play out over elevation gradients. But the overlay of biotic processes and disturbance regimes onto

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Agents of Pattern: Reprise

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the physical template seems quite general as a conceptual model of landscape pattern. Three examples illustrate this generality. The physical template of grazing system of the Serengeti is relatively homogeneous compared to the steep gradients of montane landscapes, but there is substantial variability in the physical template over time (McNaughton 1985; McNaughton et al. 1988; Fryxell et al. 2005). Seasonal variability in precipitation governs productivity (sometimes described as a “green wave” across the landscape) and changes in the distribution and activity of large herbivores. Herbivores, in turn, amplify these patterns via the redistribution of nutrients. Disturbance, especially seasonal fires, responds in turn to the spatiotemporal pattern of fuel load and moisture. Similar patterns are observed of grazing systems throughout the world (Frank et al. 1998). Mangrove systems occur in coastal areas throughout the tropics (Luther and Greenberg 2009; Giri et al. 2011; Osland et al. 2017). A simple model of these systems emphasizes the tension between freshwater inputs from the mainland and saltwater from the sea; the resulting gradient in salinity (a biophysical gradient) and wave action (disturbance) sort mangrove species into zones reflecting species growth rates and tolerance to salinity and disturbance. As appealing (and apparently widely held) as that conceptual model might be, it has rather inconsistent empirical support across mangrove systems (Ellison et al. 2000). Part of that inconsistency might stem from site-specific variation in biophysical details and mangrove diversity (which can range from a single to several dozen species per locale), as well as region variation in climate controls (Osland et al. 2017). It might be useful to explore these systems with a common framing in terms of the agents of pattern. In particular, increasing land use pressures, including alterations of riverine flow, as well as changes in freshwater inputs and shoreline processes as affected by climate change, will require a robust

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working model for managing these systems to ensure the sustainable provision of their many ecosystem services. The conceptual model developed here for terrestrial landscapes might also prove useful for seascapes (and see Pitman 2018). Cape Hatteras National Seashore, off the North Carolina coast, is an exemplary illustration.2 The physical template of this system is the result of interactions between ocean currents and bathymetry near the coast (essentially the interaction between climate and landform, as on terrestrial landscapes). At Cape Hatteras, the Gulf Stream pushes northward as part of the South Atlantic Bight while the Slope Sea displaces the Gulf Stream offshore (eastward) as part of the Mid Atlantic Bight (Lohrenz et al. 2002). With this displacement, deeper nutrient-rich waters upwell toward the coast. This upwelling supports very high primary productivity (Signorini and McClain 2007), which in turn supports high levels of biodiversity at higher trophic levels including sea turtles, beaked and sperm whales, and seabirds. The role of the physical template in governing the concentration of biodiversity is important because of increasing human pressures on this coastal system: it lies just offshore from dense human populations and development pressure and is subject to commercial and recreational fishing pressure and high shipping traffic, while also being targeted for off-shore energy development. Having a robust model for how landscapes are patterned will be important as we take deliberate actions to adapt to and mitigate climate change. The links between climate and the physical template of landscapes are fairly obvious, but we also have to attend biotic responses to climate (Parmesan 2006; Chen et al. 2011) and climatemediated shifts in disturbance regimes (e.g., Seidl et al. 2017) as these affect ecosystem resilience (Johnstone et al. 2016; Hessburg et al. 2019). We will return to these issues in Chap. 10.

3.7

Summary and Conclusions

We have developed a conceptual model for the development of landscape pattern by overlaying biotic processes onto the physical template, and then adding disturbances on top of both. This sequential layering is intuitive, but it can mask the extent to which the three agents interact. The pair-wise and three-way interactions can generate patterns that are quite complicated. These three interacting agents provide a general framework for interpreting observed landscape pattern, and for anticipating landscape change. The characteristic scaling of a disturbance regime is defined by the magnitude and frequency of disturbance events. These patterns, in turn, interact with biological processes that have their own spatial (e.g., dispersal) and temporal (e.g., plant life spans) scaling. And these patterns interact with a physical template that is itself

2

I thank former students KC Bierlich and J Shearer for this example.

References

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patchy, typically at multiple scales. Clearly, it will be important to be able to decompose the characteristic scaling of a landscape into its component parts. For this, we will need a more rigorous definition of scale and scaling, tools for detecting scale(s), and methods for using scale tactically to work with landscapes. We turn to this in the next chapter.

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Chapter 4

Scale and Scaling

4.1

Introduction

Landscape ecology’s mantra might well be “It’s all a matter of scale.” It will have become obvious over the previous chapters that much of nature is characteristically scaled, from terrain to demographic processes to disturbance regimes. This is rather intuitive and an informal, intuitive treatment has sufficed thus far. But at this point, a more deliberate consideration is appropriate. In this chapter, we explore the notion of scale in a narrative way, with anecdotal illustrations. We then proceed to the statistics of scale, and methods for discovering the characteristic scaling of variables measured over landscapes. In particular, we revisit parts of the preceding chapters to examine the scaling of biophysical agents of pattern. The discussion ends with the fundamental lesson that all empirical models in landscape ecology are scale-dependent and offers some advice on how to use scaling tactically in landscape studies. Scale is a fuzzy concept and we will require some more explicit language. To begin, scale is defined by two complementary terms: grain and extent. Grain is the minimum spatial resolution of the data. For raster images, this refers to pixel or cell size; for polygons in a map, grain is the size of the minimum mapping unit. For field samples, grain is related to quadrat size (the area of the actual sample unit) but also is influenced by the minimum spacing between samples (see Sect. 4.3.1 below). Spatial extent refers to the scope of the data, and in most instances, this is defined simply by the bounds of the study area. Grain and extent are related in that studies over small extent often make finegrained measurements, while studies over larger extent tend to sacrifice details and use coarser-grained measurements. This purely logistical relationship leads us to use rather sloppy terms such as “large scale” to denote studies over large extent and with correspondingly coarse grain, as compared to “small-scale” studies with fine grain

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over small extent. Note that this is a generalization borne of logistics: nature has an infinitely fine grain and global extent—but we do not, cannot, and should not try to embrace this empirically. While our concern here is largely in the spatial domain, it is worth noting that most of the arguments applied to space apply similarly to the temporal domain. That is, natural phenomena that are fine-grained also tend to be “fast,” while events unfolding over very large spatial extent tend to do so slowly. The Delcourts and their colleagues (Delcourt et al. 1983; Delcourt and Delcourt 1988) provided a seminal illustration of the characteristic scaling of natural phenomena; their “space–time diagrams” inspired very many others (and see below). Scale is sometimes used in loose ways that do not, in fact, refer to scale at all. One instance is the use of “scale” to refer to levels of ecological organization: population, community, and ecosystem. These distinctions are not about scale. Levels of organization are defined by the phenomena of interest: interacting individuals of the same species define populations; interacting species define communities; and interactions between organisms and the physical environment, such as nutrient cycling, define ecosystems. Each of these might be explored at any scale, from the trophic interactions in a mud puddle to continental-scale patterns in species diversity. Similarly, one sometimes encounters references to “the landscape scale.” While studies of landscapes often are conducted over the extent of kilometers, landscapes are defined by characteristic spatial pattern, and pattern might be manifest across a wide range of spatial scales. For example, Wiens and Milne (1989) promoted the use of experimental “micro-landscapes” measured in square meters (with a focus on insects), while Burke et al. (1999), working in the same ecosystem, embraced the entire Central Plains of the United States as their landscape. “Landscape” is not a scale; it is a pattern.

4.2

The Importance of Scale in Ecology

In his MacArthur Award lecture, Levin (1992: 1943) argued that: the problem of pattern and scale is the central problem in ecology, unifying population biology and ecosystem science, and marrying basic and applied science.

This issue has been reviewed and discussed from a variety of angles, including various disciplinary perspectives (Marceau 1999; Schneider 2001; Haila 2002; Chave and Levin 2003). There is also a substantial literature on the practical problem of “scaling up” measurements or models from fine-scale measurements to largerscale implications (Wessman 1992; Ehleringer and Field 1993; Wu 1999; Urban 2005). Wiens (1989) provided an early overview of scale and its ecological implications, anticipating several issues that frame landscape ecology. In his delightful monograph in which Tansley coined the term “ecosystem” (emphasis added in the quote below), he also underscored the way we partition these into objects of study (Tansley 1935: 299–300):

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The Importance of Scale in Ecology

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These ecosystems, as we may call them, are of the most various kinds and sizes. They form one category of the multitudinous physical systems of the universe, which range from the universe as a whole down to the atom. The whole method of science, as H. Levy (‘32) has most convincingly pointed out, is to isolate systems mentally for the purposes of study, so that the series of isolates we make become the actual objects of our study, whether the isolate be a solar system, a planet, a climatic region, a plant or animal community, an individual organism, an organic molecule or an atom. Actually the systems we isolate mentally are not only included as parts of larger ones, but they also overlap, interlock and interact with one another. The isolation is partly artificial, but is the only possible way in which we can proceed.

In isolating a system for study, we necessarily scale it by choosing a spatiotemporal extent and grain for the system. How we do this has profound implications. For our purposes here, there is a single important lesson to learn about scale: Scale, as defined by the grain and extent of measurements, defines an observational window onto the world. This window admits some phenomena while censoring others. Natural phenomena tend to be characteristically scaled, and so knowing which scale(s) to target can be a powerful filter, as it allows us to tactically emphasize phenomena of interest while minimizing the distraction from patterns or processes at other scales. Conversely, failing to consider this characteristic scaling or using arbitrary empirical scales can obscure or confound inferences on natural patterns and processes. While there is a vast literature on scale and scaling, a few illustrations will serve to make the key points.

4.2.1

Observational Scale as a Filter on Nature

One way to appreciate the implications of scale in ecology is to explore how ecological questions might be addressed at a range of spatial scales. In the following examples, we illustrate that (1) which processes or patterns manifest as ecologically important varies with scale; and (2) what we measure and how we interpret those measurements also varies with scale. Three examples should suffice to illustrate these general points.

4.2.1.1

Bird Communities

Robert MacArthur’s brilliant career provides a lesson in scaling. (There is good reason that one of ecology’s highest awards is named after him!) Tree-Scale Patterns MacArthur (1958), in his seminal study of niche partitioning, documented the use of space by warblers foraging in individual trees. In this, his emphasis was on how species minimized competitive overlap by foraging in various regions of the tree: one species gleaned insects from bark, while another foraged among the leaves on distal branches, and so on (Fig. 4.1). The grain in this empirical

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6 % of Total % of Total Number (2611) Number (164) of Seconds of of Observations Observation

Fig. 4.1 MacArthur’s warblers: feeding activity for myrtle (left) and black-throated green (right) warblers in conifer canopies in New England, USA. Colored areas denote regions hosting at least 50% of the observations. (Reproduced with permission of John Wiley & Sons, from MacArthur (1958); permission conveyed through Copyright Clearance Center, Inc.)

study is essentially the resolution with which MacArthur distinguished foraging locations within the tree canopy. Thus, the grain is on the order of meters. The spatial extent of the observations, though gleaned over many trees and then aggregated, is the tree itself. The phenomenon of interest here is foraging behavior of individual birds: how they partition resources spatially. Stand-Scale Patterns One might also consider bird species communities and niche partitioning at a somewhat larger scale. MacArthur also provided this illustration (MacArthur and MacArthur 1961). In this classic study, he asked how bird species diversity is related to foliage height diversity (the vertical layering of the forest canopy). Here the grain is now much larger than a tree and embraces a forest stand with many trees contributing to the canopy layering. Strictly, the grain of the data is defined by the distance between the person holding the sighting board and the person recording the density of foliage at each height class: the distance over which these measures are integrated is the grain of the data. The spatial extent is somewhat ill-defined, as it is defined by a sample of forest stands in presumably similar habitat but the dimensions of the study area are not defined precisely (the field study included stands in Maine and Vermont). The relationship of interest is that bird species diversity (the variety of species inhabiting a forest stand) is linearly related to the variety of vertical layers in the forest canopy (Fig. 4.2). The ecology behind this is that some bird species are shrub-

4.2

The Importance of Scale in Ecology

Fig. 4.2 Relationship between bird species diversity (as Shannon function of bird species abundances) and foliage height diversity (as Shannon function of vegetation density in discrete height classes) at the scale of the forest stand. Solid dots are deciduous forests; circled point 1 is tropical savanna and point 2 is pure spruce forest. (Reproduced with permission of John Wiley & Sons, from MacArthur and MacArthur (1961); permission conveyed through Copyright Clearance Center, Inc.)

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1

0 1

2

FHD

nesters while others nest in the understory, sub-canopy, and so on. Likewise, various species forage at different heights (recall Fig. 4.1). Thus, a greater variety of strata provides nesting or foraging habitat for a greater variety of bird species. The ecology behind this, in turn, evokes the spatial heterogeneity in forest structure implied by Watt’s (1947) unit pattern: the mix of successional stages within the extent of the study area should be related to the dynamics of gap-phase regeneration (and probably other disturbances) at that spatial extent (Sect. 2.2 and Fig. 2.1). Essentially, MacArthur’s work at the stand level is the spatial integration of his work at the tree level. Landscape (and Seascape)-Scale Patterns Over a larger spatial extent, in a fragmented landscape, it would be natural to consider how bird species composition varies among forest patches. In this, we collapse the details of the previous examples into measures of bird species composition per stand (relative abundances), or simply tally the number of species present in each patch. This is the extension of island biogeographic theory (MacArthur and Wilson 1963) to terrestrial habitat islands—a logical extension that MacArthur and Wilson noted explicitly in their monographic (1967) treatment of the topic. In this, equilibrium species richness in a habitat patch depends on the balance between local extinctions (a function of area) and recolonizations (a function of isolation or proximity to a source area) (Fig. 4.3). The grain of this application is dictated by the geography of the habitat patches (islands) themselves. The extent of the study—the landscape—would require a range of values for habitat patch sizes as well as a range in geographic proximity, so that the relative importance of various explanatory factors might be estimated. Some of the earliest studies in landscape ecology were of this sort, motivated by the extension

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Scale and Scaling

I

ec ie sE

Rate

of Ne w

xti nc tio n

ti ra ig m Im

on

Sp ec ies

Sp

S

P

Number of Species Present, N Fig. 4.3 The area and isolation effects on rates of local extinction and recolonization, in the theory of island biogeography. The equilibrium species number S is at the intersection of the curves. On the vertical axis, I is the immigration rate of species (new or already present), which is the intercept when there are no species already on the island. On the horizontal axis, P is the number of species in the regional pool, so that when all species are already present the immigration rate must equal 0. (Reproduced with permission from Oxford University Press, from MacArthur and Wilson 1963)

of island-biogeographic theory to terrestrial habitat islands (e.g., Burgess and Sharpe 1981; Lynch and Whigham 1984). This analysis is more complicated than we might expect (Fahrig 2003), and we will return to this in Chap. 5. For now, it is sufficient to note that at this larger scale, new phenomena—the area and isolation effects—have emerged as interesting foci while at the same time, this new level of discourse integrates the stand-level patterns of diversity documented previously (MacArthur noted that the habitat heterogeneity of an island could be a substantial component of the area effect). We could continue to increase the spatial extent of these examples, and we would next encounter MacArthur’s (1972) treatment of geographical ecology. In this, he related patterns of species diversity to large-scale patterns in climate and energy as well as considering diversity patterns as these vary in island versus mainland systems, in temperate as compared to tropical systems, and so on. There are two important points to be garnered from these examples. First: What is most interesting about a general phenomenon depends strictly on the scale of reference. Thus, in studies of bird communities over increasing spatial extent, we encounter foraging behavior in response to tree architecture, habitat selection in response to microhabitat pattern, and the effects of habitat fragmentation, respectively. We can choose to explore (or ignore) particular phenomena by using this natural filtering.

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91

Second: Phenomena at one scale integrate the details of phenomena occurring at smaller scales, while experiencing things at much larger scale(s) as a constant background or boundary conditions (O’Neill et al. 1986; Urban et al. 1987). In this example, bird species response to stand structure is the integration of finer-scale patterns of foraging and nesting behavior, the area effect of island biogeography subsumes this stand-level effect of microhabitat heterogeneity, and so on. And bird species response to foliage height diversity in a set of stands depends on larger biogeographic constraints—and these are needed as context to explain the standlevel phenomenon.

4.2.1.2

Semi-Arid Ecosystems

Ingrid Burke, Bill Lauenroth, and their colleagues working in the Central Plains of the United States provide a nice illustration of how explanatory models change with scale. They studied these systems at spatial scales ranging from centimeters to the subcontinental. Plant-Scale Pattern At a very small scale, biogeochemistry is related to differences between sites occupied by plants (mostly blue grama, Bouteloua gracilis) and bare spaces between plants. At this scale, erosion by wind and water leads to accumulation of water, soil, and nutrients beneath plants and loss of these from the interstitial spaces. Over time, this generates a positive feedback that amplifies the local resource islands with even larger local differences in productivity, plant cover and fine roots, and nutrient cycling (Burke et al. 1999). Under plants, the higher productivity of above- and belowground tissues leads to even more soil organic matter, waterholding capacity, and productivity while interstitial spaces lose these local inputs. Landscape-Scale Topography At the landscape scale defined by terrain, catenary processes (Sect. 1.4.4, Fig. 1.6) generate a hillslope gradient in soil texture (sandier on upper slopes, more clay on lower slopes). At this scale, soil texture and hillslope position explain most of the variation in soil carbon and nitrogen (Burke et al. 1999; Hook and Burke 2000). The micro- and mesoscale patterns are related in that plant cover varies directly with soil texture: sandier soils have less plant cover and so are more subject to plant–interplant differences, while lower slopes support denser vegetation. These spatial patterns are echoed in temporal dynamics. Carbon and nitrogen pools with longer turnover times (decades to centuries) are associated with hillslope position, while more labile pools with shorter turnover times (within-year to annual) are best explained by micro-site variability. The Central Plains At the regional scale of the Central Plains, variations in temperature and precipitation vary in almost orthogonal directions because of the latitudinal decrease in temperature and the longitudinal pattern in precipitation due to the rain shadow of the Rocky Mountains. At this scale, annual precipitation is the best predictor of primary productivity and soil organic carbon (Epstein et al. 2002). Soil texture (as percent clay) has an influence at this scale but this influence is small

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relative to the effect of precipitation. Controlling for precipitation (by reanalyzing the data within discrete ranges of precipitation), the soil textural effect emerges more clearly—reinforcing the results at the landscape scale. This example nicely illustrates the way that explanatory power shifts with scale, with finer-scale patterns and processes integrated into and subsumed by larger-scale constraints. We return to the biogeochemistry of this example in Chap. 8.

4.2.1.3

Modeling Evapotranspiration

One more example serves to make the lessons from these examples somewhat more precise empirically, by focusing on numerical models used to estimate potential or actual evapotranspiration. Evapotranspiration is affected by a host of factors acting over a variety of spatial and temporal scales (Ehleringer and Field 1993). For any particular modeling application, the task is to decide which factors need to be included in the model. In models, scaling is dictated by decisions about the entities to be modeled and the time-step and duration of the simulation. In the case of evapotranspiration, the typical approach is to consider potential evapotranspiration (the maximum, given temperature, radiation, and ample water), and then add terms to adjust this to actual evapotranspiration (and recall Sect. 1.3.1 on the water balance). A “Big Leaf” Model At the scale of a plant (or a canopy modeled as a “big leaf”), actual evapotranspiration (AET) is governed by an energy balance and aerodynamic resistances to vapor flux. A common approach to modeling this is the Penman– Monteith equation (Monteith 1965; Campbell and Norman 1998): λE canopy =

s Rabs - εs σT 4a - G þ γ0 λgv D=pa s þ γ0

ð4:1Þ

where E is the vapor flux (mol m-2 s-1), Rabs is the absorbed short- and long-wave radiation (W/m2), T is the temperature (°C), G is the heat flux density of the soil (W/m2), D is the vapor pressure deficit (kPa), and gv is the vapor conductance of the leaf. Other terms are scaling or thermodynamic coefficients: λ is the latent heat of vaporization, εs is surface emissivity, σ is the Stefan–Boltzmann constant, γ’ is a psychrometric constant adjusted for heat and vapor conductances (typically written γ*), and s is the slope of the saturation vapor pressure function (Δ) divided by atmospheric pressure pa. The model typically is driven by daily data on radiation, temperature, wind, and vapor pressure; model projections are typically on the order of days to weeks. A Terrain-Sensitive Model At the larger spatial extent of the landscape, and over monthly time-scales, we might adopt a different model of the water balance such as the one featured in the Sierran example (Sect. 1.4.1). At this scale, the emphasis is on factors driving evaporative demand over heterogeneous terrain, and thus the model

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93

explicitly addresses the influence of terrain on temperature and radiation. The model of potential evapotranspiration is the Priestley–Taylor approximation (Priestley and Taylor 1972):

E=a

Δ ðRn - GÞ Δþγ

ð4:2Þ

where a is an empirical correction term and other terms are as defined above. (Slightly different terms denoting radiation in Eqs. 4.1, 4.2, and 4.3 are not crucial to our discussion here.) Over the time scale of several days to a month, it is reasonable to assume that soil heat flux is essentially 0 (i.e., the air and soil are the same temperature), and that net radiant flux is proportional to air temperature. In this case, the model simplifies further (Campbell and Norman 1998): E p = aðT þ bÞRs

ð4:3Þ

where the coefficients a and b are empirical, site-specific correction terms that account for the effects of vapor pressure (which, in turn, depends on temperature). In this, the main drivers of PET are monthly temperatures and radiation. In applications at the landscape scale, the radiation estimate must be adjusted for topographic position (Bonan 1989; Nikolov and Zeller 1992; Urban et al. 2000). Actual evapotranspiration (AET) is estimated by adjusting PET for water availability (via inputs from rain or snowmelt, or storage in the soil) in an iterative approximation of a process that happens continuously in reality. Two issues are notable in comparing the Penman–Monteith model to the modified Priestley–Taylor approximation: (1) many variables that are important at finer scale are omitted, and (2) some new drivers emerge as important. The omitted variables are not unimportant; they have been averaged away or subsumed into calibration constants. Thus, the difference between soil, leaf, and air temperatures are negligible at monthly time scales; wind speed can be averaged; and so on. Conversely, variation in temperature and radiation as influenced by topography cannot be ignored. Reciprocally, topography was ignored (treated as a constant) in the finer-scale Penman–Montieth model because a plant (much less a leaf) does not witness any appreciable variability in topography. Regional Scale At a still larger spatial extent, at subcontinental scales, one might model the water balance by using the Thornthwaite approximation of monthly PET (Thornthwaite 1948; Thornthwaite and Mather 1955, 1957): PE = 1:6

10T I

a

ð4:4Þ

In this, PET depends only on mean monthly temperature, with a monthly “correction term” a that accounts for details such as latitudinal variation in radiation load due to varying daylength, and I, which relates evaporative demand to monthly temperature.

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This approach estimates PET, not AET, and Thornthwaite and Mather (1957) suggested empirical corrections to soil-water draw-down in terms of the waterholding capacity of the soil and accumulated monthly draw-down. Many others have suggested extensions to adjust PET toward AET; for example, Pastor and Post (1984) estimated a water–retention curve as an exponentially decreasing function of accumulated water deficit. The message in this illustration of alternative models is that the choice of spatial extent and time-scale forces the declaration of what variables are included in the model and whether those factors are tracked as variables or treated as constants. This decision amounts to a declaration of what is considered important for the application and thus scales the model explicitly in space and time.

4.2.1.4

Scale and Model Specification

These illustrations make the general point that what is interesting about a system, and which variables explain how it works, vary with scale. Modelers often (and should!) use this scaling to help define a system in a model for a given application. The spatial and temporal scale of the application helps dictate what processes and constraints are to be included in the model, and in what form (Carpenter and Turner 2000). One way to parse this decision is to consider that a conceptual term might be included in a variety of ways. It might be a single value, a constant: at the scale of seasonal plant processes, terrain is a constant and a plant “sees” a single value of elevation. Over time-scales of centuries, terrain itself can change and so it becomes a variable. Soil characteristics such as texture, organic matter, nitrogen levels, and so on vary substantially over very small distances; they are variables at small scales. But to a large tree, much of this variability is integrated over the rooting zone of the tree and its lifespan: the soil variables are averaged away to a constant at the scale of the tree. Similarly, although many factors influence potential or actual evapotranspiration across a wide range of scales, at large (and seasonal) scales, many of these can be ignored, or accounted for in a synthetic factor estimated as a model coefficient, an average or steady-state value, or a fitted constant. This process of deciding what is left out of a model, what is included, and whether the factors are included as constants or variables is the crucial task of model specification. While the example of modeling evapotranspiration might seem a bit technical or arcane, it is important to underscore that all applications—whether research or management—rely on an underlying model, whether conceptual or implemented as computer code. And model specification is all about scale.

4.2

The Importance of Scale in Ecology

4.2.2

95

Characteristic Scaling

Tansley’s comments on the continuum of scales at which ecosystems can be viewed, and the examples illustrated in the previous section, suggest that we can observe systems at any scale we might choose, however arbitrarily. But ecologists have long recognized that nature is characteristically scaled: ecological events or processes tend to occur over a particular domain of spatial extent and recurrence interval or time scale. Borrowing from other disciplines (especially marine sciences), ecologists sometimes use modified Stommel diagrams (Vance and Doel 2010) to depict their systems in space and time. Delcourt et al. (1983) were among the early adopters of this construct, illustrating vegetation dynamics in a space–time scaling diagram. The diagrams emphasize the localization of phenomena within this space–time framework, and also the tendency that phenomena that occur over small extent tend to also be relatively fast or frequent, while phenomena that manifest at large extent tend to be slower. From this, one might select a scale (in space and time) with which to capture a phenomenon of interest—from microsite-scale seedling establishment, through succession, to global patterns in biomes as driven by plate tectonics and long-term climate dynamics. Others have found these diagrams to be a useful conceptual space for discussions of landscape processes (Shugart and West 1981; Urban et al. 1987; Turner et al. 1993; recall Fig. 3.10 in Sect. 3.4) (Fig. 4.4). Here, the disturbance panel of Fig. 4.4 (lower left panel) is aligned at a time scale that corresponds to the life-span of trees. In a subjective sense, a disturbance to a forest is an event that kills trees prematurely; events that are far slower than that are not really disturbing to the system. To be more precise, in Fig. 4.4, each ellipse might be aligned on more of a diagonal: for example, within the “fire” scale domain, there are regimes with smaller and more frequent fires and with larger, less frequent events. This intuition about scaling implies that we can “slice” space and time scales arbitrarily to focus on particular phenomena of interest. Indeed, Tansley (1935) had the foresight to note that we could not proceed any other way, empirically. But the details of how we do this matter significantly, as we explore in the following illustration.

4.2.3

Sampling Grain and Extent, and Statistical Behavior

The illustrations above emphasize conceptual issues in scaling, or approaches somewhat removed from field measurements. Now it will be instructive to consider scaling issues explicitly in terms of the grain and extent of field measurements and sampling design. A somewhat hypothetical example provides this illustration. In the Ridge and Valley province of eastern Tennessee (southeastern United States), a series of weathered over-thrust faults has resulted in terrain that consists

Temporal Scale (log yr)

96

4 9 8 7 6 5 4 3 2 1 0

9 8 7 6 5 4 3 2 1 0

Glacial Cycles

Pedogenesis, Climate Flux Topography

MicroEnvirons

0

9 8 7 6 5 4 3 2 1 0

2

4

6

Fires

Windthrow Treefalls

0

2

4

8

10

12

Floods

Pathogens

6

8

10

12

Species Extinction Species Migration Secondary Tree Succession Replacement Inseeding

0

9 8 7 6 5 4 3 2 1 0

Scale and Scaling

2

4

6

8

10

12

Biomes

Cover Types

Provinces

Stands, Seral Stages Gaps Ground Cover

0

2

4

6

8

10

12

Spatial Scale (log m2) Fig. 4.4 Characteristic scaling of the physical template, biotic responses, disturbance regimes, and resultant vegetation patterns. Panels refer to the physical template, biotic processes, disturbances, and resulting vegetation patch types. (Redrawn with permission from Oxford University Press, from Urban et al. 1987)

essentially of a sinusoidal pattern across the landscape. This pattern, with ridges oriented along a southwest to northeast axis, is repeated over many kilometers until this province merges into the Cumberland Plateau. Forest vegetation responds to this topographic pattern, following a hillslope catena model (recall Fig. 1.6), so that the drier ridges support drought-tolerant pines (Pinus echinata) and xeric oaks (Quercus velutina, Q. coccinea); the sideslopes support a mix of oaks (e.g., Q. alba, Q. prinus) and hickories (Carya spp.), and the lower slopes are often characterized by red maples (Acer rubrum var. drummundii). This gradient is expressed over relatively short distances, on the order of a hundred meters or so from bottom to ridge. Consider what we might observe from data sets collected from sample quadrats distributed over this landscape. The quadrats will be of varying size, from nearly tree-sized (~ 100 m2) to two orders of magnitude larger. In each quadrat, we will tally trees by size and species, and we will summarize the relative abundance of each species in terms of total basal area per species, per quadrat. (Basal area, in m2/ha, is the cross-sectional area of tree stems and is commonly used as an index of ecological species importance with forest data.) The sample quadrats will be distributed

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The Importance of Scale in Ecology

97

shortleaf pine oaks, hickories red maple

Fig. 4.5 Hillslope gradient in forests in the Ridge and Valley province of eastern Tennessee, USA. Upper slopes are characterized by pines; midslopes, by oaks and hickories; and lower slopes by red maple. The task here is to anticipate the correlations between species resulting from various sampling schemes (indicated by the rectangle, a sample quadrat)

randomly over the landscape. In some cases, we will focus on forested sites only, while in other cases, we will include other nonforest land cover types. The focus of this hypothetical sampling exercise is to anticipate the nature of the correlation between species abundances, say, between oak and pine. In particular, we will want to consider the correlation as a function of sampling grain (quadrat size) and extent (sampling frame) (Fig. 4.5). Small Quadrats, All Forest To begin, consider sampling the forests with quadrats of a conventional size for this type of study, with this convention codified based on decades of practical experience. The quadrats might be roughly 0.01–0.1 ha. At this grain, a single quadrat might contain only a very few large trees. Thus, a midslope sample might include oak, a ridge-top sample would capture pines, and a low-slope sample would have maples. Pines, oaks, and maples would rarely co-occur. From this, we would expect to see a negative correlation between oak and pine and also between oak and maple, and a stronger negative correlation between maple and pine because these would almost never co-occur. Changing Quadrat Size One could arbitrarily decrease the size of the quadrats, so that a quadrat could not physically contain more than one large tree. Doing so would increase the magnitude of the negative correlation, because of the decreased likelihood that a quadrat might include two dissimilar species by chance. (The data would also be much noisier.) Similarly, we might increase the size of the quadrats, with the result that a quadrat would include more trees and, consequently, increase the likelihood that different species might co-occur on the same quadrat. The species would still be negatively correlated, but the co-occurrences would degrade the correlation (it would be less negative). In particular, the correlations between species adjacent along the topographic gradient (maple-oak, oak-pine) might degrade toward statistical nonsignificance.

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Changing Extent: Other Land Covers Of course, the ridges and valleys of east Tennessee have not escaped human impacts. Flat ridge tops have been cleared for agriculture or developed, and valley bottoms host streams, along with roads and other land uses. Thus, remnant forests are concentrated on the side-slopes, which are too steep for other land uses. A natural inclination for a forest ecologist would be to sample only the forested sites, using an appropriate quadrat size (say, 0.04 ha). Given these samples, the correlations between oak and pine or oak and maple might still be negative, but these would likely be degraded by loss of data from low slopes or ridges to drive these correlations. Possibly, maple and pine would be uncorrelated, not because they co-occur but because the sampling frame would not provide adequate sample sizes to estimate the correlations reliably. Finally, we might adopt a more egalitarian view and sample across the entire landscape, including nonforest cover types. In this, some samples would fall in developed land uses and we would record lawn grasses and other plant species; in the valleys, we might record riparian plant species or road-side weeds. For those samples falling in forests, we might expect to capture oaks as well as either pine or maple (depending on topographic position). Because of the strong dissimilarity between forested and nonforested sites, the correlation between any pair of tree species would be positive because the only places they occur are in forested sites. This would be especially true if we increased the quadrat size, as this would increase the likelihood that a single quadrat would include trees of more than one species. This illustration is hypothetical but offers a key insight into the statistical implications of scaling. In short, sampling grain (quadrat size) and extent (sampling frame) affect the magnitude and even the sign of correlations among variables. Because all inferential statistics, whether based on analysis of variance or regression, depend ultimately on the correlation structure in the data set, sampling decisions about scale directly influence the inferences we might draw from the data. That is, decisions about the scaling of data define the empirical context in which we make statistical inferences. All empirical models are scale-dependent.

4.3

Scaling Techniques

We expect natural phenomena to be characteristically scaled, and we have observed, in an intuitive way, that choosing a particular grain and extent for measurements will have consequences on what we can observe from the data. And so, we will need to be able to determine the natural scaling of ecological patterns and processes. This amounts to detecting and quantifying the scale(s) of variability in measurements collected on these patterns. We turn now to this fundamental task. The statistics of scaling are complicated somewhat by the reality that spatial data come in various forms. There are three classes of spatial data:

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Scaling Techniques

99

1. Geostatistical data are measurements at locations separated by some distance. Measures of species abundances on a collection of sample quadrats distributed randomly or stratified over a study area (as in the preceding illustration) is a familiar example. 2. Spatial point patterns are data sets comprising the locations of events of interest. In plant ecology, a common example is a mapped stand in which each plant is identified. Labeling the points, for example by species or size, constitutes a marked point pattern. 3. Lattices are data sets in which locations are regions that have neighbors or edges. Familiar examples include raster lattices (i.e., grids), in which each cell is defined to have four or eight (if the diagonals are included) neighbors. Vector lattices are maps of polygons, each of which shares edges with its topological neighbors. Graphs are lattices in which locations of interest are denoted with points (nodes) and neighbor relations are designated by links (also called edges or arcs) drawn between pairs of nodes that are considered functionally connected or adjacent. What “pattern” means, in general, is a deviation from randomness (“random” is also a pattern—but often not a very interesting one). What pattern means varies for each class of spatial data. For geostatistical samples, we are typically interested in the degree to which samples that are close together are also similar on a measured variable. For spatial point patterns, we will want to know whether the points tend to be clumped (aggregated) or more uniformly spaced (over-dispersed). For lattices, pattern refers to the similarity between adjacent neighbors, or the degree to which locations of a given type tend to be next to similar or dissimilar types. Pattern is characterized in terms of several attributes. First, it has a direction in its deviation from randomness. For example, clumped and over-dispersed are patterns in opposite directions for point patterns. Pattern also has intensity: the degree of the departure from randomness. An orchard of perfectly uniformly spaced trees is not merely over-dispersed, it is intensely so. Importantly, pattern also has scale. If measurements of a given variable tend to be patchy or clumped in nature, those patches have a characteristic size or scale. In landscape ecology, the aim in analyzing pattern is to quantify the direction, intensity, and especially the scale of pattern. How this scaling plays out statistically depends on the class of spatial data. Here, we will focus on scaling techniques used with geostatistical data and ask how sample measurements vary according to (or depend on) the distance between samples. Geostatistical data are probably the most typical in landscape ecology. The insights developed here can be generalized to other types of data.

4.3.1

Scaling Techniques for Geostatistical Data

Common forms of geostatistical data include various types of sample quadrats distributed over a study area, often according to a randomized or some sort of stratified design (the details do not matter here). Naturally, some pairs of sample

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quadrats are closer to each other, while others are farther apart. It is intuitive to ask how the measurements collected on two different quadrats depend on the distance separating these sample locations. In this, we might summarize the pairwise measurements in terms of how similar they are, or equivalently, how different (dissimilar) they are. These two perspectives have been developed in parallel in spatial statistics and geostatistics, respectively. We will attend each approach in turn, and then compare the two approaches.

4.3.1.1

Correlation and Autocorrelation

In spatial statistics, the analytic approach is to ask how the similarity of pairs of sample measurements depends systematically on the separation distance between samples. We might develop this relationship intuitively by virtually sampling—as a thought experiment—a topographically heterogeneous landscape and considering what we might “sample” as measurements of a topographic soil moisture index (Fig. 4.6). To begin, consider pairs of sample locations that are arbitrarily very close together: measurements will be essentially the same for any two points that are adjacent (i.e., the same color in Fig. 4.6). This sample similarity will hold no matter whether the two adjacent samples are in wet or dry sites or both somewhere in between. Next, consider what might be observed for two samples slightly farther apart: they will have similar but not identical measurements. Then, continue to extend the separation distance. At some distance, the two samples will be far enough apart that one might lie, for example, on a ridge while the other location falls on a midslope or nearby cove. At this distance, the sample measurements might not be very similar at all. At still farther separation distances, it might be that if one point falls on a ridge, the other is likely to be in a cove, and vice versa. At these distances, the sample measurements might be quite dissimilar as a function of separation distance.

Fig. 4.6 Topographic relative moisture index (Parker 1982) for a small watershed in the Southern Appalachians in western North Carolina, USA. Blue-violet colors are wetter; red, drier

4.3

Scaling Techniques

101

Collecting all the pairwise measurements, we could construct a graph that depicts the average similarity of measurements in relation to distance between samples. This graph summarizes spatial autocorrelation in the measurements. The task now is to quantify this. Variance, Covariance, and Correlation. We can develop a more formal index of autocorrelation from the more familiar expressions of variance, covariance, and correlation. Recall that the mean for a variable x is estimated: x=

1 n

n

xi

ð4:5Þ

i=1

for samples i, where the summation is over the n samples. The sample variance is estimated: s2x =

1 ð n - 1Þ

n

ð xi - xÞ 2

ð4:6Þ

i=1

wherein the (n–1) correction accounts for our computing the mean from the data. Taking the square root of this variance yields the standard deviation, sx. For two variables, x and y, measured at the same sample locations, we can estimate the covariance by substituting the second variable into Eq. (4.6): s2xy =

1 ð n - 1Þ

n

ðxi - xÞðyi - yÞ:

ð4:7Þ

i=1

Note, here, that variance (Eq. 4.6) is actually a special case of covariance (Eq. 4.7), wherein x and y are the same variable. If we divide this formula by the pooled variance sxsy we standardize the covariance into a correlation coefficient: r xy =

s2xy sx sy

ð4:8Þ

Because of the way deviations from the mean are tallied in Eq. 4.7, the index provides positive or negative correlations: if the two measures are both high or both low relative to the mean, the correlation is positive; if one is high and the other low (or vice versa), the correlation is negative. Again, note that in the special case where x and y are the same variable, we find (reassuringly) that a variable is perfectly correlated with itself (r = 1). Auto-covariance and autocorrelation. Consider, now, how we might modify the estimate of covariance at the same sample locations to instead estimate how a variable x covaries with itself but as measured at different locations. To do this, we can substitute locations as if they were a second variable in Eq. 4.7:

102

4

ax =

1 ð n 2 - nÞ

n

n

i=1 j=1

ðxi - xÞ xj - x s2x

Scale and Scaling

ð4:9Þ

where the indices i and j denote samples at different locations. Note that we now need two summations, as we are comparing every sample location to every other sample location, and the sample size correction inflates accordingly (equivalent to n(n–1) and thus ignoring comparisons of a sample to itself). Here, a is a very crude index of auto-correlation in x—and not a very interesting one because the index is averaged over all locations, no matter how far apart. A more interesting and useful estimate is localized over a range of distance classes d and takes the form: wij zi zj

n I ðd Þ =

i

j

W i

z2i

ð4:10Þ

which is the estimator for Moran’s I (Moran 1950; Legendre and Fortin 1989). Here, the measurements are denoted as z scores (deviation from the mean, divided by the standard deviation) to rescale the measurements for ease of interpretation. The w term is an indicator variable that takes on a value of 1 if two samples are within some specified range of distances apart (i.e., in that distance class), else it takes on a value of 0. For example, we might use 100-m distance classes, in which case in the first instance of Eq. 4.10 would consider only pairs of samples between 0 and 99 m apart (w = 1) and skip all other sample pairs (w = 0); the next instance would capture sample pairs 100–199 m apart, and so on. Through this indexing, the formula provides an estimate of autocorrelation for each distance class d. The term W is the sum of the indicator weights (number of sample pairs) in each distance class, which along with the overall sample size n rescales the index to vary on the range [-1,1], just as the familiar Pearson correlation coefficient (Eq. 4.8). This formula is equivalent to Eq. (4.9), but subset into discrete distance classes. As with more familiar correlation coefficients, very strong positive autocorrelation would approach 1.0, while strong negative autocorrelation would approach -1.0. The expected value of Moran’s I approaches 0.0 for large sample sizes (again, as with familiar correlation coefficients). A plot of Moran’s I versus separation distance (i.e., for each discrete distance class d ) yields a correlogram (Fig. 4.7) that summarizes direction (positive or negative), the intensity of the pattern (absolute magnitude of autocorrelation), and the scale(s) (i.e., distance classes) at which this pattern is expressed. In this case, the correlogram indicates positive autocorrelation over distances up to roughly 250 m, with some additional (weaker) structure at longer distances (400–600); this reflects the characteristic scaling of topography (hillslopes) in this watershed (as evidenced by the coloring in Fig. 4.6).

4.3

Scaling Techniques

103

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Moran’s I

0.5

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500

1000

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Fig. 4.7 Correlogram for measurements of a topographic relative moisture index extracted from the digital image in Fig. 4.6, estimated as Moran’s I. The dotted lines are 95% confidence levels around the expected value of 0.0 (estimated by randomization of the data)

Correlograms for ecological variables typically show positive autocorrelation, meaning that samples that are close together tend to take on similar values. Negative autocorrelation, in which nearby samples have dissimilar values, is rare in natural systems. Typically, the intensity of autocorrelation decreases with increasing distance until the index does not differ statistically from 0.0 (no autocorrelation). This test of significance can be approximated based on a large-sample normalization, or (more typically) the confidence limits around 0.0 can be estimated via a randomization procedure (as was done for Fig. 4.7). Legendre and Fortin (1989) have provided useful heuristic examples of correlograms for a variety of distinctive patterns. As a scaling technique, autocorrelation identifies pattern as distance classes within which samples tend to be similar, which indicates internally homogeneous patches at that scale. If the patches tend to be regularly spaced, the correlogram would indicate negative autocorrelation at scales corresponding to the distances between patches.

4.3.1.2

Semivariance Analysis

Somewhat independently of spatial statistics, the field of geostatistics (mostly at home in engineering and earth sciences) developed an approach to index scaling in terms of the dissimilarity of measurements as a function of separation distance (Journel and Huijbregts 1978; Isaaks and Srivastava 1989). Translating from the

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1.0

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Fig. 4.8 Semivariogram corresponding to the topographic moisture index in Fig. 4.6 and the correlogram in Fig. 4.7

somewhat different notation of geostatistics into a format consistent with autocorrelation above, semivariance, gamma, is estimated: γðdÞ =

1 2W

wij xi - xj i

2

ð4:11Þ

j

where the indicator variable w acts as in Moran’s I (Eq. 4.10) to subset sample pairs by distance class and W is the number of sample pairs in distance class d. Note that the sum of squared distances makes this a variance term (compare to Eq. 4.6). In the limit, if there is no spatial dependence, this index converges on a value of twice the simple variance in x. Dividing by 2 rescales the index so that it converges on simple variance as autocorrelation decreases to 0 (i.e., at distances where samples are independent). A semivariogram (or simply, variogram) plots dissimilarity as a function of separation distance (Fig. 4.8). A variogram is described in terms of three attributes. The curve tends to asymptote to a plateau value, which is its sill (units: semivariance). The distance at which this occurs is the range of the variogram, which here is the item of interest because it denotes the scale of patchiness. In this example, the variogram reaches its sill at a range of a few hundred meters, as in the correlogram estimated from the same data (Fig. 4.7). The Y-intercept of the curve is its nugget variance. In a perfect world, the nugget would be 0, indicating that samples measured in the same location would have identical values. For most ecological measurements, this is not the case and so the nugget suggests the natural replicate variability of the measurement. But the nugget

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Scaling Techniques

105

can also include additional information. In particular, because the variogram plots average semivariance within a distance class against the average separation distance for pairs of samples within that class, the nugget probably does not actually intercept the Y-axis but instead occurs at some distance from 0 (i.e., the average minimum distance between samples). For example, in Fig. 4.8 this distance is roughly 50 m. This means that we have no information about variability in topographic moisture at a grain finer than this distance. This contributes to the effective grain of the data set, because the spacing of samples influences the minimum spatial resolution. (This is also true of correlograms: one might note that the correlogram does not intersect the Y axis.) Meisel and Turner (1998) used semivariance analysis to explore the spatial scaling of landscape variables (slope, aspect, elevation) and vegetation pattern in landscapes in Yellowstone. To better inform their interpretations, they also analyzed a series of artificially patterned landscapes as simple and multi-scaled binary maps, to document the efficacy of variograms in detecting known patterns and the sensitivity of the analysis to missing data (by masking proportions of the data, also at varying scales). They found that variograms were quite efficient in capturing simple patterns at single scales; they were somewhat less successful with multi-scaled patterns, but robust to moderate levels of missing values in the data.

4.3.1.3

Which to Use: Autocorrelation or Semivariance?

The parallel development of spatial statistics and geostatistics is confusing in that we might choose either technique to explore scale. Fortunately, the choice does not really matter very much. As commonly computed, autocorrelation and semivariance are mirror images of each other numerically: one indexes similarity while the other uses dissimilarity, so one is the complement of the other. Beyond this, autocorrelation offers a ready test of significance, while semivariance has no formal test of significance in the conventional sense. By contrast, there is a considerable body of geostatistical theory based on variograms, especially with respect to using these for map interpolation (kriging) (e.g., Haining 2003). Thus, the choice of technique might depend in part on the aim of the application after the initial exploration of spatial scaling.

4.3.1.4

Some Further Considerations

In the examples above, autocorrelation and semivariance were illustrated for continuous, interval-scale data. Alternative forms of the indices can be computed for rank (ordinal) or categorical data (Sokal and Oden 1978). Autocorrelation and semivariance make a number of assumptions about the data. The familiar forms, as presented here, assume stationarity and isotropy. Stationarity implies, at a minimum (weak stationarity), that the mean and variance of the variable of interest are consistent across the extent of the study area. In a sense, the definition

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of a landscape as a study area would suggest that the assumption of stationarity might be met, at least loosely; the alternative would imply that the study area is not a natural unit for study because the pattern is inconsistent over the study area. Isotropy means that the pattern is the same in all directions, so that it makes sense to compute autocorrelation from all pairs of samples, regardless of the directional orientation of the samples. For terrain-based measures, this clearly is an unlikely assumption. For example, mountain ranges have an orientation that corresponds to tectonic activity, and so anything related to terrain in these systems will be anisotropic. Geostatistical techniques can be extended readily to anisotropic conditions, by computing autocorrelation (or semivariance) within discrete direction classes (e.g., four cardinal direction, or eight octants) or by weighting the autocorrelation relative to some reference direction (e.g., as a cosine function of degrees from north). These nuances can be important in applications but are not crucial to the general insights we need here concerning the scaling of geostatistical data.

4.3.1.5

Pattern Analysis with Other Spatial Data Types

Thus far, we have focused on the analysis of geostatistical data. There are corresponding analyses designed for other types of spatial data. In each case, the analysis can provide information on the direction, intensity, and scale(s) of pattern. Lattice Data With lattice data such as those represented by a raster grid or vector (polygon) map, there are variants of geostatistical methods that can be used. In particular, data in the form of raster grids can be treated simply as (particularly dense!) geostatistical data, using autocorrelation or semivariance analysis. In this, the entire grid can be analyzed, or for very large data sets the grid can be subsampled (Figs. 4.7 and 4.8 were generated from random samples of the grid shown in Fig. 4.6). Ecologists have a long tradition of analyzing data collected on grids or along transects, which yield lattice data (Greig-Smith 1983; Dale 1999; Fortin and Dale 2005). Plotnick et al. (1993) presented a technique borrowed from fractal geometry, lacunarity analysis, to characterize contagion or clumpiness in binary raster data (i.e., a grid of 0’s and 1’s) across a range of scales. Wavelet analysis would seem especially appealing as a scaling technique, because it meets most of our needs for lattice data: it identifies the direction and intensity of pattern and the scale(s) at which this is expressed. Moreover, wavelets are robust to anisotropy and nonstationarity in the data, as well as appreciable levels of noise (Dale and Mah 1998). Finally, the result of the analysis maps onto the original data and thus provides a concise graphical summary of not only what kind of pattern is present, but also where it occurs and whether the pattern changes at different locations. Bradshaw and Spies (1992) provided an accessible introduction for ecologists. Keitt and Urban (2005) used wavelet analysis to dissect the relative importance of environmental factors that varied at different scales (elevation, a proxy for radiation loading, and topographic convergence) in explaining patterns in forest productivity.

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Point Data In the case of point pattern data, there is a well-developed tradition of point pattern analysis, with tools that can identify the direction, intensity, and scale of unlabeled (or more commonly, marked) point patterns. Ripley’s K is one such technique (Ripley 1976, 1981, 1988; see also Diggle 1983). Extensions to the basic approach can also examine patterns of association between points of differing types (e.g., between species), and some extensions provide estimates of the patterns expected of hypothetical generative processes (i.e., processes other than randomness).

4.3.2

Illustration: Scaling of the Sierran Physical Template

Returning to the Sierra Nevada, to continue this extended illustration, we can revisit the characteristic spatial scaling of the physical template. Urban et al. (2000) sampled their study area at three scales, at complementary grain and extent: (1) the Kaweah Basin (50,000 ha, from a 30-m resolution digital elevation model); (2) Log Creek watershed, within the Kaweah Basin (~50 ha, sampled from a field survey at 5-m resolution); and (3) the Log Creek reference stand (~2.5-ha mapped forest stand, surveyed at 50-cm resolution). In each case, three variables were examined: elevation, a proxy for temperature over large scales; a proxy for radiation load estimated from slope aspect transformed after Beers et al. (1966), recall Sect. 1.3.2); and a topographic convergence index used as a proxy for topographic drainage. The three geospatial variables represent three distinct contributors to the water balance. All are geospatial data, censused completely over the stem map and watershed and densely over the basin (N = 20,903). In addition, soil depth measurements were available at 60-m intervals over Log Creek watershed (N = 154) and at 5-m intervals for the central 1-ha of the stem map (N = 100); no soils data were available over the extent of the entire Kaweah Basin. In each case, variograms are displayed as semivariance divided by simple variance, so they should sill to a value of 1.0 in the absence of any spatial dependence. The variograms (Fig. 4.9) illustrate typical forms for terrain-based geospatial variables (see also Legendre and Fortin 1989). Elevation shows the signature variogram of a gradient: as samples are measured at locations farther apart, they take on ever more dissimilar values. Thus, the elevation variograms do not reach a sill and have no characteristic range. This is true at all three spatial scales. Topographic convergence has a more typical form, reaching a clear sill at a range of ~300 m at the scale of the basin. At the watershed scale, the range is shorter (note different measurement scales on the axes). At the scale of the stem map, the range is less obvious and there is a substantial nugget variance; this is due, in part, to the fact that the stem map straddles Log Creek and so has rather nonstationary topography. Slope aspect behaves similarly to topographic convergence, but has a larger range (coarser grain) at all three scales. The less pronounced shoulder as the variable sills reflects the greater variability in the size of slope facets. As with topographic

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1.2 1.0 0.8

Elevation Aspect TCI Soil Depth

0.6 0.4 0.2 0.0 400 Semivariance (γ(d)/s2)

Fig. 4.9 Spatial scaling, as semi-variograms, of elevation, slope aspect (transformed to NE-SW axis), topographic convergence, and soil depth at three scales: (top) The 90,000-ha Kaweah Basin was sampled at 30-m resolution (no soils data were available). (middle) Log Creek watershed in Kaweah Basin was sampled at 5-m resolution; soils were sampled at 60-m intervals. (bottom) A 2.5-ha stem map in Log Creek watershed was sampled at 50-cm resolution; soils were measured at 5-m intervals for a 1-ha portion of the center of the stand. (Reproduced with permission from Springer Nature, from Urban et al. (2000); permission conveyed through Copyright Clearance Center, Inc.)

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convergence, the scaling of slope aspect is confounded at the scales of the stem map, as the stand straddles the creek and so the two “halves” of the stand face opposite directions. Variograms for soil depth, at the scale of the watershed and stem map, show very large nugget variances (essentially all nuggets, on the stem map), reflecting the high level of fine-scale variability in soil. That is, there is some weak spatial dependence with soils based on hillslopes at the watershed scale, but local variability is the rule at finer scales. Urban et al. (2000) also summarized these variables simply in terms of their means and variances over the basin, watershed, and stand. As they “zoomed in” from the basin, to the watershed, to the stem map, they saw less variability in elevation— as expected: the standard deviation is reduced by an order of magnitude from 700 to 70 to 8.6 m, respectively.

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109

Something more complicated was observed with transformed aspects and topographic convergence. Here, as they zoomed in, the standard deviations stay roughly the same. That is, higher-resolution measurements revealed increasingly finergrained manifestations of the same thing: macrotopography, topography, and microtopography, respectively. Likewise, finer-grained measurements of soil depth simply revealed additional local variability. That is, the ability to resolve pattern depends in part on the length scale of the measurements (here, cell size), and so the apparent scaling of a variable depends on its natural scaling but this is also conditional on arbitrary decisions about measurement scale.

4.4

Tactical Scaling

Most ecological data show some level of autocorrelation. Autocorrelation arises from two causes: spatial dependency and spatial process (Legendre 1993). Spatial dependency might arise, for example, because plant species respond to biophysical constraints and the physical template of landscapes is patchy (Chap. 1 and Fig. 4.9). Thus, a plant species that is responsive to soil moisture might itself show spatial structure at scales corresponding to environmental factors that influence soil moisture. Purely spatial processes include population processes such as dispersal, interspecific interactions such as predator/prey dynamics and competition, and contagious disturbances such as fire, pests, or disease. We have already explored some of these processes as pattern generators in themselves and as they interact with the physical template. Often, the task in landscape analysis is to infer the relative importance of these factors in causing observed patterns (Levin 1992). But whatever the cause, autocorrelation cannot simply be ignored. Autocorrelation—and more specifically the range of autocorrelation—is what reveals the characteristic scaling to natural phenomena. If we are interested in capturing the signal from a particular environmental constraint or spatial process, we need to know its characteristic scaling so that we can capture this signal empirically in sampling. This fundamental role of autocorrelation in ecological data presents two decision points for landscape-scale studies. First, we need to choose which scale(s) to sample, to target (or to ignore or downplay) particular candidate explanatory variables. Second, we need to decide whether we will embrace the complications of autocorrelation in our data, or avoid them. Here we attend to each of these decision points in turn.

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Tactical Targeting of Sampling Scale(s)

An appreciation for the natural scaling of a phenomenon provides an opportunity to be tactical about scale in sampling and analysis. The strategy is to know the scales of the patterns or processes of interest, and to arrange samples spatially to cover those scales. Random samples might, in fact, represent the scale(s) of interest; but at the large extent typical of landscape studies random samples are, at best, an inefficient solution. An example will illustrate this approach of tactical scaling. Assume that we wish to explain some features of vegetation (cover, biomass, dominance by a focal species) in terms of soil moisture. We expect that local topography should influence soil moisture via topographic convergence and hillslope processes. We also expect a larger-scale elevation gradient in soil moisture due to reduced evaporative demand and (probably) higher precipitation at higher elevations (recall Sect. 1.3.2 for both factors). We might choose to focus on local topographic influences only, in which case we would stratify field samples within a single elevation zone. Samples would be placed (probably in some sort of stratified random approach) to capture a range of values in topographic position, spanning local coves and ridges. This sampling design would emphasize the effects of topography; at the same time, it would also censor elevation because the range of variation in elevation would be too narrow to provide any explanatory power. This is a simple regression design, a univariate regression on a topographic convergence index. We might instead choose to focus on elevation as well as local topography. In this case, we might stratify clusters of samples across a range of elevations. Within each cluster, samples would be arranged to capture a range of topographic conditions. The replication of the clusters along the elevation gradient would allow elevation to show its influence. This is a partial regression inferential design, in which topography is nested within elevation, and the sampling design allows us to separate the effects of the two predictor variables (Fig. 4.10). This example illustrates tactical scaling aimed at capturing one or more explanatory variables by sampling at the characteristic scale(s) of those variables. This approach does not yet attend the complexities of autocorrelation in the data collected this way.

4.4.2

Avoid or Embrace Space?

There are two reasons why we might want to know about natural scaling: we either care about scale and wish to embrace space, or we do not care and wish to avoid the complications of autocorrelation (Legendre 1993; Legendre et al. 2002). In the latter case, the immediate implication of autocorrelation is that, if present, it prevents us from using conventional parametric statistics because we cannot meet the

Tactical Scaling

111

(-)

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Residuals

(+)

4.4

Elevation

TCI

Fig. 4.10 Tactical scaling for a partial regression design. Top: Samples are stratified over an elevation gradient, with clusters of samples at multiple elevations. Samples are color-coded to imply drier (red), wetter (blue), or intermediate (green) moisture status, with the presumption that the response variable Y increases with elevation and relative moisture (as a topographic convergence index, TCI). Within each cluster, samples are located to capture the range of variation in local topography. Bottom: The partial regression. The vegetation response variable is first regressed on elevation. Then, the residuals of this fit are extracted (as vertical distances from the regression line), and the residuals are regressed on the topographic convergence index. The nested design allows for the separation of the effects of the two predictor variables

assumption of independence among samples. To be clear: when we say that samples are independent, what we mean is that they are not autocorrelated. Autocorrelation means that the values measured on different samples are partially dependent on each other; they are not independent samples.

4.4.2.1

Avoiding Spatial Complications

To avoid the consequences of autocorrelation for parametric analyses, we must ensure that no samples are closer together than the range of autocorrelation in the data. To do this, the range of autocorrelation must be known, and typically this

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would be estimated from a pilot study (perhaps a virtual pilot study, using biophysical proxies for the variables or processes of interest, Sect. 1.3.2). One way to ensure sample independence is to generate random points (sample locations) and then check to make sure that no sample is closer to any other sample than the range of autocorrelation. This is typically done by generating points sequentially and discarding new points that are too close to previously generated points. The specification of an exclusion distance (the range of autocorrelation) around points makes this an interference process, and the sequential nature of adding new points beyond the exclusion distance is a sequential interference sampling design. A sequential interference design ensures samples that are independent, using the range of auto-correlation in the variable of interest as the exclusion distance. In the illustration above, for a parametric regression, this approach would mandate that samples placed to capture local topographic influences would be separated by at least the distance corresponding to the range of autocorrelation in the topographic convergence index. The effects of autocorrelation in elevation are a bit more complicated. As elevation is a gradient, its autocorrelation is significant at essentially all scales (Sect. 4.3.2), and so there is really no separation distance that guarantees sample independence. In practice, enough separation to reduce autocorrelation somewhat helps minimize the statistical consequences of violating the assumption of independence. It is worth digressing to consider a naive approach to the simple model involving topographic influences. In this, we might sample randomly within an elevation zone, in which case we likely would collect some samples that were so close together that they would be spatially dependent. One “fix” to this problem is to discard offending samples until all samples were independent—that is, applying the exclusion distance after-the-fact. This is expensive, of course. The analytic solution is to adjust the test (e.g., a t-test for correlation) for autocorrelation; the common approach is to reduce the degrees of freedom to represent the effective number of independent samples (Legendre 1993). Another aspect of this design is the relative importance of environmental factors. In this illustration, random sampling across the longer elevation gradient would likely collect samples at varying topographic positions at whatever the elevation. In principle, this should allow us to estimate the relative importance of local topography by partial regression (as in Fig. 4.10). But in practice, the presence of the very strong elevation gradient likely will mask the weaker contributions of other factors that might covary with elevation. Indeed, in a spatial analysis of the Sierran system illustrated here, Urban et al. (2002) found it difficult to resolve anything except elevation using partial regression designs. To estimate these effects, it works better if we sample tactically to capture them.

4.5

Summary and Conclusions

4.4.2.2

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Embrace Space

The alternative to avoiding the consequences of spatial structure in data is to embrace this rich complexity. This requires a tactical approach to sampling, to ensure that the data capture this complexity. It also requires the adoption of analytic tools that can use this information, instead of more familiar parametric tools. To focus on variables operating across a range of scales, samples must be spaced to represent the targeted scale(s), as “distances apart” in the sampling design. For large study areas, an efficient way to do this is to stratify samples in clusters, where the within-cluster spacing is at distances corresponding to smaller-scale patterns and the cluster centroids themselves are stratified over larger distances. In this, samples would be allowed to fall within the range of autocorrelation for each process of interest. Stratifying samples randomly would also increase the likelihood that other scales(s), as distances apart, would also be represented in the sample. Some tactical sampling designs for landscape-scale studies are illustrated in Urban (2002). A clear message from tactical sampling studies is that being deliberate about where data are collected can be immensely efficient relative to simpler (random) sampling designs. Analytically, the task is to partition explanatory power to variables at each scale, and typically, to also summarize residual variation in the dependent variable expressed at particular scales. Such analyses can get rather complicated (e.g., Legendre 1993; Fortin and Dale 2005; Legendre and Legendre 2012). We will revisit this approach in Chap. 7, when we consider landscape-scale patterns in biodiversity. For now, suffice it to say that unless the data are collected deliberately to capture the spatial patterns of interest, no amount of analytic sophistication will salvage the study.

4.5

Summary and Conclusions

The natural world is scaled implicitly by the way in which events that are fine-scale (and high frequency) are integrated into larger-scale and slower phenomena. Spatial scaling, defined by grain and extent, opens an empirical window onto the natural world, highlighting some phenomena while deemphasizing others. This means that careful attention to choosing a scale of analysis (by specifying grain and extent) can focus a study by declaring which phenomena are of interest, and conversely, which will be downplayed. This is an exercise in model specification, and all models are scale-specific. The logical flow in a landscape-scale analysis is to first identify the processes or phenomena of interest for the application. The second step is to characterize the spatial scaling of these processes or patterns. This can be done via pilot field studies or (perhaps more efficiently) by doing a virtual pilot study using geospatial proxies for the variables of interest. The final step is to design the field study using a tactical sampling design that captures the target variables in a way appropriate to the intended analysis (i.e., using either parametric tests or methods that embrace autocorrelation).

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The next logical step in analyzing pattern is to ask why the pattern occurs: what causes the characteristic scaling? In general, autocorrelation is due to either a spatial constraint (e.g., vegetation responding to soil moisture, with soil moisture exhibiting patchiness because of topographic influences) or to an explicitly spatial process (e.g., dispersal, or a contagious disturbance). Isolating these causes and estimating their relative importance quantitatively is central to landscape ecology (and ecology in general: Levin 1992), and this will occupy us in the next chapter as well as in subsequent chapters. Natural scaling typically is communicated in terms of a characteristic patch size for continuously varying data, and so is concerned with patchiness. This leads quite naturally to the complementary view of landscapes as mosaics of discrete cover types, or patches. Such mosaics have more attributes than patch size alone. This will lead us, in the next chapter, to consider a variety of aspects of pattern and spatial configuration. From this, we will turn to the logic and mechanics of making inferences about ecological processes based on measures of landscape pattern.

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Priestley, C.H.B., and R.J. Taylor. 1972. On the assessment of surface heat flux and evaporation using large-scale parameters. Monthly Weather Review 100: 81–92. Ripley, B.D. 1976. The second-order analysis of stationary point processes. Journal of Applied Probability 13: 255–266. ———. 1981. Spatial statistics. New York: Wiley. ———. 1988. Statistical inference for spatial processes. Cambridge: Cambridge University Press. Schneider, D.C. 2001. The rise of the concept of scale in ecology. BioScience 51: 545–553. Shugart, H.H., and D.C. West. 1981. Long-term dynamics of forest ecosystems. American Scientist 69: 647–652. Sokal, R.R., and N.L. Oden. 1978. Spatial autocorrelation in biology. 1. Methodology. Biological Journal of the Linnean Society 10: 199–228. Tansley, A.G. 1935. The use and abuse of vegetation concepts and terms. Ecology 16: 284–307. Thornthwaite, C.W. 1948. An approach towards a rational classification of climate. Geographical Review 38: 55–94. Thornthwaite, C.W., and J.R. Mather. 1955. The water balance. Publications in Climatology 8: 1–86. ———. 1957. Instructions and tables for computing potential evapotranspiration and the water balance. Publications in Climatology 10: 183–311. Turner, M.G., W.H. Romme, R.H. Gardner, R.V. O’Neill, and T.K. Kratz. 1993. A revised concept of landscape equilibrium: Disturbance and stability on scaled landscapes. Landscape Ecology 8: 213–227. Urban, D.L. 2002. Tactical monitoring of landscapes. In Integrating landscape ecology into natural resource management, ed. J.L. Liu and W.W. Taylor, 294–311. Cambridge: Cambridge University Press. ———. 2005. Modeling ecological processes across scales. Ecology 86: 1996–2006. Urban, D.L., R.V. O’Neill, and H.H. Shugart. 1987. Landscape ecology. BioScience 37: 119–127. Urban, D.L., C. Miller, N.L. Stephenson, and P.N. Halpin. 2000. Forest pattern in Sierran landscapes: The physical template. Landscape Ecology 15: 603–620. Vance, T., and R.E. Doel. 2010. Graphical methods and cold war scientific practice: The Stommel diagram’s intriguing journey from the physical to the biological environment. Historical Studies in the Natural Sciences 40: 1–47. Watt, A.S. 1947. Pattern and process in the plant community. Journal of Ecology 35: 1–22. Wessman, C.A. 1992. Spatial scales and global change: Bridging the gap from plots to GCM grid cells. Annual Review of Ecology and Systematics 23: 175–200. Wiens, J.A. 1989. Spatial scaling in ecology. Functional Ecology 3: 385–397. Wiens, J.A., and B.T. Milne. 1989. Scaling of ‘landscapes’ in landscape ecology, or, landscape ecology from a beetle’s perspective. Landscape Ecology 3: 87–96. Wu, J. 1999. Hierarchy and scaling: Extrapolating information along a scaling ladder. Canadian Journal of Remote Sensing 25: 367–380.

Chapter 5

Inferences on Landscape Pattern

5.1

Introduction

Making inferences from observations of landscape pattern is the core of landscape ecology. We are heavily invested in the pattern–process paradigm (Sect. 2.2): that processes generate patterns and are, in turn, constrained by pattern. There are several reasons why we might explore landscape pattern empirically. Often, we will be interested in how agents of pattern are expressed: How does some process generate pattern? How do management or land use practices influence pattern? How does clear-cutting a forested landscape affect the geometry of remnant forest and the extent of forest edges? Reciprocally, how does landscape pattern influence ecological processes such as population demography or disturbance? How do forest bird communities respond to the pattern generated by clear-cutting? How do these pattern–process relationships vary regionally or over time? Answering such questions requires a richer and more nuanced vocabulary about pattern, and a practical approach for making inferences about pattern. “Pattern” is a vague term and it often will be useful to be more explicit about what is meant by that term. As outlined below, there are myriad aspects of pattern, and different aspects of pattern might be appropriate for particular applications. In this chapter, we delve into landscape pattern: how to quantify its various aspects, how to interpret measures of pattern, and how to make inferences about pattern–process relationships. Methods for characterizing pattern have occupied landscape ecologists from the beginning of the discipline, and there is a vast literature on the topic (e.g., Forman and Godron 1981; Forman 1983; Urban et al. 1987; O’Neill et al. 1988; Turner 1989, 1990; Turner et al. 1989a, b; Riitters et al. 1995; Gustafson 1998, 2019; Costanza et al. 2019). In this chapter, we take a rather tactical view of methods for indexing landscape pattern. In this, we begin by changing our focus from spatial heterogeneity or patchiness as in the previous chapter, to a focus on discrete patches, which has

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been the focus of much of the work on landscapes. We then outline the main aspects or components of pattern, as captured in landscape metrics, and consider how we can interpret these measures. We turn then to the task of making inferences about indices of pattern. This task is illustrated with a few examples of applications using pattern metrics. One of these applications, aimed at distinguishing the effects of habitat area as compared to its configuration, raises an issue that helped launch landscape ecology as a discipline and one that still continues to motivate research and practice. The confounding of area and configuration effects invites a deeper consideration of inferential design for pattern–process studies on landscapes. This inferential logic, in turn, informs subsequent chapters on the implications of pattern for populations, communities, and ecosystems. This is a busy chapter! But the mechanics of making inferences about pattern and process are fundamental to landscape ecology and warrant the attention.

5.2

Patchiness and Patches

In the previous chapter, we were concerned with patchiness, especially the scale(s) at which ecological variables exhibited patchiness. Strong spatial autocorrelation in a variable at a particular scale suggests that the variable is patchy—it manifests in relatively homogeneous and characteristically scaled patches on the ground. We couched that discussion of pattern in terms of alternative types of spatial data: geostatistical samples, raster grids or other lattices, and point patterns (Sect. 4.3). It would be reasonable to assume that landscape ecology would have developed inferential methods corresponding to these data types and to focus on patchiness. For the most part, that has not been the case. Much of landscape ecology is based on a conceptual model of landscapes as mosaics of discrete patches, the patchmosaic model (e.g., Forman and Godron 1981; Urban et al. 1987; Turner 1989). For example, perhaps most of the earlier studies of landscape pattern were based on maps of land cover types (e.g., forest, agriculture, developed lands); and very many studies were based on binary maps comprising patches of “habitat” for a focal species embedded in a matrix of “nonhabitat.” This focus, perhaps, reflects the availability of landscape-scale data in the early years of the discipline: digital land cover maps were a primary data source. One consequence of this empirical view of landscapes is that much of the early work on pattern (and much current work) is concerned with humans as agents of landscape pattern. Alternative frameworks clearly would make more sense for other kinds of applications. Studies of stream or river networks naturally invite a network model representing stream reaches as linear features that join together as tributaries. Features represented on maps as discrete points (e.g., small watering holes, wind turbines) or events (e.g., fire ignitions, points of origin of disease outbreaks or invasions) invite analyses based on point pattern analysis. Because so much of landscape ecology is based on the patch-mosaic concept, we adopt that framework

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for most of this chapter. We consider some alternative framings later in this chapter. We return, finally, to the issue of evaluating ecological agents of pattern—the physical template, biotic processes, and disturbance regimes—near the end of the chapter.

5.2.1

Patch Definition

Patches are often defined by visually obvious but arbitrary criteria and this is often sufficient. For example, patches might be defined administratively (counties or other government entities) or by other criteria that are not ecological but nonetheless useful or interesting (e.g., ownership parcels, or patches that are visually distinct to human observers). In some cases, the boundaries are ecological but objective (e.g., watersheds). But there are also cases when it is not so obvious where to draw the lines around patches, cases that demand some objective and quantitative technique for delineating patches. Two approaches are commonly available.

5.2.1.1

Simple Aggregation

Virtually all Geographic Information Systems (GIS) allow one to aggregate adjacent, like-valued cells into discrete patches (“regions” in GIS lingo). There are three approaches to aggregation, named after chess moves: rook’s moves (cardinal directions only; four neighbors), bishop’s moves (diagonals only), and queen’s moves (cardinal plus diagonals, or eight-neighbor rules). Of these, rook’s and queen’s moves seem universally available in GIS packages. In practice, this aggregation might be applied to existing categorical data such as land cover classes (Fig. 5.1). In other instances, a continuous variable is converted to a categorical descriptor through some decision rule, and then aggregated; a common example is the use of habitat suitability models to generate a continuous index of habitat quality that is subsequently reclassified relative to some threshold value into binary “habitat” and “not habitat” categories.

Fig. 5.1 Patch definition from land cover data. (Adapted from Urban and Keitt 2001). Base data are land cover, overlaid with known occurrences of Mexican spotted owls (black dots, left panel). Cover types associated with owls were used to create a raster of “habitat” versus “not habitat” (center panel), which was then converted into discrete patches using an 8-neighbor adjacency rule (right panel; patches are colored arbitrarily)

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This approach should make it clear that “patches” are specific to an application and defined functionally: the patches for one application or species need not be the same as the patches for another application (Urban et al. 1987). Indeed, Betts et al. (2014) argued that we might more readily find general relationships between species distributions and habitat pattern if we adopted an explicitly species-centric definition of habitat. Typically, aggregation simplifies the value of the region into a single value: the most frequent or average value of cells comprising the patch. There is no reason to not incorporate some measure of within-patch heterogeneity, a logical extension to which we will return. Similarly, there is no compelling reason why we could not aggregate cells that are similar in terms of multivariate, continuous variables; software approaches to this are available (e.g., Legendre 1987) but have not been widely used. Computational constraints on this approach are probably no longer an issue. Approaches that would admit for within-patch heterogeneity would represent a significant step toward more general approaches that might not require the definition of discrete patches at all. (We return to this later.)

5.2.1.2

Boundary-Detection Methods

For data in cells (pixels) on a transect or grid, an alternative approach to patch definition is methods often referred to as edge- or boundary-detection algorithms. In one version, a window of a few cells is defined, and a local variance term is computed for each window. This measure can be univariate or multivariate; there are several indices available. The variance measure is saved to the center cell of the window. The window is then moved systematically along the transect or grid, and a map of local variance is produced. Peaks in this windowed variance show up as “ridges” on the map, and these become edges that outline patches. Similar to moving-window variance methods is a method called wombling (Fortin 1994; Fortin and Drapeau 1995; Fortin et al. 2000). This involves computing the local rate-of-change on the mapped value (i.e., the partial derivative with respect to X and Y ). In lattice-wombling, this is done over a four-cell window for regular data. For irregularly spaced data, the approach is triangulation-wombling, which computes partials on three nearest-neighbor points. There is also a categoricalwombling variant, which computes dissimilarity indices as a measure of local rateof-change. In any case, the map is processed (wombled) and the largest partials (steepest rates-of-change) are identified as boundary locations (edges). Regardless of how the edges are defined, the final step in this approach is to select the highest variance values (ridges in the map) and then convert these ridges to vectors that outline patches as polygons. Windowing techniques also can quantify the contrast or boundary discreteness between patches, because the windowed variance (or partials) indicates local variability in the region of the boundary. For example, the ecotone between an agricultural field and a forest has higher contrast than the ecotone between an oak forest and a pine forest because the forest types are not as different from each other; likewise,

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the agriculture-forest boundary might be quite discrete (a straight plow-line) while the forest-forest edge might include some interdigitation or blending of types. Thus, edges can have both height (contrast) and width (discreteness) as identified with local variance techniques. Most GIS’s include automatic functions to do locally windowed statistics. Wombling is a common edge-detection algorithm used in image processing. It is perhaps worth noting that ecologists do not seem to use these techniques as much in patch delineation as they use local aggregation; this might reflect familiarity with software.

5.3

Landscape Pattern Metrics

Once patches have been defined, the task is to describe them in terms that are ecologically useful. Patches can be characterized compositionally in terms of the variables measured within them. This might include the mean or modal value and internal heterogeneity (variance, range). In spatial applications, additional information about the patch’s shape or spatial configuration is also of interest. A patch has only a few basic attributes (Table 5.1). All indices of landscape pattern stem from these four basic attributes. To anticipate just a bit, this is one reason why many landscape indices are correlated: they are constructed from the same basic terms. Also, in what follows the discussion will be in terms of discrete patches (however defined). But most of these indices could also be applied to individual cells in a raster grid (in which case, the patches are those single cells).

5.3.1

Levels of Analysis

While an individual patch has relatively few attributes, collections of patches can have a variety of aggregate properties. To complicate our discussion somewhat (at least initially), it is important to note that collections of patches can be defined at various levels. Commonly, indices of patchiness can be computed or summarized at four levels:

Table 5.1 Basic attributes of a patch (or single cell in a grid) Attribute Value Area Perimeter Neighbor(s)

Definition Categorical, rank, or interval-scale measure or label Size (in map units or proportion of map area) Lineal measure of the boundary Topologically or functionally adjacent patches

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• Patch-level metrics are those defined for individual patches. For raster data, these are often computed (e.g., averaged) from cell-level values within each patch. • Class-level metrics are integrated over all the cells or patches of the same categorical type (class). These may be calculated by simple summation (e.g., total forest area), by averaging over patches, or through some sort of weightedaveraging scheme. For example, FRAGSTATS (McGarigal and Marks 1995; McGarigal et al. 2002) provides class-level metrics that are simply averaged, as well as averages weighted by patch area; in the latter case, large patches contribute more to the average. • Landscape-level metrics are calculated over all patch types or classes. In some cases, these indices are class-level metrics aggregated or averaged over patches of all classes. In other cases, the metrics are computed directly for the landscape (i.e., without going through patch-level calculations). • Zonal metrics are calculated within a specified subregion of a landscape. These subregions may be specified as within bounding polygons (in which case the polygons define sample landscapes), or as a window that is moved over the region to provide local estimates of various metrics. This windowing can be applied to metrics at the patch, class, or landscape level. While many metrics at higher levels are derived from lower-level attributes, not all metrics are defined at all levels. In particular, collections of patches of different types have aggregate properties that are undefined (or trivial) at lower levels. It should be emphasized that applications using pattern metrics at least implicitly assume that the pattern itself is homogeneous over the study area. Statistically, this is an assumption of stationarity: with weak stationarity, the mean and variance of the measured variable are the same over the study area. In cases where this is unlikely to be true, zonal calculations can provide metrics that account for nonstationarity.

5.3.2

Components of Pattern

“Pattern” can be a multifaceted concept, and there has been a great deal of effort expended on articulating various aspects of landscape pattern (O’Neill et al. 1988; Gustafson 1998, 2019). In general, pattern metrics describe either landscape composition or configuration. Composition refers to the variety of cover types represented in the study area, while configuration refers to the geometry and arrangement of those types. Here we consider a few aspects of landscape pattern, not to be exhaustive in this but to simply illustrate the variety of measures available and the nuance they provide. Aspects of pattern are described here mostly in terms of adjectives—not as technical definitions or equations, but aimed at a more intuitive appreciation. For technical description, a few seminal papers (O’Neill et al. 1988; Gustafson 1998) motivated many of the definitions. Metrics in current usage are documented thoroughly as implemented in FRAGSTATS (McGarigal and Marks 1995;

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McGarigal et al. 2002), a software package that has been widely used for computing fragmentation statistics. This package has been updated over the years to incorporate metrics from other applications and improved or revised versions of older metrics; it also has served as a benchmark for other software implementations (e.g., Hesselbarth et al. 2019).

5.3.2.1

Landscape Composition

Patch Diversity Composition indices summarize the variety and relative abundance of cover types. A useful summary of composition is simply the proportion of the landscape in each type. Various indices borrowed from studies of species diversity summarize simple richness (number of types) or might reflect the relative abundances of types. Dominance (abundance concentrated in one or a few classes) and equitability (abundances spread more evenly across types) are two contrasting aspects of diversity. There are landscape diversity indices based on nearly every diversity index used in community ecology (e.g., Shannon, Simpson, and so on). FRAGSTATS computes several such diversity indices. Because diversity indices focus on various types, these indices only make sense at the zonal or landscape level. Diversity indices such as these invite comparison to other species diversity concepts used in ecology. Ecologists often consider diversity at three levels. The diversity of types (species) at a single point (i.e., within a sample quadrat) is α (alpha) diversity. The variation in α diversity among points, for example, species turnover along an environmental gradient, is termed β (beta) diversity. At the landscape scale, total diversity within the study area is γ (gamma) diversity. Most landscape metrics as described above are estimates of γ-diversity. By contrast, the species-turnover definition of β-diversity implies a local rate-of-change of this term; this aspect of β-diversity has not been emphasized in landscape metrics, but spatial variability in α diversity could be estimated via zonal statistics. For example, the local variation of land cover types is readily apparent in any map (e.g., the peripheral as compared to central regions of Fig. 5.2).

5.3.2.2

Landscape Configuration

There are very many landscape metrics designed to index landscape geometry or spatial configuration. Here we consider a few examples to emphasize contrasting aspects of configuration. Mean Patch Size and Patch Size Distribution One simple measure of landscape structure is average patch size. More informative is the number (or frequency, or percentage) of patches per size class. The size distribution may indicate something about the processes that generated the patches. In real landscapes, patch size distributions are often highly skewed, with many more small patches than large patches. Because of this, the simple average patch size is not a good estimate of this

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Fig. 5.2 A simplified land cover map of the area including Chapel Hill, North Carolina, provided as a visual guide to interpreting components of landscape pattern as summarized in the text

variation; other indicators of typical size are often used instead (median, mode). Gardner (1999) suggested that the size of the largest patch is a robust indicator of a variety of landscape-level patterns and processes (and see below). Shape Complexity Shape complexity can be summarized in terms of a simple edge/area ratio. Most patch-definition procedures provide for such indices easily, even automatically. More commonly, edge/area ratios are normalized for easier interpretation. These patch-level metrics can be averaged to the class or landscape level, or a landscape-level index can be computed directly from total edge and area. Because boundaries of one patch might also be boundaries of adjacent patches, perimeter/area ratios also yield information about the overall shape complexity of a landscape. One such measure is the fractal dimension (Milne 1991). Landscapes dominated by simple geometric shapes (e.g., square agricultural fields) have low fractal dimension (approaching 1.0) while more interdigitated, irregular shapes yield higher fractal dimension (approaching 2.0 for plane-filling linear features).

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Shape complexity metrics generally can be computed at the patch, class, zonal, and landscape levels (some regression-based fractals are undefined at the patch level). Edge Metrics Many applications have been motivated by studies of edge effects, the incidence of higher rates of productivity, (some forms of) diversity, predation, and avian brood parasitism in forest/field edges (and see Sect. 8.3.3). Edges can be tallied in several ways: (1) lineal measures, based on border length (and summarized per unit area); (2) cell-level counts (e.g., the number of forested cells adjacent to nonforest); or (3) areal tallies (e.g., in which forest edges are defined by buffering the perimeter of forested cells or patches to a specific edge width). In this last case, edge width would be defined relative to some process that is localized to edges, and the width would vary for different processes. Edge metrics can be computed at the patch, class, landscape, or zonal level. These are interesting, of course, only in applications concerned with processes that occur differentially in edges. In many cases, the areas that are not edges, called core areas, are indexed instead. Contrast Edge metrics focus on the boundaries between cover types. But this does not account for the reality that all boundaries are not created equal: an edge between a mature forest and a lawn, agricultural field, or parking lot is different from an edge between a hardwood forest and a mixed forest or between hardwoods and evergreens. Landscape metrics incorporate these differences by incorporating a measure of edge contrast or dissimilarity into edge metrics. The contrasts must be specified for each pairwise combination of classes (cover types) in a landscape. These are typically provided as a matrix of relative contrast measures, each scaled on [0,1] (1 = maximum contrast). Contrast-weighted edge metrics can be computed based on edge length or area (McGarigal et al. 2002). (It might be noted here that color schemes used for land cover maps typically indicate contrast implicitly or explicitly, as in Fig. 5.2.) Contrast metrics can be computed at the patch, class, landscape, and zonal level. These are most interesting in cases where contrast is presumed to matter, such as studies of edge effects or boundary permeability as it might affect species movement (Wiens et al. 1985). Dispersion For a single cover type, class-level dispersion indicates the tendency for it to be contagious (clumped) or uniform (over-dispersed) across the landscape. There are myriad indices, some of which are also used as scaling or point-pattern techniques (recall Sect. 4.3.3). A common approach is based on nearest-neighbor distances. This index is interpretable in terms of dispersion only for a single class. This index can be averaged over all cover types to yield an average index of dispersion for a landscape. More typically, overall dispersion is subsumed by adjacency, contagion, or interspersion indices based on the tendency for cover types to occur next to each other.

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Adjacency and Contagion Adjacency indexes the tendency for types to occur next to each other. This can be computed from patches (i.e., as polygons) but more typically it is computed from raster data and aggregated from cell-level tallies of the frequency with which a cell of one type occurs next to another cell of the same or a different type. Because these frequencies also depend on the relative abundance of each type, these indices tend to account for relative abundances as well as adjacencies. In particular, a cover type that tends to occur in pure clumps exhibits high contagion. Interspersion and Juxtaposition By contrast to contagion, interspersion or juxtaposition indices emphasize patterns in which cells of a given type tend to occur next to cells of a different type. Thus, if high contagion reflects pure clumps of the same cover type, high interspersion corresponds to a finer-grained “salt and pepper” mix. In Fig. 5.2, developed land covers (red) show higher contagion than the more interspersed open spaces (yellow). Connectivity Connectivity refers generally to the extent to which patches are functionally joined together (Taylor et al. 1993), and so can be related to adjacency or dispersion. Connectivity might refer to shared borders but often connections are defined according to some application-specific criteria of reachability, for example, whether an animal species can disperse between patches. The former case, where connections are based on physical contiguity, is sometimes referred to as structural connectivity. By contrast, actual material transfer rates define functional connectivity; for example, some maximum dispersal distance thresholds might define connections between habitat patches. In some applications, the distance might be weighted by a resistance term (navigability, steepness, permeability) so that distance itself becomes a relative or functional measure (Gustafson and Gardner 1996; Bunn et al. 2000). However defined, connectivity indices refer to the degree to which patches are mutually connected. Note that while these indices are computed over an entire landscape, they are restricted to consider a single cover type (e.g., “habitat” for a focal species, or for a group of species using similar habitats). Connectivity is sometimes defined indirectly, based on the reality that it depends on the amount of “habitat” represented in a landscape (similar arguments can be made of the spread of contagious disturbances or other spatial processes). Because such indirect approaches can be quite useful but also can be confounding, we return to these later in more depth (see Sects. 5.4.1 and 5.5.3, below).

5.3.3

Correlation and Redundancy

Riitters et al. (1995) computed 55 landscape metrics and then conducted a multivariate analysis, factor analysis, to reduce these to a smaller set of factors that could be captured with a small number of nonredundant indices. Their data consisted of 85 land use/land cover maps from throughout the United States (the same basic data

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used by O’Neill et al. 1988). They interpreted the analyses to suggest five general factors, each of which could be represented by a single indicator metric for that factor. Similar efforts have produced similar but not identical results (e.g., Cushman et al. 2008; Wang et al. 2014), presumably because the analyses used slightly different sets of metrics, different study areas, and different analytic tools. The important result from these analyses is, however, quite robust. The key result is that because of the limited number of primary measurements, one can make on a map (e.g., type, area, perimeter, adjacency), the various synthetic indices derived from these measurements tend to be intercorrelated. The topology of landscapes also tends to induce correlations among the metrics (and see below). Further analyses might confirm a small set of nonredundant indices that cover the different aspects of pattern outlined above (e.g., patch sizes, shape complexity, contrast, dispersion, contagion, and so on). These, in turn, could be construed as the “proper” metrics to use as a nonredundant set of variables that were statistically independent, perhaps to use as predictors in a regression analysis. Emphatically, this is not to argue that these are the landscape metrics that should be used in all landscape studies. Which metrics to use should reflect an explicit hypothesis about the patterns of interests and the mechanisms underlying that pattern (Levin 1992). Thus, the “proper” metrics to choose are those that make ecological sense for a particular application.

5.3.4

Alternative Framings for Landscape Pattern

Thus far, this discussion has focused on cell- or patch-level metrics, often aggregated to the class or landscape level. Such applications at least implicitly adopt a patchmosaic conceptual model of landscapes. As noted in the beginning of this chapter, there are alternative framings for landscape pattern. Gradient Model A simple alternative to the patch model is to treat each cell in a raster lattice as a patch in its own right. This means that patches need not be defined at all, though it also means that all analyses (including measurements of response variables) also need to be conducted at that level. This approach would be appealing in applications where there is not an obvious or intuitive way to define patches. A cell-level approach also makes it easier to embrace continuous gradients over a landscape, whether these be biophysical gradients (elevation, temperature, moisture) or biotic responses to such gradients (e.g., species abundance). If the patterns of interest are species occurrences or abundances, the cell-based gradient model implies cell-level measurements of these responses, as well. This essentially amounts to point tallies or tallies in small sample quadrats—which is how we typically census species anyway. Thus, a gradient model of landscape pattern might be more consistent with the way we sample species composition.

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McGarigal et al. (McGarigal and Cushman 2005; McGarigal et al. 2009; Cushman et al. 2010) have advocated for the application of surface metrics as an alternative to patch-level metrics, a so-called gradient model to complement the more familiar patch-mosaic model (and see Lausch et al. 2015). Surface metrics are indices computed from the “height” and “topography” of cell-level values such as those derived in remote-sensing data products. Some of the indices are familiar to ecologists, as they correspond to local slope, aspect, and terrain shape metrics as computed from digital elevation models; others borrow from other disciplines such as microscopy and address textural aspects of angular orientation and anisotropy (McGarigal et al. 2009). Such measures could expand our toolkit of landscape indices for use in inferential analyses. Spatial Point Patterns By contrast to the gradient model and graph model (below) of landscape pattern, the use of point pattern analysis has been less frequently adopted by landscape ecologists. This is not because the theory and analytic techniques are not well developed: they are (Ripley 1981, 1988; Diggle 1983; Wiegand and Moloney 2004; Dale and Fortin 2014; Velázquez et al. 2016). Rather, the complications arise because the inferential tools used in point pattern analysis are not as readily integrated with the long tradition of patch-focused analysis in landscape ecology. Graph-Based Models Increasingly, graph-theoretic approaches have been extended to landscapes (Urban and Keitt 2001; Fall et al. 2007; Urban et al. 2009; Dale and Fortin 2010; Saura and Rubio 2010). Graph theory (Harary 1969; Gross and Yellen 1999) is concerned with issues of connectivity, flow, and routing among sets of points (nodes) as defined by pairwise connections (links, or edges) between these points. Like raster grids and polygon (vector) maps, graphs are lattice data structures. A graph is a set of nodes, represented as points, and a set of links or edges that denote functional connections between pairs of nodes. One common implementation is that of a stream network in a GIS: each stream segment (reach) is a line that is joined by tributaries at nodes. The segments are directed links, arcs, as defined by stream flow. This explicit topology greatly facilitates computations done on the network. Similarly, road networks are also implemented as graphs, with road intersections as nodes and street segments typically attributed with information on direction (one-way vs. two-way streets) and traffic volume or speed limit. Graph models have become quite popular as a way to represent networks of habitat for focal species (e.g., Urban and Keitt 2001; Fall et al. 2007; McRae and Beier 2007; McRae et al. 2008; Minor and Urban 2008; Urban et al. 2009; Dale and Fortin 2010). In this, the graph can be implemented either for a patch-mosaic conceptual model or for a raster (cell-based) model. We will spend some time with these models in Chap. 6 when we consider population connectivity. One motivation for constructing graph models of habitat mosaics is that the theory is quite well developed in other disciplines (e.g., transportation, communication, social networks, electrical engineering), and we expect that we might take advantage of this theory to make inferences about landscapes.

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The consideration of alternative framings or models of landscape pattern is important because they might offer a better conceptual or empirical fit for particular applications. If such measures can be reconciled with or integrated into more conventional (patch-based) measures of pattern, they can substitute for or augment patch-level analyses. For example, a gradient model would substitute cell-level measures for patches, while graphs can augment patch-level approaches. In any case, this sets the stage for a more deliberate effort to make inferences from measures of pattern. Such inference is the crux of landscape ecology.

5.4

Interpreting Landscape Metrics

Landscape metrics comprise a heterogeneous mix of indices devised to capture various aspects of pattern. Over time, these have been reasonably well studied and we are learning more about how the metrics behave individually and collectively (e.g., Turner and Gardner 1991; Riitters et al. 1995; Gustafson 1998; Klopatek and Gardner 1999; Tischendorf 2001; Kupfer 2012; Wang et al. 2014; Lausch et al. 2015; and see Costanza et al. 2019; Gustafson 2019). This is good, in that it provides a richer vocabulary about pattern and an opportunity to make more subtle inferences about which aspect of pattern might be most germane to a particular application. But the proliferation of indices is also problematic, in that the sampling distribution and expected values of the indices are not well known, which makes it difficult to interpret the indices. For example, what is a high value for the contagion index? How might we decide whether the estimated fractal dimensions for two landscapes are significantly different? Especially, what should we expect as a value for any particular landscape metric? In landscape ecology’s early years, the issue of expected values for pattern metrics relied heavily on the use of neutral landscape models as a means of generating expectations and thus, an inferential framework for landscape metrics.

5.4.1

Neutral Models and Neutral Landscapes

A neutral model is a generative model that provides an expectation about measurements on a system. Typically, the generative model is simple and excludes, by design, a process of interest: it is neutral on that process. Often, the model is random (a null model), or as random as can be devised subject to some over-arching constraints. Ecology has used neutral models in the past (Harvey et al. 1983; Gotelli and Graves 1996; With and King 1997). Ecological examples have been concerned with the distribution of species abundances, species–area relationships, and co-occurrences of species. In community ecology, the process of interest is often competition and the aim is to model what we would expect, by chance, in the absence of competition.

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More generally, this process amounts to assessing a model as being a plausible explanation for the measurements observed of a system. This broaches the field of Monte Carlo methods (“games of chance”) in general (Crowley 1992; Manly 2007), and the logic of model selection in particular (Burnham and Anderson 2002). In Monte Carlo methods, a process is posed as a model and the model is used to generate expected values. These expectations are compared to measurements taken on the system, and the model is either accepted or rejected depending on whether the observed values are consistent with model expectations. In this, the model typically is implemented stochastically to generate a range of expected values, and the observed values are matched with a given likelihood or probability to these expectations: we might reject the model if the observed values were outside the 95% confidence limits of the model expectations. Monte Carlo methods admit a range of generative models, from complete randomness to highly constrained and detailed process models. Indeed, the simplest generative model is randomness, and this provides the foundation upon which more complicated (and perhaps more satisfying) models are built. In landscape ecology, percolation theory provided the initial neutral model.

5.4.1.1

Percolation Theory

Percolation theory (Stauffer 1985) was developed in materials science to explain, among other things, the behavior of metal foils in conducting electric current. The focus was on foils made of precious metals, and the aim was to perforate the foils to minimize the amount of expensive material—but not to the point where conductivity is compromised (Gardner et al. 1987). The “landscape” in this application is an infinite random lattice of 1’s (metal) and 0’s (holes), and the aim is to determine what proportion of the lattice should be retained in metal in order to ensure conductivity across the lattice. In theory, this critical proportion Pcrit is 0.5928, at which value the lattice percolates: it will carry a current. Gardner et al. (1987); see also Gardner and O’Neill 1991; Gardner et al. 1992) have translated percolation theory to provide expectations about the behavior of various aspects of pattern, based on the proportion of a raster map occupied by a focal cover type in a binary map (e.g., forest vs. nonforest, or “habitat” for a focal species as compared to “not habitat”). The approach is to generate a series of random raster maps with p varying between 0 and 1, and to compare landscape metrics computed from this map series. Ecologically, this might evoke a sequence in which an initially intact forested landscape ( p = 1) is cleared (randomly, one cell at a time) until no forest remains ( p = 0). Several insights emerge from this exercise. Essentially all aspects of pattern vary as a function of p, the proportion of the map occupied by the focal cover type. In particular, the number of patches, the size distribution of patches, the size of the largest patch, the linear extent of edge, and so on, all vary systematically—and nonlinearly—with p (Gardner et al. 1987) (Fig. 5.3).

Interpreting Landscape Metrics

131 6000 5000 4000 3000 2000 1000 0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 p 4000

Size of Largest Clusters

Fig. 5.3 Trends in (top) number of clusters and (bottom) size of the largest cluster as a function of the proportion of the map occupied by the focal type (“habitat” as compared to “not”). The probability that the map “percolates” is related directly to the size of the largest cluster. This is Fig. 6.2 from Turner et al. (2001), drawn from data in Gardner et al. (1987). (Reproduced with permission from Springer, from Turner et al. (2001); permission conveyed through Copyright Clearance Center, Inc.)

Number of Clusters

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The analysis of neutral landscape models has provided useful insights into the interpretation of landscape pattern (reviewed by Gardner and Urban 2007). Beyond the expected behavior of landscape metrics, these insights also include some general recommendations on the analysis of landscape pattern. Because pattern depends on p, the configuration of different landscapes can be compared rigorously only at similar values of p. Real landscapes are often difficult to distinguish from random patterns above Pcrit so that the most useful landscapes for studying pattern/process relationships are at lower values of p. For example, we might study a landscape map of potential “habitat” (vs. “not habitat”) for a focal species; if p is much greater than 0.6, the analysis is unlikely to yield much insight into habitat connectivity. The reality that essentially all aspects of landscape pattern covary also implies that efforts to relate process to pattern will be confounded by this covariance. Thus, studies aimed at accounting for the influence of landscape configuration on

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population processes must use a design that controls for the covariance among various indices of landscape pattern. And note, because most metrics vary in a nonlinear way with p, partial correlation or regression approaches—which are linear models—will not adequately control for p (and see Lausch et al. 2015). The alternative approach is to control for p by examining configuration effects within a narrow range of p. This approach is recommended in general and we illustrate this approach later (Sect. 9.4.1).

5.4.2

Neutral Templates for Landscape Processes

Neutral landscapes were rapidly adopted by ecologists interested in using this framework to explore the implications of pattern for processes operating on landscapes, especially population processes (With 1997; With and King 1999; With et al. 1997) and disturbance spread (Turner et al. 1989a, b). In this, the attractive feature of neutral models was that they provided a variety of patchy landscapes that could be controlled for statistical comparisons. In particular, multi-level neutral models (e.g., hierarchically curdled maps, multifractal landscapes) were developed to provide a means to systematically vary p (representing habitat area, as proportion of the landscape) independently of the degree of contagion or fragmentation of the map. For example, one might generate a series of random maps with the same value of p but which vary in terms of contagion (or connectivity). This allowed researchers to assess the relative importance of area as compared to fragmentation or isolation in terms of their relative importance to population processes. What emerged from these studies is the generalization that habitat area is the dominant effect of landscape pattern on population process, with isolation exhibiting a substantial effect only at a rather narrow and low range of habitat area (With and Crist 1995; With and King 1999; Flather and Bevers 2002). Tischendorf (2001) used neutral landscape models in conjunction with a population simulation model to examine the degree to which landscape metrics could explain population processes. He simulated a model population on a variety of random (and some real) landscape maps, and then correlated population processes with 16 landscape metrics. While he found the metrics generally useful in explaining population processes, he also flagged some issues of concern. For example, some landscape metrics did not map unambiguously to landscapes: landscapes with very different values of p might yield the same value on a given metric (this is because so many metrics vary in a nonlinear manner with p, as noted above). Somewhat disturbingly, correlations between landscape metrics and population processes often changed in magnitude—and sometimes in sign—as a function of p. This finding reinforces the generalization that comparisons among landscape configurations must be narrowly bracketed to similar ranges of p (Gardner and Urban 2007). Tischendorf (2001) further suggested that, while random landscapes can serve as useful models of real landscapes, inferences about real landscapes can be strengthened if the artificial landscapes are constrained to resemble real landscapes as closely

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Interpreting Landscape Metrics

133

as possible. Finally, because of the proliferation of landscape metrics, some correlations are likely to emerge from a “shotgun” approach simply by chance. Inferences can be made most strongly if a specific hypothesis is generated about the process of concern, and then tested explicitly using an explanatory metric tailored to the hypothesis.

5.4.3

Extending Neutral Models: Agents of Pattern, Revisited

The adoption of neutral landscape models as tools for exploring population response to landscape pattern was a logical and useful extension of the approach. While many early applications focused on understanding how processes generated pattern, these later applications focused on the implications of pattern for processes. Here we return briefly to the question of how processes generate pattern. Neutral landscape models have provided a framework for interpreting measures of landscape pattern observed on real landscapes, by suggesting the values we might expect if the pattern-generating process were completely random. But in terms of a more nuanced strategy of model selection, this approach provides only the first step: a model of complete randomness. The approach, however, is quite general and might be extended to more complicated and more interesting models. Gardner and Urban (2007) offered a logical next step in this approach. They developed a constrained model, in which landscapes were compared in terms of their land use patterns but in which the comparisons were restricted to the “free” elements of pattern, masking out land covers such as water bodies that were not subject to human land uses. They also developed a more explicit method to compare patterns, based on a test of homogeneity of adjacency matrices from different landscapes. We explore this approach briefly here, as an invitation to further efforts in this direction. There is plenty of opportunity to develop richer inferential models about landscape patterns. An illustration based on the deforestation and landscape pattern in Cadiz Township, southern Wisconsin, provides a useful heuristic (Curtis 1956; Sharpe et al. 1981). Cadiz Township was settled over several decades after the American Civil War. The area was almost entirely forested historically, but was soon carved into small farms. Each landowner was required to retain some acreage in forest to provide wood for fuel and fence-posts. As development proceeded, forest cover declined dramatically (Fig. 5.4). It is entirely reasonable to ask whether the trajectory of deforestation is consistent with the null model that the process was random. In this, a model based on percolation theory provides expectations about patch size distribution, the amount of forest edge, and so on, based on the proportion of the landscape in forest ( p). Even without doing this analysis, it is easy to envision that the real landscape might well be consistent with the neutral model. That is, a set of landscape metrics computed from the current landscape might not be statistically different from the values expected from random landscapes with the same proportion of forest cover.

134 Fig. 5.4 Trajectory of forest clearing and resulting landscape pattern in Cadiz Township, southern Wisconsin, USA. Forests are shaded green; nonforest, white. (Redrawn with permission from University of Chicago Press, from Curtis (1956); permission conveyed through Copyright Clearance Center, Inc.)

5

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Even if the Cadiz landscape were consistent with a random neutral model, we need not conclude that the landscape was shaped by random processes. It would be perfectly logical to ask whether there might be some other model that better matched the observed pattern. For example, we might hypothesize that settlers retained forests (or reciprocally, cleared land) in response to soils, or topography, or distance to roads (or to the farmstead); the farm fields also might have been of a characteristic size (Iverson 1989). Curtis (1956) discussed some of these very factors. To test these hypotheses would require a model that could generate the landscape patterns implied by these hypotheses. For example, we might envision a simulation model in which we assign a probability of clearing for any forested cell in the map, based on soil type, or topographic position, or distance to road, or whatever. A set of stochastic simulations would then be generated, in Monte Carlo fashion, to produce the distribution of expected values for each landscape metric of interest. An explanatory model would be rejected if the observed pattern was inconsistent with the model’s predictions (e.g., if the data fell outside the model’s 95% confidence limits). One would, of course, implement alternative models separately and compete them using the observed data as arbiter: the most likely explanatory model is the one that best matches the data. This hypothetical example perhaps suggests why landscape ecology has not adopted this approach widely: the generative models can be rather complicated to specify and to implement! But such models would help us take a next step beyond random, in interpreting landscape pattern.

5.5

Explanatory Models and Inferences

5.5

135

Explanatory Models and Inferences

What we would like to do, of course, would be to assess the relative importance of multiple factors in shaping landscape pattern, or in shaping ecological responses to landscape pattern. For example, we might ask “How does clear-cutting forests affect landscape pattern?” Here, landscape pattern is a response variable and we are asking how a particular process affects pattern. We might also ask, “How do habitat patch size and connectivity influence forest bird populations?” In this, we are asking how pattern affects a process. Both approaches are common, and they illustrate the pattern–process reciprocity that defines landscape ecology. In this section, we review a few approaches to interpreting the relationships between landscape processes and patterns. We begin with an overview of approaches—experimental and inferential models—and then proceed to a few examples selected to illustrate these approaches. One of these examples is a more in-depth consideration of a fundamental issue that has engaged landscape ecology since its inception: the “area versus configuration” debate.

5.5.1

Approaches to Inferences on Pattern

McGarigal and Cushman (2002) reviewed studies of landscape pattern and focused on two general approaches. The first is experimental, in which pattern is directly manipulated to contrast habitat area or spatial configuration. The second, which they termed mensurational, makes inferences from observations of patches of varying sizes or configurations but does no manipulation. Fahrig (2017) reviewed the same approaches and added a third, the so-called SLOSS design (see below). An experimental approach is the gold standard for inference. Results of an experimental manipulation are analyzed in a “before/after” or ideally, a “before/ after control/intervention” (BACI) design, and the logical strength of the design stems from the direct intervention—which can show, through temporal antecedence, that the intervention caused the result observed after the intervention. The statistical power of the design depends on the quality of the controls (i.e., the ability to actually control what happens on non-treatment sites) and the level of replication. With landscapes, of course, logistical challenges make it hard to do experiments easily; most examples are at rather smaller spatial scales so that the treatments and replications are easier. Correspondingly, these examples tend to be concerned with taxa that inhabit smaller-scale landscapes (e.g., insects, small mammals, herbaceous plants). A related issue with experiments (and especially for longer-lived taxa) is that if species response to the intervention is slow or time-lagged, the experiment must be long-running . . . which further complicates the logistics. Unsurprisingly, manipulative experiments over a very large extent are quite rare (and quite impressive when they are conducted).

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By contrast, observational studies of landscape pattern typically measure pattern (e.g., habitat patch sizes, isolation, or other metrics) and responses (e.g., species abundances or diversity) over a set of patches chosen randomly or (more typically) tactically to explore hypotheses about various aspects of pattern. In this, the inferential design is partial regression, and because this is correlational, there can be no claims about causality. The statistical strength of the approach depends on sample size and how well the samples can distinguish the relative explanatory power of different pattern metrics. This issue is at the crux of the area versus configuration debate (below). The third design considered by Fahrig (2017) is narrowly focused on the so-called SLOSS debate: Which supports more species, a single large or several small reserves? These assessments are a particular form of mensurational approach, and as the focus is more narrow than our current interest we do not consider this design further here. We return to SLOSS in Chap. 7. We might add another approach to this set. Many studies aim to assess the outcomes of various management activities or alternatives, using simulations of some kind. These are essentially virtual experiments. They cannot have the statistical power of actual manipulations, yet they serve a useful role in decision-making because they can suggest the relative merits of alternative actions. This approach often is implicit in applications concerned with site prioritization, where the task is to decide which site(s) or location(s) would best meet the management objective (and see below).

5.5.1.1

Units of Analysis

Approaches also vary in terms of level of analysis and the choice of what constitutes a sample (Fig. 5.5). In a patch-level approach, pattern metrics and response variables are measured at level of the patch; the patch is the observational unit (Fig. 5.5, top right). For example, we might regress patch-level species richness on patch size or an index of shape complexity or isolation. In a landscape-level approach, the unit of analysis is a sample landscape “clipped” from a larger area, and these sample landscapes are replicated over gradients in habitat area and configuration (Fig. 5.5, top left). At this level, the predictor variable(s) are aggregate measures over all of the patches within the clipped sample landscape. For example, we might regress species richness for the sample landscape in terms of an aggregate measure of habitat fragmentation. A third approach would be to sample at discrete points within habitat patches across a landscape (Fig. 5.5, lower right). This would be appropriate in cases where the natural sampling unit is a point or a small area (e.g., point surveys for birds). In this case, there might be multiple sampling points within a single large patch, perhaps with one point in the interior and one at the edge. In this case, we might measure predictor variables at or in the local vicinity of the sampling point, and use these measures to predict species richness at that sampling point.

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Explanatory Models and Inferences

137

Fig. 5.5 Sampling designs for studies of habitat area and fragmentation. Top left: sample landscapes, as delineated by the rectangles. Top right: patches as samples (selected patches are outlined in black). Bottom right: a point-based design, with points (black dots) located within patches

These three levels of analysis can be applied in experimental or in mensurational approaches. McGarigal and Cushman (2002) noted another, hybrid level in which the unit of analysis is the patch, but patches are described by patch-level variables as well as larger-scale variables intended to capture the spatial context of each patch. As the logistics of replicated experiments are even more challenging when the units are landscapes, most of these studies have been mensurational. These approaches have different strengths and weaknesses. As we discuss below, the topology of landscapes makes it very difficult to separate the effects of habitat area and configuration at the patch level. Moreover, the patch is often not a natural sampling unit: sampling effort must be adjusted for patch size, with more effort per unit area. This differential sampling effort can itself confound estimates of species richness. That is, a large patch will have more species in part because those tallies are accrued from multiple samplings within the patch—even if the patch is relatively homogeneous in terms of habitat. In many cases, a point sample at the edge of a patch might yield a very different list of species as compared to a point sample in the

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interior of the same patch. For these reasons, point samples often make more sense than patch-based estimates because they allow for local differences while avoiding the confounding effects of sampling intensity. Because of the topology of landscapes and the way that this confounds patchlevel inferences, sample landscapes can provide a more robust level of analysis because patch-level influences of area and configuration are subsumed into an aggregate estimate over the entire sample area. This, of course, introduces the trade-off that the logistics of sampling (much less direct manipulation) are more complicated for the sample landscape.

5.5.2

Illustrations

5.5.2.1

Process Affecting Pattern

In an early study of landscape pattern, Franklin and Forman (1987) simulated forest harvest patterns in the Pacific Northwest of the United States, to explore the implications of clear-cutting on landscape pattern. They simulated simple “checkerboard” landscapes (forest/not), and in their simplest scenarios of random harvests, their results are very similar to the hypothetical sequences using percolation theory (Sect. 5.4.1 above). While simple, their study was also ground-breaking in that it was among the first to illustrate the result that even moderate levels of forest harvest, if dispersed across the landscape, convert essentially all remnant forest into edge habitat. Krummel et al. (1987) used digital maps of forest cover to explore agents of pattern. They focused on shape complexity, indexed as a fractal dimension. This index was estimated from a regression of patch perimeter on patch area (both terms log-transformed); the slope of that regression is the fractal dimension. Krummel et al. took this analysis one step further, and estimated shape complexity over a range of scales. In this, they first sorted all patches in terms of their areas, from smallest to largest. They then computed the perimeter/area regression within a sliding window of 200 patches: that is, using patches 1–200, then 2–201, 3–202, and so on. They found that smaller patches had simpler shapes than large patches (Fig. 5.6), with two apparent scale domains. The smaller patches had more regular shapes because their boundaries were often formed by survey section lines (hence roads, property lines, and plow-lines), while large patches had irregular boundaries governed by topography and hydrography. This example illustrates a use of a landscape metric, shape complexity, to make inferences about processes generating landscape pattern. It also demonstrates that, in many applications, the metric is only a part of a larger algorithm for analyzing landscape pattern. In this case, the scaling exercise adds another level to the analysis.

Explanatory Models and Inferences

Fig. 5.6 Shape complexity, as fractal dimension D, for forest patches in the region of Natchez, Mississippi in the southern United States. Maps (inset) confirm that smaller patches have simpler shapes with rectilinear edges, while larger patches have boundaries influenced by terrain and hydrology. (Redrawn with permission from John Wiley & Sons, from Krummel et al. (1987); permission conveyed through Copyright Clearance Center, Inc.)

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5.5.2.2

Pattern Affecting Process

A very large number of early studies in landscape ecology examined relationships between forest birds and various aspects of landscape pattern (e.g., Forman et al. 1976; MacClintock et al. 1977; Whitcomb et al. 1981; Lynch and Whigham 1984; Freemark and Merriam 1986; Urban and Shugart 1986; Hansen and Urban 1992; McGarigal and McComb 1995). Many of these have been complicated, if not confounded, by strong correlations among different aspects of landscape pattern— an issue to which we turn shortly. But not all such studies are so confounded. Stanley Temple and his students conducted a number of studies of birds in woodlots of the midwestern United States. A focus of much of this work was the high incidence of nest predation and brood parasitism in forest edges (e.g., Brittingham and Temple 1983). Temple (1986) synthesized this effort by competing two explanatory models in a regression framework. He used patch area as the straightforward approach, as many studies at that time were couched in island biogeographic theory with its expected area effect. He competed this model with one based on core area for each patch (i.e., total area minus edge area). The core-area models consistently out-performed the models based on total area. This is an example of using data to select between competing models. This example is appealing because the variation in patch shape at any given size made it possible to separate, statistically, the effects of core and edge area. That is often not the case with other patch-level metrics (and see below).

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Inferences on Landscape Pattern

Evaluating Scenarios: Site Prioritization

Keitt et al. (1997) provide an example of the use of landscape metrics to inform management. In this case, the work was in support of the federal Recovery Plan for the Mexican Spotted Owl (Strix occidentalis lucida) (USDI 1995). The aim of this analysis was to identify habitat patches that might be important for the long-term persistence of the owl, by providing for long-distance dispersal at the landscape scale. Keitt et al. use correlation length to index connectivity. In a raster map, a cluster is a set of grid cells that are defined (or assumed) to be functionally connected. A cluster’s radius of gyration is its effective size, as the mean Euclidean distance from each cell in the cluster to that cluster’s centroid: Ri =

ni

1 ni

rk

ð5:1Þ

k=1

where the values rk are for all ni cells in clusters i: ð xk - x Þ 2 þ ð yk - y Þ 2

rk =

ð5:2Þ

k

where x’s and y’s are the Cartesian coordinates of each cell k in the cluster. Mean cluster size (mean radius) is an index of effective patch area that essentially reflects contagion. A weighted index that also reflects the amount of the map occupied by the cover type of interest is the map’s correlation length: CL =

Ai Ri

ð5:3Þ

i

where Ai is the area of patch i, as the proportion of the map it comprises (proportion of cells in patch i) and R is the radius of gyration for that patch. Computed this way, correlation length estimates the distance that one might be expected to traverse on the focal cover type, from a random starting point and moving in a random direction—and so can serve as an index of connectivity (Stauffer 1985). Keitt et al. developed their analysis by first computing correlation length for the entire study area, comprising patches of potential owl habitat over much of the southwestern states of Arizona, New Mexico, Utah, and Colorado. They then recursively removed each patch from the landscape and recomputed correlation length, saving for each patch the change in correlation length resulting from its removal. They ranked the patches in terms of this change. Not surprisingly, the largest patches have the largest effect (because patch area contributes to correlation length). Keitt et al. then relativized these values by dividing each by patch area, and re-ranked the patches. This analysis revealed patches that were important to

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Explanatory Models and Inferences

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100 km

Smallest Effect

Largest Effect

Fig. 5.7 Relative importance of habitat patches to landscape connectivity, in terms of the reduction in correlation length on removal of each patch (corrected for patch area). Patches with a large effect are potential stepping-stones for dispersal. (Adapted from Keitt et al. 1997)

connectivity not because of their area but because of their location in the landscape: potential stepping-stones for dispersal (Fig. 5.7). This amounts to a site prioritization, first based on area and then based on location.

5.5.3

Inferences on Pattern: Area Versus Configuration

Perhaps one of the biggest challenges in landscape ecology and conservation practice has been inferring the relative importance of habitat area (especially, loss of habitat) as compared to the spatial configuration of that habitat. This was a seminal issue in the discipline, beginning with the application of islandbiogeographic theory to habitat patches (islands) surrounded by a “sea” of inhospitable land uses (e.g., Burgess and Sharpe 1981). While such studies have been conducted with various taxa, a disproportionate number focused on forest birds.

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400 300 Nearest200 Neighbor Distance (m)

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Fig. 5.8 Changes in isolation (as nearest-neighbor distance) and edge proportion as a function of loss of forest area in Cadiz Township, southern Wisconsin (Fig. 5.6). (Redrawn with permission, from Sharpe et al. 1981)

Initially, these studies focused on the island-theoretic area and isolation effects. This focus was later expanded to include the edge effects of predation and brood parasitism, which are especially important with forest birds (e.g., Gates and Gysel 1978; Brittingham and Temple 1983; Wilcove 1985; Donovan et al. 1987; Robinson et al. 1995). (Edges, of course, also can be important for other taxa and other processes; see Sect. 8.3). The challenge in this application is unavoidable and driven by the topology of landscapes: as forest cover is lost to other land uses, remnant patches become smaller, proportionately edgier, and farther apart (Fig. 5.8). The area versus configuration issue has been studied intensively (see Fahrig 1998, 2003, 2013, 2017, 2018, 2019; Bender et al. 1998; Haila 2002; McGarigal and Cushman 2002; Cushman and McGarigal 2003; Lindenmayer and Fischer 2006; Prugh et al. 2008; Didham et al. 2012; Quesnelle et al. 2013). It should be emphasized that we know that within-patch habitat heterogeneity (e.g., Roth 1976), edge effects (Hansen and di Castri 1992, and see Sect. 8.3), and connectivity (Haddad et al. 2015) each can have an effect on species distributions. The question is, how can we estimate the relative importance of these empirically? This is partly a problem in statistical attribution. The problem is not that these effects do not occur, but that we cannot adequately separate them statistically. Lenore Fahrig has played a central role in this issue. In an early review, Fahrig (2003) concluded that most studies that looked for area and configuration effects failed to demonstrate configuration effects, typically because they failed to account

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Explanatory Models and Inferences

143

for the confounding influence of area. She later (2013) posed the “habitat amount hypothesis,”, which argued that habitat area, as tallied within a biologically relevant distance of a sampling point, is a sufficient explanatory variable; that is, the configuration or isolation of the specific patch containing the sampling point are not needed. This hypothesis has found some empirical support (Evju and SverdrupThygeson 2016) but also has met some resistance (e.g., Hanski 2015 but see Fahrig 2015; Haddad et al. 2017) or incomplete support (Lindgren and Cousins 2017; Seibold et al. 2017). In a subsequent analysis that focused on studies of habitat area as compared to configuration (i.e., studies that found significant effects of fragmentation per se), Fahrig (2017) found that the majority (76%) of documented fragmentation effects have been positive rather than negative. This result was robust in terms of focal taxa (single- or multi-species cases), geography, and rarity status of the focal species. Fahrig noted that part of the confusion might be a semantic association: as habitat area is lost, it typically is fragmented as well—leading us to use the two terms together. Put another way: if the focus is on fragmentation of a once-intact habitat, then fragmentation by other land covers can happen only if there is loss of habitat area. But while habitat loss undeniably has negative implications, that does not imply that fragmentation effects need to be negative as well. We return to this theme in Chap. 6. Fahrig’s habitat amount hypothesis is still being tested, but Watling et al. (2020) found broad support for its predictions in a global meta-analysis. This support and Fahrig’s earlier results on fragmentation per se have an important implication for conservation practice: it implies that preserving small patches of habitat might be as effective as protecting the same area within a larger patch. That is, the key to conservation, in general, is to preserve more habitat, regardless of how it is arranged. But this begs a related question. While area might be an adequate explanatory variable, it is not very efficient in terms of informing management. To be clear: if we want to mitigate the impacts of habitat loss, the best solution is to create more habitat. This is not always feasible. So, we might like to know whether management efforts with existing habitat should be invested in creating more diverse microhabitats, improving connectivity or buffering edge or other aspects of habitat quality. To do this, we need clean estimates of the relative importance of the three effects, and we need to distinguish these fragmentation effects from the area effect. Note that as these are questions about management activities, they essentially invite experiments. That is, they can avoid the inferential problems caused by the natural correlation among these three aspects of habitat configuration. This might be one reason that experimental manipulations of habitat connectivity, by creating (or removing) corridors between patches, consistently show significant and lasting effects of such manipulations (e.g., Haddad et al. 2017). Further experimental manipulations of habitat quality or heterogeneity, connectivity, and edge conditions clearly could help resolve key uncertainties and better inform landscape management.

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Inferences on Landscape Pattern

Inferences on Pattern: The State of the Art

In this chapter, we have considered a variety of ways to describe pattern, and some ways to interpret these metrics and use them inferentially. Progress on these three fronts has been uneven—as might be expected in the development of a discipline. It is fair to say that we now have plenty of landscape pattern metrics, probably many more than we need. We also have a reasonably mature sense of how to interpret these metrics. Our skill in using pattern metrics inferentially still lags somewhat. The evolution of inferential models in landscape ecology parallels a similar progression in ecology in general, and it is useful to step back and consider this larger trend. In ecology we have witnessed a transition in the logical framework for inference. Initially, we posed analyses in terms of tests that compared observations on real systems to expectations from randomness—the conventional statistical null model. In terms of landscape ecology, this is completely parallel except for the complication that the expectation under the null model of randomness depends on p, the proportion of the landscape represented by the focal cover type. In practice, ecologists have moved away from a null-model approach to a competing model approach in which alternative (and, we hope, at least plausible) explanatory models are competed against each other in a process that uses data to arbitrate among alternative explanatory models (e.g., Burnham and Anderson 2002). Thus, the inference switches from “data versus random” to “data versus alternative (nonrandom) models” comparisons. This then becomes a process of model selection, as compared to a process of rejecting the null hypothesis that nature is random. Perhaps not surprisingly, there is a considerable literature that has argued that pattern–process inferences are simply elusive for any but the most trivial cases. Many of these studies have used simulation models to generate patterns, and then tried to capture the process with simple measurements of the system. Indeed, in many cases, it is very difficult to recover the process from measurements of pattern (e.g., Cale et al. 1989; Moloney et al. 1991; Levin 1992; reviewed by McIntire and Fajardo 2009). Indeed, Watt (1947, Sect. 2.2) warned us about this! McIntire and Fajardo (2009) suggest that the case is not so dire, that we can indeed make strong inferences from measured pattern. Their recommended approach entails hypotheses that are articulated explicitly in terms of scale and pattern, ideally with competing hypotheses predicting different spatial patterns or patterns at different scales. This is entirely consistent with the general approach of model selection outlined above, but enriched by an explicit focus on scale and pattern (Levin 1992).

5.6

Summary and Conclusions

5.6

145

Summary and Conclusions

Landscape pattern connotes a wide variety of measurements used to index various aspects of landscape composition and spatial configuration. Because most of these metrics ultimately stem from the same basic patch-level attributes (cover type, area and perimeter, and the distance to or type of neighboring locations), most landscape metrics are correlated and partially redundant. The onus is on the investigator to choose the metric(s) that makes sense for any particular application, and to devise tests that will evaluate the metrics unambiguously. Neutral landscape models provide a framework for the interpretation of the behavior of landscape metrics as a function of the proportion of a landscape occupied by a cover type of interest. The basic approach of neutral models—using a hypothesized model to generate expectations—provides general guidance for the evaluation of much more nuanced explanatory models for landscape pattern and process. This approach has not yet been fully embraced, in part because of the challenge of developing (and programming!) the explanatory models and also because of the empirical demands of evaluating such models. Efforts to estimate the relative importance of different aspects of pattern in explaining ecological processes are confounded by the way that most landscape metrics covary. This seriously complicates analyses based on partial regression, and invites more tactical analytic approaches in combination with controlled manipulations as field experiments. The preceding chapters lay a foundation for, and also a vocabulary and syntax for exploring the implications of pattern in ecology. That is, rather than merely proclaiming that pattern is important to landscape processes, we now have the language to articulate which aspect of pattern is important, and why we expect this. This will unfold in the following three chapters.

5.6.1

Homage to John Curtis

Curtis’s (1956) discussion of human impacts on forests and grasslands is known for his now-iconic graphic summarizing forest loss and fragmentation in Cadiz Township in southern Wisconsin (Fig. 5.4). But his paper might well serve as an invitation to the remainder of this book. In his closing discussion, Curtis noted that “The small size and increased isolation of the stands tend to prevent the easy exchange of members from one stand to another” (p. 729), an invitation to metapopulation models (Chap. 6). He later speculated about reduced gene (pollen) flow among forest patches and the microevolutionary implications of this, anticipating the field of landscape genetics by a few decades (Chap. 6).

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He discussed species composition of remnant habitat patches in some depth, describing trends in plant and animal communities characteristic of small forest patches; his conclusions echo ideas by Watt (1947) on the propagation of chance events through communities while broaching the question of the relative importance of environmental filtering as compared to local dispersal or other spatial processes in governing community composition (Chap. 7). Curtis also noted that forest loss had dramatic implications for hydrology: with forest loss, Cadiz Township lost a substantial proportion of its perennial streams and also experienced changes in streamflow and the incidence of flash floods (Chap. 8). He also described, in terms of life-history traits, the shift in species composition in fragmented habitats such that remnant patches are characterized by a small set of cosmopolitan and mostly weedy species—the process of biotic homogenization now applied to habitats in urban landscapes (Chap. 9). Finally, Curtis speculated about the potential for broad-scale landscape conversion to feed back to the climate system through changes in transpiration and albedo (Chap. 10). In short, while his compelling graphic on landscape change has received a lot of attention, it is even more compelling to revisit the rest of his discussion of habitat loss and fragmentation. His insights are timeless.

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Chapter 6

Implications of Pattern: Metapopulations

6.1

Introduction

A fundamental result of landscape heterogeneity and habitat fragmentation is the potential to create metapopulations. A metapopulation is a population of populations: populations in discrete habitats in a matrix of other land covers or habitat types. In this chapter we explore our current understanding of metapopulations in theory and practice. While ecologists have long been interested in patchy environments and populations (Levin 1976; Wiens 1976), many landscape ecologists came to metapopulations via island biogeographic theory and its application to communities in discrete habitat patches (e.g., Burgess and Sharpe 1981, and see Chap. 7). But metapopulation theory has a much longer history and deeper roots in ecology. We will begin by tracing some of this history. We also will consider the practical implications of attempting to deal with metapopulations empirically. Network models of habitat mosaics provide a particularly compelling and popular analytic framework. Metapopulation concepts— especially notions of limited habitat connectivity—were adopted early on as a guide conservation practice. Such applications have been facilitated by the conceptual appeal of the model and the availability of software to implement connectivity models in map-based applications, often using rather limited data. We close by considering some emerging approaches that can contribute substantially to these models. More generally, the main implication of spatial heterogeneity and landscape pattern is that locations (discrete patches or different positions along environmental gradients) vary in quality or type, and these locations might be coupled to varying degree by dispersal or other system-level fluxes such as energy, biomass, or nutri-

Supplementary Information The online version contains supplementary material available at https://doi.org/10.1007/978-3-031-40254-8_6. © Springer Nature Switzerland AG 2023 D. L. Urban, Agents and Implications of Landscape Pattern, https://doi.org/10.1007/978-3-031-40254-8_6

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ents. Thus, we might consider communities of communities or systems of ecosystems. We will develop these parallel concepts of metacommunities and metaecosystems in the next two chapters.

6.2

Metapopulations in Theory

There are several metapopulation models of historical interest as well as more recent variations on the theme (Hanski and Gilpin 1991, 1997; Gilpin and Hanski 1991; Hanski 1999). For our purposes, we can focus on four seminal models. We will then look at another model, not for its theoretical content but as a simple means of illustrating some key issues related to (at least theoretical!) metapopulations. In the following sections, we focus on the conceptual foundations and key insights from the various models. Details on model formulation and analysis are included as a supplement to this chapter (Supplement S6.1).

6.2.1

The Levins Model

The original metapopulation model is that of Richard Levins (1969). The Levins model is framed in terms of local extinction rates and likelihoods of recolonization after extinction. The model predicts the proportion of habitat patches expected to be occupied, in terms of given extinction and recolonization rates. The Levins model (Supplement S6.1.1) is rather abstract: all the patches are assumed identical, and they do not exist at specific locations; rather, any patch can suffer extinction or be recolonized with equal likelihood. This abstraction also simplifies the model’s solution: the proportion of occupied patches depends only on the balance between the extinction and recolonization rates. In a nutshell, if the recolonization rate is greater than the extinction rate, some proportion of the patches will always be occupied. This model is difficult to apply directly to real landscapes, where patches are not identical and occur at specific locations. But the key model result—that dynamic local extinctions and recolonizations might still result in a persistent and stable metapopulation—is a profound insight that provides a foundation for all subsequent work on metapopulations. Conceptually, this insight parallels Watt’s (1947) two-scaled notion of the unit pattern (Chap. 2, Sect. 2.2), wherein local sites undergo continuous dynamics but the aggregate exhibits a steady state. The dependence of the Levins model on the balance of extinction and recolonization also presages the theory of island biogeography (Chap. 7, Sect. 7.2).

6.2

Metapopulations in Theory

6.2.2

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The Spreading-of-Risk Model

A second metapopulation model is the spreading-of-risk model (den Boer 1968, Supplement S6.1.2). This narrative model begins with the empirical observation that natural populations are quite heterogeneous and they live in heterogeneous, naturally fluctuating environments. Den Boer argued that heterogeneity buffers a population against environmental fluctuations, that this heterogeneity is a positive feature and should not be treated as a distraction or noise. Den Boer discussed multiple sources of variability affecting populations. For example, phenotypic variation buffers environmental fluctuations because different environmental signals (e.g., warmer or cooler weather) act selectively on different phenotypes within the population. Similarly, populations can spread their risk over time through different life stages (e.g., stages that can escape extreme weather through dormancy). Another mechanism focuses on avoiding risks posed by other species (i.e., predators or competitors) by avoiding them in space or in time. Den Boer’s model that has attracted the attention of landscape ecologists is spreading-of-risk in space. In this, a (meta)population (he did not use the term metapopulation) will be more likely to persist if distributed over a number of loosely connected populations in different patches or locations. The argument is that environmental perturbations (e.g., extreme weather) or disturbances that impact a local population—perhaps extirpating it—would be unlikely to affect the entire metapopulation. The adage, “Don’t put all your eggs in one basket!” is a perfect analogy. Applied to environmental fluctuations, the argument is that a condition that is unfavorable for some populations would at the same time not affect or even be favorable for other populations—moderating these fluctuations when averaged over the metapopulation. A companion piece—important on patchy landscapes—is that the patches have to be sufficiently connected that dispersal is possible, so that local extinctions can be recolonized from nearby patches. An implication of the spatial spreading-of-risk model is that there is a “sweet spot” in connectivity: patches must be sufficiently separated that a local disturbance or environmental fluctuations cannot perturb the entire system; yet patches must be sufficiently connected that local extinctions can be recolonized from other patches. Collectively, these mechanisms serve to dampen what would otherwise be more extreme fluctuations in response to environmental drivers. This works better if the subpopulations are not in synchrony (den Boer 1981).

6.2.3

The Source-Sink Model

A third seminal metapopulation model is Pulliam’s (1988) source-sink model (Supplement S6.1.3). By contrast to the Levins model in which all patches are alike, the Pulliam model is based fundamentally on local variation in habitat quality, and it is this variation that drives dispersal dynamics.

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Pulliam defined a source habitat patch as one in which net reproduction is positive; that is, the local birth rate exceeds the death rate. Reciprocally, a sink patch is one where the local birth rate is less than the death rate. Source patches thus have a net surplus of individuals, which surplus can then disperse to nearby patches. Sink patches have a net deficit, and so their populations depend on dispersal from nearby source patches for their long-term persistence. The landscape-scale interplay of source and sink patches can be quite dynamic in space and time, and Pulliam’s model has some rather surprising implications. Perhaps the most critical of these is that a metapopulation can persist even though a substantial proportion—even most—of its populations are local sinks, as long as local sources are sufficiently strong (have a high enough reproductive surplus) to subsidize the sinks. The prediction of Pulliam’s model that a substantial proportion of individuals in a metapopulation might be inhabiting sink habitats itself has a confounding implication for wildlife habitat suitability or species distribution modeling (Guisan and Zimmerman 2000; Elith et al. 2006; Franklin 2010; Pearson 2010; Guisan et al. 2013). In most models of species distribution, we assume that locations where a species has been observed to occur represent “habitat.” The task is to contrast locations where the species occurred to locations where it was observed to not occur, the stronger case, or to locations where the species might occur, the weaker but more common case, in which available habitats are represented by a random sample of habitats available on the landscape. The possibility that some species occurrences are in sink habitat or “nonhabitat” invites a deeper and spatially explicit analysis of model outcomes. The case where a model predicts a site to be “not habitat,” but the site is actually occupied, is, strictly speaking, a model failure—but this is a “failure” predicted by metapopulation theory: such cases would be expected near source habitats. Pulliam’s emphasis on variation in habitat quality echoes a long history in wildlife management, in which managing for a focal species often amounts to managing its habitat. For a population to persist, there must be habitat available (it must exist); the habitat must be accessible (i.e., connectivity matters); and the species must be able to survive and reproduce in the habitat patches. Pulliam’s model addresses these conditions explicitly.

6.2.4

The Incidence Function Model

Ilkka Hanski was a leading spokesman for metapopulation theory (e.g., Hanski 1994, 1998, 1999; Hanski and Gilpin 1991, Hanksi and Gilpin 1997; Hanski and Ovaskainen 2000; and see especially Ovaskainen and Saastamoinen 2018 for a review of Hanski’s career and legacy). He is also responsible for one of the more practical models. His model is especially interesting from a historical perspective, in that it derives from island biogeographic theory or, rather, from the failure of island

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theory to provide predictions of interest to many landscape ecologists (and see Chap. 7). Without preempting our consideration of island theory in the next chapter, we might simply note that the theory makes predictions about the number of species expected on an island of a given area and isolation from a species-rich source (the “mainland”). Ecologists and conservationists who were interested not so much in how many species but which species might occur soon turned to incidence functions as a means to make inferences about island occupancy on a per-species basis (Diamond 1975). An incidence function describes the likelihood that a given species will occur on an island, as a function of species number per island. Incidence functions were initially derived empirically, based on observed species occurrences on islands of varying species richness (generally related to island area). An early focus was to interpret incidence functions in terms of life history traits of the species (Hanksi 1992). For example, what traits distinguish a species that occurs essentially everywhere, as compared to a species that occurs only on the most species-rich islands? (Hanski 1992, 1994) refined the incidence function to model the likelihoods of local extinction and colonization explicitly in terms of species life-history traits and habitat patch characteristics. His model looks complicated (Supplement S6.1.4), but it has only a few parameters, and these can be estimated empirically given a collection of patches, their occupancy status, their areas, and their locations relative to each other. In this, the metapopulation model makes a significant transition from elegant theory to applications with real, surveyed populations. This model carries with it elements of the Levins and source-sink models. It has been applied empirically to many populations (Hanski 1999), e.g., butterflies (Hanski 1994), pikas (Ochotona; Moilanen et al. 1998), and spotted owls (Strix occidentalis lucida; Urban and Keitt 2001) (and see Ovaskainen and Saastamoinen 2018). A result expected from the model is that patches near a threshold size and connectivity would tend to be occupied, while smaller or more isolated patches would tend to be unoccupied. That is, connectivity can compensate for small patch size, while large patches do not really need to be connected to be persistent.

6.2.5

Commonalities Among Metapopulation Models

While these four seminal models highlighted here might appear rather different, they are essentially the same model but with varying emphasis on the details about habitat patches and dispersal (Table 6.1). That is, they are different realizations of the same model template. The Levins model is an endpoint in terms of habitat and dispersal, in that all the patches are equivalent and every patch can be colonized; likewise, all patches suffer the same extinction likelihoods. By contrast, the spreading-of-risk model emphasizes patch-level differences in extinction risk (this might be due to either location or habitat characteristics). Pulliam’s source-sink model focuses on variation in habitat quality as this influences the potential availability (or lack) of dispersers to other

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Table 6.1 Seminal metapopulation models and the factors they emphasize Model Levins (“classical”) Spreading-of-risk Source-sink Incidence function

Factors emphasized Global extinction, recolonization rates Habitat heterogeneity; asynchrony; rescue Habitat quality drives local dispersal Patch-specific extinction and dispersal

habitats. And the incidence function model admits patch-level variation in extinction rates as well as patch-level colonization likelihoods. It should be underscored here that what makes landscapes landscapes is the spatial heterogeneity in habitat quality as this influences natality, mortality, or extinction likelihood (as in Pulliam’s model) and landscape configuration as this influences dispersal success and the likelihood of recolonization of individual patches (Hanski’s model can, and Pulliam’s could in principle). From this perspective, none of these models explicitly embraces all of these factors. We return to this later.

6.2.6

Characteristic Behaviors of (Model) Metapopulations

From the multi-threaded origins of metapopulation theory, there has been a proliferation of metapopulation models. These vary considerable in detail and purpose, and some reflect developments in enabling software. For example, metapopulation ecologists were early adopters of spatially explicit, individual-based simulation models (e.g., Urban and Shugart 1986; DeAngelis and Gross 1992; Pulliam et al. 1992; McKelvey et al. 1993; Dunning et al. 1992; 1995), an approach that (at the time) was computationally quite challenging. Regardless of the details of model implementation, many metapopulation models share some common behaviors. These include the characteristic dynamics of small as compared to large habitat patches, how metapopulations integrate patch-level dynamics, and the interaction between species life-history traits and landscape context. It might be helpful to illustrate some of these behaviors using an early metapopulation simulator. METAPOP1 (Urban and Shugart 1986; Urban et al. 1988) was an individualbased model (now known as an agent-based model) that simulated the habitat use, nesting behavior, dispersal, and mortality of each (male) bird inhabiting a set of habitat patches of varying size (Supplement S6.1.5). Patch locations were spatially explicit, and dispersal among patches depended on the size, occupancy, and location of patches (much as in Hanski’s incidence function model). A bird species was defined in terms of basic life-history traits describing its habitat use, nesting behavior, longevity, and dispersal capacity.

Metapopulations in Theory

Fig. 6.1 Population dynamics of a small and larger patch, and the entire metapopulation integrated over 50 patches, as simulated with an individual-based metapopulation model. (Redrawn from Urban et al. 1988)

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In the model, a landscape was defined as a set of patches, each with its area (and hence carrying capacity for the species), patch geometry (percent edge) as this affected nest predation and brood parasitism, and dispersal likelihoods between pairs of patches (reflecting patch locations and dispersal range of the species). The model is largely detailed bookkeeping: each year, each bird in each patch attempts to breed and experiences some nesting success; birds suffer overwinter mortality; survivors disperse to nearby habitat patches (if space permits); and the cycle repeats. All processes are stochastic so that, in particular, chance outcomes that affect individual birds in a given patch can propagate behaviors to nearby (connected) patches in subsequent years. Though it predates them, the model incorporates key elements of Pulliam’s source-sink model and Hanski’s incidence function approach. The model was developed partly in response to questions about forest loss in mid-western landscapes, with some supporting field studies conducted in Cadiz Township in Southern Wisconsin (Fig. 5.4). Simulations were conducted using random landscapes of ~50 “polka dot” patches (i.e., circles with readily computed edge/core geometry), with patch sizes and densities loosely based on Cadiz Township. The model generates intuitive behaviors that we have come to expect of metapopulation dynamics. Population dynamics are qualitatively different in small as compared to large habitat patches (Fig. 6.1). In very small patches, occupancy is limited to a single breeding pair, and so a patch is either occupied or not; this can vary substantially over time (i.e., each time the resident bird dies), resulting in a so-called flicker effect (Pielou 1981) as the population switches between “off” and “on.” Larger patches are more consistently occupied, but their populations might vary erratically over time due to stochastic mortality and dispersal events. Very large patches are mostly self-sustaining due to within-patch recruitment. The net effect in a

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mosaic of patches of varying size is that populations in very small patches might persist for a while but typically “wink out” frequently; medium-sized patches persist but only if they are subsidized by nearby source patches (recall Pulliam’s model); and populations in large patches persist although they might lose significant numbers to nearby sink patches. The metapopulation integrates these dynamics over all patches (Fig. 6.1, top line; note change in scale). For a landscape consisting of a mix of many small, some medium, and few large patches, these dynamics play out with the permanent loss of populations from the smaller patches first, especially isolated patches. Large patches and some nearby patches subsidized by these sources persist longer, but eventually the lack of recruitment (through nesting failures and mortality of dispersers) results in local extinctions of these patches as well. The landscape integrates these as a rapid decline of the metapopulation, to global extinction in most cases (Fig. 6.2). The interplay between species life history traits and landscape context can be illustrated by contrasting different species in the same landscape or the same species in different landscapes. In landscapes subject to high rates of nest predation and brood parasitism (both edge effects), a vulnerable species (open nesting, low nest height, preferred host for brood parasites) experiences a dramatic population decline and might go extinct, while a less vulnerable species (cavity nesting, permanent resident, high dispersal capacity) suffers no such decline (Fig. 6.3). Simulations (not shown) of the same vulnerable species in a landscape with large habitat patches (with little edge) as compared to a landscape with the same total habitat area but in many small patches suggest the importance of edge effects on nesting success in such situations. Simulations in which edge effects are “turned off” underscore edge effects and their impact on fecundity as a crucial constraint on forest bird populations in habitat mosaics (e.g., Wilcove 1985; Temple and Cary 1988). Simulations also help illustrate the implications of habitat connectivity for metapopulation dynamics. At the patch level, connectivity matters for small patches

Metapopulations in Theory

Fig. 6.3 Population dynamics of two species in the same landscape (redrawn from Urban et al. 1988). The ovenbird is a forest interior specialist, builds an open nest on the ground, produces a single brood per year, and is a neotropical migrant. The woodpecker is a cavitynesting habitat generalist and year-round resident

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that would otherwise not be self-sustaining. Large patches can be self-sustaining even if isolated. Thus, to persist a population needs to be either large or connected— an intuitive result and consistent with Pulliam’s and Hanski’s models.

6.2.6.1

Context and Takeaways

This and other metapopulation models suggest that connectivity matters over a relatively narrow range of total habitat area (the exact range varies among models but tends to be in the neighborhood of 20%) (e.g., Lande 1987; Fahrig 1997, 1998; Bascompte and Solé 1996; With and King 1999; Flather and Bevers 2002). It is easy enough to interpret this as a reflection of the correlation between habitat area and connectivity: as habitat area decreases, remaining habitat patches become farther apart and less connected. Urban et al. (1988) used simulations to suggest that the critical range of connectivity occurs when average between-patch distances resonate with the dispersal range of the focal species. In many simulation studies, area and connectivity are separated by design (e.g., by varying habitat area and connectivity independently). Urban et al. (1988) also controlled for area and configuration in their simulations of connectivity effects. This is possible in simulations, but as we have already considered (recall Sect. 5.5.3), less easy in real landscapes where overall habitat area, patch sizes, and isolation are correlated. Again, Fahrig has argued repeatedly (Fahrig 2003, 2017, 2018, 2019; Fahrig et al. 2019) that the loss of habitat generally far outweighs the effect of decreased connectivity. Indeed, Urban et al. (1988) were unable to find any empirical evidence of an isolation effect, controlling for area, in bird censuses in Cadiz Township.

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Also note that even when isolation or connectivity effects can be demonstrated with a metapopulation model, the results are not always as simple as we might infer. There is a positive feedback aspect to this: as habitat is lost, overall population decreases and, with this, the number of individuals and (especially) the number of individuals available as a dispersal pool (locally and overall). Locally, the loss of dispersers means that some patches will not be colonized in any given year and so will not produce dispersers themselves in the following year. Likewise, if a substantial proportion of patches are sink habitat (in the sense of Pulliam’s model), then local dispersers from source patches might not generate offspring in sink patches, again leading to a positive feedback in population decline. A key factor underlying this is the rate of mortality suffered by dispersing individuals (Wennergren et al. 1995; Fahrig 2002). In most model implementations, dispersers suffer higher mortality rates, so that as the landscape gets sparser, more dispersers die before finding a suitable patch to inhabit. In models, this leads to a threshold effect, whereby metapopulations crash after reaching a threshold value in total area and which is reflected in the relative importance of connectivity. Perhaps more to the point: while local population dynamics depend on connectivity, connectivity also depends on local population dynamics. It is important to put the preceding model illustrations into context. Fahrig (1998) conducted an intensive simulation study in which she systematically varied a range of species- and landscape-level parameters to identify the conditions under which habitat configuration really matters. She showed that connectivity is important in a very narrow range of conditions simultaneously (i.e., all of these conditions must be met): 1. Average dispersal distances are on the order of 1–3 times the average inter-patch distance.; 2. Habitat area is around 20% of the landscape. 3. Habitat is not ephemeral. 4. The species has a high site fidelity. 5. Mortality is much higher in nonbreeding (including matrix) habitat than in breeding habitat. Each of these conditions is met in the simulations shown here that show dramatic population declines (Fig. 6.2, the ovenbird in Fig. 6.3). Thus, these illustrations portray an ecologically compelling but relatively uncommon set of circumstances. Note, however, that this might be precisely the set of circumstances of concern in conservation practice! Importantly, when these conditions are not met, the metapopulation is governed mostly by habitat area, and connectivity is not very important. Further, for species that are not sensitive to edge effects or other size- and shape-dependent factors, patch geometry matters only to the extent that small patches support small populations that are more prone to stochastic extinctions. Again, the same basic model can represent a broad spectrum of cases, depending on the particulars of habitat variability and the life-history traits of the focal species. That is, the model is quite general, but the details really do matter in every case.

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Metapopulations in Practice

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It might also be emphasized here that metapopulation theory—especially the Levins and den Boer models—is clear in the implications that populations occurring in different patches or locations provide stability and resilience to the metapopulation. It is important to remember, as we emphasized in the area versus configuration debate (Sect. 5.5.3.), that while habitat loss is generally bad, habitat fragmentation is not necessarily so and often is a good thing. Metapopulation theory is rather well developed, and the models often seem quite intuitive and compelling. This invites the question: how well does the theory match the data?

6.3

Metapopulations in Practice

As all landscapes are naturally patchy to some degree, the question easily arises: how might one know if a focal species is behaving as a metapopulation in a given landscape? This will be influenced by the life-history traits of the species but also by the scale and variability of landscape pattern. Susan Harrison has been a leading voice in evaluating the theory against data (Harrison 1991, 1994; Harrison and Taylor 1997; Harrison and Bruna 1999). Harrison found a few empirical cases that matched the classical Levins model in balancing local extinctions and recolonizations. More typically, one of more aspects of the theory does not quite match the real system. To represent these alternative cases, Harrison (1991) offered four variations on the general metapopulation theme (Fig. 6.4). In the classical case, local extinctions are balanced by recolonizations (the Levins model, Fig. 6.4a). In a mainland-island model, the mainland population subsidizes other patches, but the mainland is not itself subject to extinction; this model can also be applied to sourcesink situations with a strong source (Fig. 6.4b). In some instances, patches are so well connected by dispersal that they function as a single patchy population, in which case local extinctions are not observed (Fig. 6.4c). In a nonequilibrium case, extreme habitat loss and isolation leave remnant patches subject to local extinction but without any chance of recolonization (Fig. 6.4d). Harrison suggested that species might behave as a classical metapopulation in some landscapes while behaving as some other variant in other regions. For example, in Southwestern USA, the Mexican spotted owl (Strix occidentalis lucida) lives in large, intact forests in parts of its range; in patchy but well-connected riparian forests in the canyons of the Basin and Range province; and in isolated “sky islands” on mountains separated by deserts or arid grassland in its southern range (Fig. 5.1). The sky island populations, at least, would seem a likely candidate for a metapopulation, but the population overall would seem a mix of systems (Urban and Keitt 2001). It should be underscored again that the same general model template—here, habitats coupled by dispersal—can be applied in any case, and the details can play out differently in every case.

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Fig. 6.4 Variations on a metapopulation theme. Solid patches are occupied; open patches, unoccupied. Dashed lines delimit population boundaries. Arrows indicate dispersal. (a) The classical (Levins) case, in which local extinctions are recolonized by other populations. (b) A mainland-island (or sourcesink) case, in which the mainland is persistent. (c) A single patchy population. (d) A nonequilibrium case in which local extinctions are unanswered by recolonization. (e) A mix of these cases. (Reproduced with permission of Oxford University Press, from Harrison (1991); permission conveyed through Copyright Clearance Center, Inc.)

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Implications of Pattern: Metapopulations

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Are There Real Metapopulations in Nature? The Evidence

Clearly, documenting metapopulation dynamics for a real case is data-intensive in that it requires, minimally, synoptic tallies of species occurrence (or abundance) on each of the sites in a constellation of patches over a landscape; ideally, these tallies would be repeated over time in order to estimate local extinction and recolonization rates. Unsurprisingly, there are rather few studies that have that richness of data. Hanski noted the conditions that must be met for an empirical system to qualify as a metapopulation (Hanksi et al. 1995): 1. Populations must exist in discrete habitat patches (i.e., as separate populations). 2. Extinction risk must be real for any patch in the collection of patches (i.e., no single patch can guarantee persistence of the metapopulation). 3. Recolonization is feasible for any patch after suffering local extinction.

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4. Population dynamics in discrete patches are asynchronous (i.e., all patches do not lose their populations at once, for example, because of disturbance events that are larger than the collection of patches). These conditions may be relaxed somewhat (Harrison 1991, 1994; Harrison and Taylor 1997; Hanski 1999) without degrading the metapopulation concept, at the expense of also relaxing the usefulness of the theory. Indeed, as Harrison has suggested, relaxed versions of the theory (Fig. 6.4) probably apply to more empirical cases than the classical theory fits. These criteria have been met for a sampling of real populations including butterflies (e.g., Harrison 1991; Hanski 1999; Thomas et al. 1996) and amphibians (e.g., Sjögren 1991; reviewed by Marsh and Trenham 2001). Butterflies have been a popular focus for such studies because they renew annually and often “habitat” is defined in terms of a single host plant species—and so habitat patches or habitat quality can be measured directly. Amphibians are popular targets because many live in habitats that are naturally discrete (e.g., ponds) and they are relatively easy to survey, although the “ponds as patches” model does not fit all amphibians (Marsh and Trenham 2001). Similarly, pikas (Ochotona) have been studied as model systems because their habitats (montane rocky scree slopes) are discrete and the animals are easy to census (Moilanen et al. 1998). That said, it remains that empirically documenting metapopulation dynamics is a challenging enterprise. Indeed, Smith and Green (2005) found, in a meta-analysis of amphibian studies, that Hanski’s criteria were not evaluated in 74% of the studies. As a result, some studies were probably looking at metapopulations; some were not; and it was not possible to determine whether most cases were real metapopulations. Demonstrating metapopulation dynamics empirically is further complicated by the realities of censuses. Ideally, we would like clean estimates of extinction and colonization rates. But if a population goes locally extinct and is recolonized before the next census, that event is unrecorded. This is the rescue effect, and it is presumed to occur more often in less isolated habitats (Hanski 1999). Related to this is demographic rescue, in which individuals colonize a patch and prevent an otherwise likely extinction (Brown and Kodric-Brown 1977). Van Schmidt and Beissinger (2020) have reviewed the rescue effect and its implications for metapopulation-level inference.

6.3.2

Macroscopic Approaches to Metapopulations

One of the difficulties of matching metapopulation theory to field applications is the challenge of collecting all the necessary data. Metapopulation models are bracketed by cases that are “too simple to be realistic” and “too realistic to be simple.” At the one extreme, the Levins model makes assumptions that are at odds with a landscape ecologist’s perspective. For example, Wiens (1997) noted four such themes: patches vary in quality; patch boundaries play a role in mediating species use of them; the

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intervening matrix is not uniformly “not habitat”, and this differential connectivity matters; and patch location and spatial context matter. None of these is addressed with the Levins model. At the other extreme, more realistic models pose a logistical challenge of collecting the necessary data: this approach requires, ideally, complete surveys of a set of habitat patches, over time. To document source-sink dynamics, such a model also requires patch-specific estimates of demographic rates (fecundity and mortality), the parameters that define habitat quality (van Horne 1983). And a dispersal model requires estimates of site fidelity, dispersal behavior, dispersal range, and mortality rates during dispersal. Even when such models can be constructed for wellstudied species, the variability arising from uncertain parameter estimates can compromise practical applications of these models (Urban et al. 1988; McKelvey et al. 1993; Dunning Jr. et al. 1995; Turner et al. 1995; Wennergren et al. 1995; Minor et al. 2008). We return to this issue with more promising updates, below. Given a disappointing but realistic dearth of field data, how might one guess that a target species is acting as a metapopulation? This question has motivated more macroscopic approaches. Keitt et al. (1997) wrestled with this issue in contributing to the federal Recovery Plan for the threatened Mexican spotted owl in Southwestern USA (USDI F&WS 1995). In this case, the task was to identify habitat patches that might be important to the range-wide persistence of the species (Recovery Plans are implemented at the scale of the geographic range of the listed species). While there were reasonably useful data available to document habitat affinities, breeding behaviors, and (some) data on dispersal, the data were not sufficient to support a detailed metapopulation analysis. Instead, Keitt et al. developed a macroscopic approach in which the relative importance of habitat patches was inferred indirectly. They took advantage of the general result, from percolation theory, that landscapes tend to coalesce or connect as a threshold function of dispersal distance (or equivalently, between-patch distance). They found that the southwestern landscape of the owl’s range tended to connect at dispersal distances of about 40 km. This analysis simplified the landscape-scale assessment to the simpler question whether owls were capable of dispersing 40 km (limited data from banding studies of fledgling dispersal suggests they are). This analysis is, in principle, entirely general to any landscape and any species. Thus, if a given landscape coalesces (connects) at a threshold distance d*, we really need to know only if a focal species has that dispersal capacity. If not (dispersal capacity < d*), the population will experience the landscape as largely discrete patches; if dispersal capacity is well beyond d*, the species would experience the landscape as a single (patchy) population. With a dispersal capacity near d*, the species might well behave as a metapopulation. This approach inspired Brooks (2003, 2006) to posit a general expectation that the dispersal capacity of species should evolve or adapt to correspond to the spatial grain and temporal dynamics of habitat patches in its native landscape—the natural scaling of the landscape, a “scale-matching” argument. Thus, an approximate knowledge of the scaling of connectivity of a landscape relative to the dispersal capacity of a focal species can help match that species with variations on metapopulation models (Fig. 6.4).

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6.4

Network Models of Metapopulations

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Network Models of Metapopulations

A landscape mosaic of habitat patches in a matrix of other land cover types invites a network model of metapopulations. Graph theory (Harary 1969) provides this model. A graph is a set of nodes (or vertices) and a set of links (or edges) that denote functional connections between pairs of nodes. In this case, the nodes are discrete habitat patches or locations, and the links denote connections via dispersal. Graph theory is well developed in many application areas, including communications, social networks, traffic routing (e.g., for cars and airplanes), and so on. Graph theory was applied to landscape network topology long ago (Cantwell and Forman 1993) and then more specifically to habitat mosaics (recall Sect. 5.3.4; Ricotta et al. 2000; van Langevelde 2000; Urban and Keitt 2001; O’Brian et al. 2006; Fall et al. 2007; Bodin and Norberg 2007; Saura and Pascual-Hortal 2007; Minor and Urban 2008; Urban et al. 2009; Dale and Fortin 2010; Saura and Rubio 2010; Galpern et al. 2011); applications have since flourished. In the simplest case, a habitat graph is a set of nodes that denote discrete patches, and the links are drawn between each pair of nodes that are functionally connected (Fig. 6.5, top). For example, links might be drawn if the Euclidean distance between a pair of nodes is less than a typical or maximum dispersal range for a focal species. But graphs can be constructed with varying levels of detail or complexity, depending on the application and available data. For example, we might envision a series of increasingly nuanced graphs in which the links are first denoted as binary (0/1 for unconnected/connected); then we might replace the binary links with distances. To make distances scale with dispersal likelihood, we might use an inverse function of distance, or we could use an empirical dispersal function with even more information.

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Recall that the incidence function model uses donor patch area and occupancy to estimate dispersal likelihoods. In this, the occupancy status of the donor patch reflects the reality that an empty patch does not contribute any dispersers, and a larger (occupied) patch likely provides more immigrants than a smaller one. This can be modified further to include the size of the recipient patch if there is a substantial “target area” effect on dispersal success (Hanski and Ovaskainen 2000). Finally, given data on habitat quality or productivity (as required by Pulliam’s source-sink model), we could replace area with an empirical estimate of habitat quality as this might influence fecundity or mortality (e.g., Minor and Urban 2008 and Drake et al. 2021 provide a more in-depth review). In terms of graphs, the simplest case here would imply an undirected, unweighted graph where all the links have the same value and all are symmetric (i.e., link AB is the same as link BA). In the more nuanced cases that include donor patch area or quality, the links are weighted differently, and the links also may be asymmetric (link AB ≠ BA); this yields a weighted directed graph or weighted digraph (Fig. 6.5, bottom). For example, we might expect links to be stronger between habitat patches that are closer together rather than farther apart. In riverine systems the connections would be asymmetric because of flow direction (Fagan 2002); similarly, in steep topography, uphill as compared to downhill movement might yield asymmetric links. Practitioners often compute links as least-cost paths (LCPs; Adriaensen et al. 2003). In this, a cost surface is generated to represent the relative resistance to dispersal (cost) for each land cover type. A geographic information system (GIS) then finds the least-cost path between nodes, a routing algorithm standard to any GIS. The LCPs are appealing in that they suggest how a species might actually traverse a heterogeneous landscape (Fig. 6.6, and see below). Graph theory has a rich jargon, and worse, because the theory has developed in multiple disciplines, the jargon is inconsistent across disciplines. Key terms are defined elsewhere for ecological applications (Urban and Keitt 2001; Minor and Urban 2008; Urban et al. 2009; Dale and Fortin 2010), but a few key terms are useful here. Much of graph theory is concerned with how a graph might be traversed. A walk on a graph is a series of steps, from node to node and via explicit links. A path is a walk that does not backtrack. The length of a path is the sum of the weights of the links (for an unweighted graph, this is the number of links). For any pair of nodes, there might be many alternative paths that connect them; each of these might have a different length, and one of these will have the minimum length: the shortest path. Finding the set of pairwise shortest paths for a graph is a fundamental task in graph analysis. For a graph with N nodes, there are N(N-1)/2 shortest paths (assuming the paths are symmetric), and one of these will be the longest overall: the graph’s diameter is its longest shortest path. In Fig. 6.5 (top), the length of the path from node A to F as ABDF is the graph’s diameter; in Fig. 6.5 (bottom), that path does not exist, but FDBA does (the paths must follow the arrows in a digraph). A graph’s average (shortest) path length and its diameter are convenient indices of its overall traversability.

6.4

Network Models of Metapopulations

169

Fig. 6.6 An example of a graph constructed with least-cost paths (black lines) connecting hardwood forest patches (in black). Background is land cover colored to indicate dispersal resistance: dark green, low-resistance hardwood forest; light green, pine forest; yellow, moderate resistance open space; red, high-resistance developed areas; dark blue, highresistance open water

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A second set of fundamental tasks with graphs is to identify subgraph structure or clusters of nodes that are more or less connected. In the extreme case, subsets of connected nodes that are completely disconnected from other subsets are separate graph components. In other cases, the subsets are partially connected, and the task is to identify effective subgroups or modules (also called community structure in social network analysis, a branch of graph theory). In landscape applications, we are interested in traversability and community structure because they relate directly to metapopulations. While much of graph theory addresses the topology of the entire network, there is also considerable interest in the role of individual nodes in the network. One example is the notion of centrality of a node. There are many ways to index centrality, but two common forms are degree centrality and betweenness centrality. A node’s degree is the number of other nodes that are connected to it, and degree centrality is a simple tally of this (nodes central to the graph tend to have more neighbors, while peripheral nodes would have fewer). Betweenness is computed from the shortest paths between pairs of nodes. This is a tally of the number of the shortest paths in which a particular node occurs, that is, a node has a high

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betweenness if it lies along stepping-stone paths between many pairs of nodes and is thus central to the graph. Applied to metapopulations, nodes with high centrality would be important to overall connectivity of the network. Computationally, a graph is a rather simple data structure. A graph consists of a list of nodes (habitat patches), probably annotated with attributes such as area, perimeter or edge, habitat quality, and location as spatial coordinates. The links are stored as a node x node matrix that, depending on the data, might be binary (connected/not) or be represented as weights (i.e., distances, functional distances from least-cost paths, or dispersal probabilities). Most such matrices would be very sparse, as most patches are connected only to a few nearby patches. (In such cases, there are more efficient ways to store the data, but these are not crucial to this discussion.)

6.4.1

Graphs and Metapopulations

It should be intuitive that graph models can represent metapopulations in at least an abstract way. If we modify the area term to denote habitat quality, the graph model can represent Pulliam’s source-sink model rather handily. In this, a source patch would have a high row sum in the link matrix, meaning that it contributes immigrants to many other connected patches (and has the size or habitat quality to do so). A sink patch, by contrast, would have a low row sum (not contributing much to other patches) and would persist only if it had a sufficiently high column sum in the matrix (indicating that it receives dispersal subsidies from nearby source patches). Urban and Keitt (2001) showed that graph models can also provide a quantitative representation of den Boer’s spreading-of-risk model. They indexed graph connectivity in terms of graph diameter (diameter of the largest component, for unconnected graphs) and looked at the trend in graph diameter as dispersal capacity was systematically increased (i.e., by specifying a threshold distance or joining distance). At very short joining distances, the graph is largely unconnected, and graph diameter is small because it is defined by subgraphs. As the joining distance increases, the graph connects up, but with relatively long (shortest) paths along stepping-stones. At long joining distances, the shortest paths (hence graph diameter) are direct connections and so become shorter (Fig. 6.7). That is, there is an intermediate joining distance at which the graph is connected via long paths: the spreadingof-risk condition where it is not so connected that any disturbance could spread rapidly throughout the network, but sufficiently connected that recovery from local disturbance is possible. Of course, in reality, connectivity might be defined differently for a contagious disturbance as compared to a focal species, and for conservation purposes we would hope that the species had a longer dispersal capacity than the disturbance!

Network Models of Metapopulations

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Threshold Distance (m) Fig. 6.7 Graph connectivity in relation to the threshold distance at which pairs of nodes are considered connected, for a graph of 50 randomly located nodes (from Urban and Keitt 2001). The number of components (blue line) is the number of separate subgraphs at a given threshold distance (e.g., 50 = number of patches at distance 0 and 1 = a completely connected graph at distance 1650). Diameter is for the graph’s largest component at any given threshold distance. In the shaded zone where diameter decreases from its maximum, longer stepping-stone paths are replaced by shorter direct links (shown at left)

The source-sink and spreading-of-risk models of metapopulations suggest that individual patches might be important for different reasons in a landscape: a patch might be simply a good habitat (large area or highly productive) regardless of its connectivity; it might be productive and well connected locally (a source); or it might be important to overall connectivity but not highly productive (e.g., a stepping-stone connector, even if sink habitat). Urban and Keitt (2001) illustrated a graph-based method to distinguish these modes of importance, based on an approach previously developed by Keitt et al. (1997). Working with random landscapes, Urban and Keitt (2001) found that different nodes were important for each mode (i.e., it wasn’t the same nodes in each case). Bunn et al. (2000) found similar results using the same methods for two focal species in a real landscape. Saura and Rubio (2010) further generalized this approach. For conservation practitioners, this sets up a potential trade-off: patches that are important because they are high-quality habitat might compete as conservation targets with patches that are lower quality but more important for connectivity. In such cases, it is important to be explicit about why each patch is considered valuable. It should be clear that graph models have much to offer as a way to implement metapopulation models. Depending on how links are implemented, this same approach could be used with Hanski’s incidence function model (and see Urban and Keitt 2001). Indeed, the individual-based metapopulation simulator illustrated

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earlier in this chapter (Sect. 6.2.6) was implemented as a graph.1 More recently, Minor and Urban (2007) revisited this simulator and compared it directly to graphtheoretic indices of network topology; they found that graph indices could capture most of the simulator’s results and, beyond this, the graph model offered some additional topological information that was not readily available from the simulator. Graph models have become quite popular, in part because of software innovations that make it much easier to construct them from geospatial data, such as CircuitScape (McRae and Beier 2007; McRae et al. 2008, 2012), Linkage Mapper (McRae and Kavanagh 2011, Corridor Designer (Majka et al. 2007), and Conefor Sensinode (Saura and Torné 2009). Carrea Ayram et al. (2016) provide a recent review of connectivity tools, and Dutta et al. (2022) review tools for constructing the resistance surfaces used in many of these tools. There is a lot more graph theory that might be applied to metapopulations (e.g., Bodin and Norberg 2007; Minor and Urban 2008; Pascual-Hortal and Saura 2006, 2008; Prugh 2009; Urban et al. 2009; Saura and Rubio 2010; Fletcher Jr. et al. 2011, 2013; Rayfield et al. 2011; Saura et al. 2014; Haase et al. 2017). A thorough review of these topics would be exhausting and would still fall short of what is available. For our purposes here, it is perhaps sufficient to underscore that graph or network models can readily represent landscape-scale variability in habitat quality or geometry, as well as location-specific dispersal that reflects the intervening matrix—the factors that define metapopulations.

6.4.1.1

Caveats and Uncertainties

Landscape ecologists have been quick to embrace graph-based methods to explore metapopulations. But much of this effort has been directed at constructing and displaying graphs, with less effort in analyzing the graphs as networks. But perhaps a larger concern with graph-based models is the extent to which the relevant ecology can be estimated, with confidence, from field data. Again, the full model would require patch-specific demographic rates, extinction likelihoods, and recolonization likelihoods. Precise estimates of these parameters are not strictly necessary for useful applications, but reducing the uncertainty around these estimates would build more confidence in applications. Foltête et al. (2020) provide a review and assessment of efforts to link graph models to field biology. With graphs, much of the uncertainty revolves around the extent to which the links, and especially least-cost paths, represent actual dispersal behavior. In the next section, we begin with a quick foray into a popular application area and then return to emerging approaches that should bolster our confidence in these applications.

1

Somewhat embarrassingly, I did not fully realize this until more than a decade later.

6.5

Metapopulations and Connectivity Conservation

6.5

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Metapopulations and Connectivity Conservation

Despite the many challenges in applying metapopulation theory directly to empirical applications, conservationists were quick to adopt this conceptual framework (e.g., McCullough 1996; Crooks and Sanjayan 2006; Hilty et al. 2006; Rudnick et al. 2012; see Chetkiewicz et al. 2006 and Carrea Ayram et al. 2016 for reviews). As noted, software availability has had some role in this, but it certainly also reflects the conceptual appeal of the metapopulation construct. An interesting outcome of these applications is that, on review, it is not clear that managing for connectivity (e.g., by creating corridors) always has the intended outcomes: some have argued that connectivity rarely matters (Harrison and Bruna 1999; Fahrig 1997, 2002, 2003), while others point to cases where it clearly does (e.g., Haddad et al. 2015; Fletcher Jr et al. 2016, 2018; Resasco et al. 2017; Damschen et al. 2019). We have already considered the inferential complications in estimating the relative importance of habitat area, condition, and connectivity or isolation (Sect. 5.5.3). In conservation applications, reviews suggest that habitat area is mostly important, and habitat condition (especially degradation via abiotic and biotic edge effects) is also important (Hodgson et al. 2011). Connectivity is less commonly the most important issue, although it has been shown to be very important in several cases— including cases where it has been experimentally manipulated and monitored over time (Haddad et al. 2015; Damschen et al. 2019). In a meta-analysis of corridor effectiveness, Gilbert-Norton et al. (2010) found that corridors did promote movement and dispersal among habitat patches, and that natural corridors tended to be more effective than constructed ones; they cautioned, however, that longer-term monitoring is needed to verify corridor effectiveness over time. As conservation applications seem to be pursuing connectivity more and more, and such applications will only increase as we address climate change more deliberately (e.g., Phillips et al. 2008; Nuñez et al. 2013; Keeley et al. 2018; see Chap. 10), it is worth delving into how we might improve and validate these applications. There are two emerging areas that can contribute substantially to conservation applications: better estimates of connectivity in terms of actual dispersal, and better estimates of the successful integration of dispersers into populations.

6.5.1

Structural and Functional Connectivity

Landscape connectivity is the degree to which landscape composition and configuration facilitate or impede movement among resource patches (Taylor et al. 1993). There are two distinct aspects to this definition. Structural connectivity refers to the configuration of natural or other land covers on the landscape. Functional connectivity refers to behaviors that mediate dispersal and the outcomes of dispersal.

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Structural connectivity often is defined in terms of a focal cover type (e.g., forest) from a geospatial land cover data set. This is especially the case in multi-species applications, where the focus might be forest birds or small mammals and it is convenient to consider the habitat guild collectively. Other times, we focus on umbrella species, especially charismatic larger animals, and hope that other species will be handled by association. But connectivity varies for different species using the same habitat patches (Bunn et al. 2000; Minor and Lookingbill 2010), in part because dispersal capacity tends to scale with body size (Hartfelder et al. 2021). More generally, functional connectivity need not be the same as, nor even directly related to, structural connectivity. Functional connectivity has been a challenge to model in landscape applications. This element of connectivity is defined, in large part, by dispersal behavior, and dispersal is rarely observed directly and so is difficult to estimate empirically (Tischendorf and Fahrig 2000a, b; Calabrese and Fagan 2004; Bélisle 2005). Approaches to modeling functional connectivity have evolved substantially and now comprise a broad spectrum of methods (Bélisle 2005; Kindlmann and Burel 2008; Spear et al. 2010; Laita et al. 2011; Zeller et al. 2012; Baguette et al. 2013; Fletcher Jr et al. 2016; Howell et al. 2018; Drake et al. 2021). Initially, connections (e.g., least-cost paths or corridors) were based on expert opinion. In the case of leastcost paths, uncertainty about the relative dispersal costs of different land covers or habitat types can induce substantial uncertainty in connectivity (Rayfield et al. 2010; Parks et al. 2013). It might be noted here that the “cost” of least-cost paths is a carryover from construction costs transportation routing; LCPs typically do not model actual biological costs of dispersal (for which see Bonte et al. 2012). Later estimates were derived from habitat suitability or species distribution models, often by inverting or rescaling estimates of habitat suitability (e.g., Chetkiewicz and Boyce 2009; Poor et al. 2012; Trainor et al. 2013; reviewed by Zeller et al. 2012). Keeley et al. (2017) used animal movement and genetic data to show that habitat suitability was a poor proxy for connectivity, as habitat use during dispersal was different than breeding. Vasudev et al. (2015) illustrated how the approaches used to model habitat suitability for breeding (i.e., species distribution modeling) could be extended to modeling habitat suitability for dispersal. Keeley et al. (2017) further suggested that we might focus more on identifying actual barriers to movement or factors contributing to mortality during dispersal (and see below). McRae et al. (2012) developed a computational approach to identify barriers and prioritize these for the restoration of connectivity. Observational studies of behavior (reviewed by Fahrig et al. 2022) suggest that many of the assumptions embedded in connectivity modeling are inadequate: for example, dispersing individuals often move faster and in straighter paths in the matrix than the use of resistance surfaces assumes, and observational studies of movement are difficult to relate to their population-level consequences. Fahrig et al. (2022) argued that a full model of connectivity would account for the interaction between structural connectivity (i.e., based on defined “habitat”) and movement behavior to demonstrate dispersal success, as well as the integration of that dispersal at the population level. Relative to their full model, early applications in

6.5

Metapopulations and Connectivity Conservation

175

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Fig. 6.8 Schematic of the basis for step-selection functions based on telemetry data. Observed paths (blue) are shown as step lengths and directions (angles). These are compared to possible alternate steps from the same starting points (3 random options shown in green). Observed steps are compared to possible steps using conditional logistic regressions or related techniques. The weights on these regressions indicate relative preferences and behaviors of dispersing individuals. (Figure reproduced from Thurfjell et al. 2014)

conservation have focused overly on habitat while not focusing enough on matrix (nonhabitat) conditions and dispersal behavior nor on integration into the breeding population (and see below). This integration of structural and functional connectivity, subject to species-level biology and behavior, is sometimes termed effective connectivity (Vasudev et al. 2015; Robertson et al. 2018; Drake et al. 2021; van Moorter et al. 2021). This is the direction than connectivity modeling is heading, and this integration depends on several emerging technological and analytic innovations.

6.5.1.1

Improved Estimates of Functional Connectivity

Direct measurements of dispersal are becoming increasingly available, largely because of improving technology in georeferenced telemetry. This technology provides direct measurements, as mapped movement tracks, of how an organism moves during dispersal. In this approach, observed movement paths are summarized in terms of a sequence of steps of varying lengths and directions (Fig. 6.8). At each step, possible alternative steps are generated as random movements based on the observed steps. The observations and randomly generated alternatives are overlaid onto land cover or habitat maps, and the observed and available samples are

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distinguished using resource selection functions (typically discrete-choice or conditional logistic regression: McCracken et al. 1998; Manly et al. 2002). These models can be applied at the level of individual points, steps, or entire paths (see Chap. 8 in Fletcher and Fortin 2018) and are becoming more common in connectivity applications (e.g., Fortin et al. 2005; Johnson et al. 2008; Thurfjell et al. 2014; McClure et al. 2016; Keeley et al. 2017; Zeller et al. 2012, 2016, 2018; Potts and Börger 2023). Such applications are crucial to connectivity modeling because they directly estimate movement behavior and its interaction with landscape structure. Fletcher Jr. et al. (2019) extended this approach to also include a direct estimate of dispersal mortality along with the estimate of habitat preferences during dispersal. In this, they begin with a model of movement behavior based on overlaying observed movement with a map of habitat types or land covers. They model resource selection as a Markov process, wherein at each step of the observed path, an organism has a choice of which type to move to in its next step. The novel extension is to include a so-called absorbing state, mortality, as a “choice” at each step. Their spatially absorbing Markov chain (SAMC) approach provides a direct estimate of movement behavior as well as mortality during dispersal—the pieces missing from connectivity models based on habitat alone. But even direct measurements of dispersal behavior fall somewhat short of what metapopulation theory really needs: information not only on dispersal but also on the success of the individuals in becoming contributing members of the population in the habitat patch to which they move (Robertson et al. 2018). Landscape genetics and related genomic approaches can provide this information.

6.5.2

Metapopulations and Landscape Genetics

Landscape genetics provides the perspective and the empirical methods to address the population-level consequences of successful dispersal, integrated over multiple generations. Population genetics as a discipline is concerned with the frequency distribution of alleles and changes in these distributions as influenced by processes including natural selection, mutation, drift, and gene flow (i.e., via dispersal). Landscape genetics is concerned with gene flow across landscapes and the landscape-scale facilitators of or barriers to gene flow (Manel et al. 2003; Storfer et al. 2007; Segelbacher et al. 2010; Holderreger and Wagner 2008; Manel and Holderegger 2013). In landscape genetics, a powerful empirical boon has been the ability to measure genetic markers and to compute indices of genetic similarity, based on shared markers, among spatially separated populations. A key to this approach is to find markers that are not under selection, so-called neutral markers (Holderreger et al. 2006). Neutral markers are appealing in this context because they integrate gene flow—not only successful migration but also successful integration, as breeders, into the target population. It is reasonable to expect to observe that populations that are

6.5

Metapopulations and Connectivity Conservation

177 Two-dimensional IBD

N Noatak Nome Russian Mission

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Fig. 6.9 Comparison of Euclidean, least-cost, and circuit-integrated distances with genetic dissimilarities for the wolverine in boreal North America. Shown are the geographic distances estimated as (top to bottom) Euclidean, least-cost path, and circuit flow. These distances explained 24, 37, and 68% of genetic differentiation, respectively. (Reproduced from McRae and Beier (2007); copyright (2007) National Academy of Sciences, USA)

close together geographically are also genetically similar. Conversely, populations that are farther apart should also be genetically more dissimilar: the isolation by distance phenomenon (Wright 1943). The tools of landscape genetics are typically applied to assess the relationship between geographic distances between pairs of populations and their genetic dissimilarity. McRae and Beier (2007) contrasted Euclidean (straight-line) distances with least-cost path distances and integrated multi-path distances (from CircuitScape) relative to genetic dissimilarities of populations of wolverines (Gulo gulo) in boreal North America. They found stronger correlations for the integrated paths relative to the LCPs, which were stronger than correlations for the straight-line distances (Fig. 6.9). This illustrates the potential for genetics to validate and improve estimates of connectivity as commonly used in conservation applications. In subsequent studies, researchers have used climate-change scenarios to forecast the distribution of spring snowpack, which is critical to wolverine denning and movement (Schwartz et al. 2009; McKelvey et al. 2011). They found that under future climate scenarios, the number of least-cost paths among known populations decreased by an order of magnitude. The reduced connectivity was estimated in

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terms of changes in resistance to dispersal, as average cost (effective distance) of the least-cost paths, as a result of reduced snowpack. Importantly, genetic similarities among populations reflect successful dispersal integrated over multiple dispersal events (e.g., via stepping-stones) over multiple generations and need not correspond directly to single dispersal events. Boulanger et al. (2020) used landscape genetics to illustrate this space- and time-integrated relationship for the striped red mullet (Mullus surmuletus) in the Mediterranean Sea. Landscape genetics approaches have provided useful insights into empirical metapopulations including studies of barriers to gene flow in desert bighorn sheep (Ovis canadensis nelsoni) in southern California, USA (Epps et al. 2005, 2018); assessing Hanski’s criteria for metapopulations for boreal chorus frogs (Pseudacris maculata) in Colorado, USA (Billerman et al. 2019); and revealing population bottlenecks and genetic rescue in the Rocky Mountain Apollo butterfly (Parnassius smintheus) in Canada (Jangjoo et al. 2016). Murphy et al. (2010) have extended the connectivity approach to include local, site-level factors in addition to between-site connectivity based on distance and resistance. They used a so-called gravity model to add the local, at-site factors. This approach is consistent with but in some ways more explicit as compared to similar efforts to incorporate patch-level estimates of size or habitat quality directly into graph-based approaches to connectivity (Hanski and Ovaskainen 2000; Minor and Urban 2008). Their incorporation of site productivity with between-site resistance and dispersal ties this approach more directly to Pulliam’s source-sink model. Lamb et al. (2019) argued for greater use of genetic tags as an aid to better modeling dispersal. Genetic tags are small segments of DNA that can be used to identify individuals as well as lines of inheritance such as via matrilineal relationships. These can be used to measure vagility—how far from a natal location an offspring travels before settling—and thus provide yet another richer perspective on dispersal. Their review also underscores the usefulness of noninvasive sampling method to collect genetic data, allowing genetic methods to be extended to more species. More recently, genomic tools have been incorporated into landscape genetics, yielding the emerging discipline of landscape genomics (e.g., Joost et al. 2007; Sork et al. 2013; Rellstab et al. 2015; Balkanhol et al. 2019; Forester et al. 2021). In this, new laboratory methods can generate multivariate datasets that measure genetic similarities in terms of hundreds to thousands of markers. Clearly, this improves our ability to quantify genetic dissimilarities among subpopulations. More intriguingly, genomic markers can be associated (correlated) with environmental variables and thus can be inferred to be under possible selective pressure. This provides an opportunity to make inferences not only about dispersal but also gene flow related to environmental filtering through selection (Fig. 6.10). We return to this issue in the next chapter.

A Model Template for Applications

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Contributing factors

Is this a metapopulation?

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Fig. 6.11 Model template for the development of metapopulation applications. Considerations flow from preliminary scoping (left), to implementation (middle), to management options (right). See text for discussion of what each stage might entail

6.6

A Model Template for Applications

The sheer volume of information—theoretical, empirical, and technological— related to metapopulations is more than a little daunting. Here we collate some of this information into a generic template for applications (Fig. 6.11). As with previous templates, the task is to articulate the relevant details. In this case, the template is intended to guide considerations of issues that would lead to the adoption of a metapopulation approach in a particular application.

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Metapopulations are defined by local differences in habitat quality and connectivity (Fig. 6.11, left). Habitat quality affects fecundity or survival, which in turn influences the source/sink status of local populations (Sect. 6.2.3). Local population dynamics (birth vs death rates) and population size determine relative extinction risks. Connectivity depends on structural and functional connectivity (including dispersal behavior) as this contributes to the likelihood that local extinctions are recolonized or prevented via dispersal subsidies. Each of these considerations might be informed by expert opinion or (ideally) supported by field-based measurements. Information about habitat condition and connectivity support a litmus test to gauge whether a focal species might be represented as a metapopulation (Fig. 6.11, middle panel). This invokes Hanski’s criteria (Sect. 6.3.1), though perhaps more loosely or generously then he originally intended. Thus, a landscape might support a metapopulation if habitat exists in more-or-less discrete patches, with local extinction possible for most patches, and recolonization feasible (perhaps based on a macroscopic scale-matching consideration, Sect. 6.3.2). While metapopulations in theory are asynchronous in their dynamics, in real systems we would expect some synchronization by regional weather or large-scale disturbances (e.g., Moilanen et al. 1998); this does not mean that the metapopulation concept cannot be applied usefully. Management alternatives depend on whether habitat or connectivity is most limiting in a given application (Fig. 6.11, right panel). If habitat area or quality is limiting, then management aimed at increasing or improving habitat is recommended. If connectivity is limiting, then management would focus on managing the matrix rather than the habitat itself. In any case, given the uncertainty typical of such applications, management interventions should be implemented as experiments, so that we can monitor and assess the efficacy of the treatments.

6.7

Summary and Conclusions

Metapopulations are clearly an intuitive and compelling construct for ecologists. There is a substantial body of theory on the topic, and several models provide reasonably consistent suggestions of what we might expect to observe of real metapopulations. That we have some but not an overwhelming number of empirically documented cases suggests that metapopulations do occur in nature. That there are not more well-documented cases is perhaps due to the strict empirical demands for establishing such cases, rather than the likelihood of their existence. Graph-based models of metapopulations have surged in popularity, partly because of the intuitive conceptual fit and partly because of advances in software availability. There is a great deal of practical guidance available to landscape ecologists, which can be borrowed from other disciplines concerned with general issues of flow, connectivity, and network structure. Landscape ecologists should be more deliberate in adopting these tools to our applications.

References

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Applications focusing on connectivity will only become more common as they are applied in conservation, land use planning, and adapting to climate change. We have the ability and opportunity to improve these models with better data and a better understanding of how real populations respond to landscape heterogeneity and pattern. There remains a rather large gap between theory and application in metapopulation ecology. New data sources on habitat pattern from high-resolution remote sensing platforms, new methods to record movement and dispersal outcomes via telemetry, and new sources of information on the genetic structure of populations on spatially structured landscapes should bolster rapid advances in metapopulation theory applied to real systems. This could aid a reconciliation of theory and practice. Empirically based network models, well informed by relevant theory, should contribute to our ability to adapt population ecology to respond to increasing landscape heterogeneity and climate change.

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Schwartz, M.K., J.P. Copeland, N.J. Anderson, J.R. Squires, R.M. Inman, K.S. McKelvey, K.L. Pilgrim, L.P. Waits, and S.A. Cushman. 2009. Wolverine gene flow across a narrow climatic niche. Ecology 90: 3222–3232. Segelbacher, G., S.A. Cushman, B.K. Epperson, M.-J. Fortin, O. Francois, O.J. Hardy, R. Holderegger, P. Taberlet, L.P. Waits, and S. Manel. 2010. Applications of landscape genetics in conservation biology: Concepts and challenges. Conservation Genetics 11: 375–385. Sjögren, P. 1991. Extinction and isolation gradients in metapopulations: The case of the pool frog (Rana lessonae). Biological Journal of the Linnean Society 42: 135–147. Smith, M.A., and D.A. Green. 2005. Dispersal and the metapopulation paradigm in amphibian ecology and conservation: Are all amphibian populations metapopulations? Ecography 28: 110–128. Sork, V.L., S.N. Aitken, R.J. Dyer, A.J. Eckert, P. Legendre, and D.B. Neale. 2013. Putting the landscape into the genomics of trees: Approaches for understanding local adaptation and population responses to changing climate. Tree Genetics & Genomes 9: 901–911. Spear, S.F., N. Balkenhol, M.-J. Fortin, B.H. McRae, and K. Scribner. 2010. Use of resistance surfaces for landscape genetic studies: Considerations for parameterization and analysis. Molecular Ecology 19: 3576–3591. Storfer, A., M.A. Murphy, J.S. Evans, C.S. Goldberg, S. Robinson, S.F. Spear, R. Dezzani, E. Delmelle, L. Vierling, and L.P. Waits. 2007. Putting the ‘landscape’ in landscape genetics. Heredity 98: 128–142. Taylor, P.D., L. Fahrig, K. Henein, and G. Merriam. 1993. Connectivity is a vital element of landscape structure. Oikos 68: 571–573. Temple, S.A., and J.R. Cary. 1988. Modeling dynamics of habitat-interior bird populations in fragmented landscapes. Conservation Biology 2: 340–347. Thomas, C.D., M.C. Singer, and D.A. Broughton. 1996. Catastrophic extinction of population sources in a butterfly metapopulation. The American Naturalist 148: 957–975. Thurfjell, H., S. Ciuti, and M.S. Boyce. 2014. Applications of step-selection functions in ecology and conservation. Movement Ecology 2: 4. Tischendorf, L., and L. Fahrig. 2000a. On the usage and measurement of landscape connectivity. Oikos 90: 7–19. ———. 2000b. How should we measure landscape connectivity? Landscape Ecology 15: 633–641. Trainor, A.M., J.R. Walters, W.F. Morris, J. Sexton, and A. Moody. 2013. Empirical estimation of dispersal resistance surfaces: A case study with red-cockaded woodpeckers. Landscape Ecology 28: 755–767. Turner, M.G., G.T. Arthaud, R.T. Engstrom, S.J. Hejl, J. Liu, S. Loeb, and K. McKelvey. 1995. Usefulness of spatially explicit population models in land management. Ecological Applications 5: 12–16. Urban, D.L., and T.H. Keitt. 2001. Landscape connectivity: A graph-theoretic perspective. Ecology 82: 1205–1218. Urban, D.L., and H.H. Shugart. 1986. Avian demography in mosaic landscapes: Modeling paradigm and preliminary results. In Modeling habitat relationships of terrestrial vertebrates, ed. J. Verner, M.L. Morrison, and C.J. Ralph, 273–279. Madison: University Wisconsin Press. Urban, D.L., H.H. Shugart, D.L. DeAngelis, and R.V. O’Neill. 1988. Forest bird demography in a landscape mosaic, ORNL/TM-10332, ESD Publ. No. 2853. Oak Ridge: Environmental Sciences Division, Oak Ridge National Laboratory. Urban, D., E. Minor, E. Treml, and R. Schick. 2009. Graph models of habitat mosaics. Ecology Letters 12: 260–273. USDI Fish and Wildlife Service (with 14 primary authors). 1995. Recovery Plan for the mexican spotted owl (Strix occidentalis lucida). Albuquerque: U.S. Fish and Wildlife Service. van Horne, B. 1983. Density as a misleading indicator of habitat quality. Journal of Wildlife Management 47: 893–901. van Langevelde, F. 2000. Scale of habitat connectivity and colonization in fragmented nuthatch populations. Ecography 23: 614–622.

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Chapter 7

Communities and Patterns of Biodiversity

7.1

Introduction

At the landscape scale, patterns in species diversity are governed by spatially structured environmental constraints, interspecific interactions, spatial processes such as dispersal, and chance. As with metapopulations, these patterns arise in part because of spatial heterogeneity in habitat type or quality as well as the possible coupling of habitats via dispersal or other spatial processes. Thus, metacommunities inherit substantially from metapopulations (Chap. 6) while adding interactions among the multiple species that comprise communities. As with metapopulations, metacommunities have a multi-threaded history in ecology, with several overlapping lineages or traditions. One lineage is more observational, deriving from the incidence tallies of island biogeographic theory but evolving to focus on observed patterns of species occurrences: community assembly rules. Another tradition is metacommunity theory itself, which focuses on the processes that generate patterns that we might observe of communities. A third lineage is more statistical and aims at partitioning the relative explanatory power of environmental factors as compared to spatial signals in community-level datasets. This approach is firmly rooted in gradient analysis, a long tradition in community ecology and one that has more recently evolved to embrace space. Finally, habitat suitability modeling has long focused on the environmental correlates of species distributions; these techniques have been extended to attend covariances among multiple species and to include spatial predictors. In this chapter we consider the logical basis for assessing the relative importance of the factors or processes that govern metacommunities, and we probe the lineages of metacommunity ecology, seeking evidence and common insights. We focus on candidate processes or mechanisms that we might expect to observe in real

Supplementary Information The online version contains supplementary material available at https://doi.org/10.1007/978-3-031-40254-8_7. © Springer Nature Switzerland AG 2023 D. L. Urban, Agents and Implications of Landscape Pattern, https://doi.org/10.1007/978-3-031-40254-8_7

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communities and how we might account for these empirically. We begin with a historical perspective, in which island biogeographic theory at first enchanted terrestrial landscape ecologists and then motivated the adoption of alternative approaches that now characterize the discipline.

7.2

Island Biogeography and Landscapes

The theory of island biogeography (MacArthur and Wilson 1963, 1967) launched an industry aimed at documenting patterns of species richness in habitat islands of various sizes and distance to the mainland. The two key relationships in the model— that extinction rates increase while colonization rates decrease with increasing species number—led to the fundamental empirical observations expected of islands: 1. Large islands should have more species than small islands because the larger populations on large islands would be less likely to suffer stochastic extinctions. 2. Islands farther from a species-rich (mainland) source should have fewer species for their sizes because of lower colonization rates (Fig. 7.1). MacArthur and Wilson noted in the introduction to their book that the theory would likely be applicable to terrestrial habitat “islands” isolated in a sea of other land covers, and it was not long before these studies proliferated. Area effects, of

Small

Far

Large

Rate

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Number of Species Present, N

Fig. 7.1 Predictions of island biogeographic theory, in terms of how extinction and colonization rates vary for islands of varying size and distance from source. Equilibrium species number S occurs at the intersection of the extinction and colonization curves: “small/far” islands are more depauperate, while “large/near” islands support more species. (Redrawn with permission from John Wiley & Sons, from MacArthur and Wilson 1963); permission conveyed through Copyright Clearance Center, Inc.)

7.2

Island Biogeography and Landscapes

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course, were not difficult to find. Isolation effects, though less common, were also documented for at least a few systems. The book Forest Island Dynamics in Man-Dominated Landscapes (Burgess and Sharpe 1981), a compendium of studies of habitat islands, is a good illustration of the state-of-the-science at that time.

7.2.1

Area and Isolation Effects

Area effects are relatively easy to come by in ecology, and there is no shortage of studies that have documented an increase in species richness with increasing patch (island) size (Connor and McCoy 1979; Lomolino 2000) (Fig. 7.2). Isolation effects were not as easy to document in terrestrial habitat islands, but common enough to encourage the application of island theory to terrestrial habitat patches in mosaic landscapes. For example, MacClintock et al. (1977) found lower bird species richness in isolated forest patches. (Recall that the correlation between area and isolation might confound these cases, as discussed in Sect. 5.5.3.) An important result of this era of studies motivated by the predictions of island theory is that many conservation-minded researchers had to embrace the larger implications of this work. As island theory makes predictions about species number—not about which species should be present on an island—researchers interested in species-level responses found less support in the theory. For example, Whitcomb et al. (1981) noted that the species-area relationship varied substantially for forest birds that were habitat generalists, forest interior specialists, or edge species; area-sensitivity also varied according to migratory strategy, with neotropical 35 30 Number of Bird Species

Fig. 7.2 Species-area relationship for forest birds in woodlots of Cadiz Township, southern Wisconsin (Fig. 5.4) (unpublished data from Urban et al. 1988). Note log-linear relationship

25 20 15 10 5 0 -0.5

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migrants being more area-sensitive. At the same time, the effects of habitat degradation—especially edge effects of nest predation and brood parasitism— were implicated as causes of apparent area sensitivity in some forest birds (e.g., Gates and Gysel 1978; Brittingham and Temple 1983; Wilcove 1985). Further, it became increasingly clear that the spatial context of terrestrial habitat islands was important—that edges and the navigability of intervening land covers between habitat patches really mattered to species distributions. In short, island biogeography was largely abandoned as a theoretical framework for terrestrial habitat patches, and landscape ecology moved on (Laurance 2008). Island biogeographers interested in individual species turned to species-specific incidence functions to assess patterns of occupancy across islands of varying size (Diamond 1975a), and this path led ultimately to the incidence function model of metapopulations (Hanski 1994, 1998, 1999; and recall Sect. 6.2.4). Landscape ecologists focused more explicitly on the ecology underlying area and isolation effects, including the role of habitat heterogeneity in explaining patterns in species diversity (e.g., Freemark and Merriam 1986). This latter emphasis has evolved into an effort to assess the relative importance of habitat features as compared to spatial processes (especially dispersal) in explaining local species diversity. This effort continues and is the focus of active methodological developments. Predation, brood parasitism, and competition are interspecific biotic interactions—which leads us from metapopulations to metacommunities.

7.2.2

Island Biogeographic Theory and the SLOSS Debate

It was not long before island theory was applied to conservation science and management (Fig. 7.3). This proved surprisingly contentious, with the main debate revolving around the practical question: Which is better, a single large or several small reserves? This so-called SLOSS debate turned out to be complicated on several fronts, not the least being that island theory does not explicitly make many of the predictions implicit in the reserve design rules attributed to it (Simberloff and Adele 1982; Soulé and Simberloff 1986). The answer to the SLOSS question was, perhaps unsurprisingly, “It depends.” Fahrig (2020) has provided an intensive review of the SLOSS debate, especially relative to conservation interests. She explored the evidence for several hypotheses put forward to explain SLOSS and evaluated the evidence from field studies. The weight of evidence is that several small patches tend to support more species than a single large patch of the same area. Of the several explanations put forward, an intuitive explanation is that small patches tend to support different species among themselves, and so they collectively support more species than a single large patch. (By contrast, a single large patch would support more species if all of the small patches had the same, redundant species.) For small patches to support different species assemblages, the assemblages must be spatially heterogeneous. This would happen, readily enough, due to spatial structure in the environment, which would

7.2

Island Biogeography and Landscapes

Fig. 7.3 “Predictions” of island biogeographic theory as applied to the design of nature reserves. In each row, the design on the left is preferred to the design on the right. The second row (B) motivates the SLOSS debate. (Redrawn with permission from Elsevier, from Diamond (1975b, which was modified from Wilson and Willis 1975))

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provide for different habitats among a set of small patches arrayed along an environmental gradient. The same result would accrue, even if the environment were rather homogeneous, if species tended to be spatially structured through demographic or other processes. There is an abundance of evidence for spatial structure in the environment (recall Sect. 4.4) and for spatial structure in species composition. In particular, compositional similarity tends to be spatially structured, yielding a general trend for a distance-decay of similarity: sites close together tend to be compositionally similar, while sites farther apart tend to be less similar with increasing distance (Necola and White 1999; Soininan et al. 2007). Applied to conservation, Wiersma and Urban (2005) used this spatial structure to suggest a spacing of reserves that would tend to capture different species, so that species could be represented as efficiently as possible in a reserve system. More interesting, in retrospect, is the way that the SLOSS debate refocused attention on the distinction between the predictions of island biogeographic theory and the aims of conservation practice: island theory makes predictions about species richness, and in this all species are equal; conservation is interested in species richness, but differences among species are interesting (and some species—rare ones—might be more interesting than others). That is, we care about which species are present and why. And that has made all the difference, in landscape ecology.

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A Diversity of Diversities

A more important consequence of the movement of landscape ecology away from island theory is the more recent focus of attention on collections of patches as functional entities, as an extension of studies of collections of patches considered individually. There are two important threads in this evolving discussion. First, the realization that individual species might respond individualistically to area and isolation invited a species-specific focus of analysis. In a sense, the failure of island theory to adequately address individual species opened the door for metapopulation theory, which addresses explicitly the response of a single species to habitat area, geometry, and isolation. Metapopulation theory had been around, at least in concept, for decades by this time—but its emergence into practical applications required the timely attention on species-level distribution patterns and the absence of a readily available context for this research; the incidence function model of metapopulations (Sect. 6.2.4) is a direct result of this conceptual evolution. The other conceptual thread that emerged from this patch-level exploration of species diversity patterns was a growing interest in how biodiversity patterns vary over space—not simply as variation among patches but as patterns in species diversity over landscapes. That is, the focus shifted from patch-level to landscapescale studies of biodiversity. Patterns of biodiversity can be examined at a range of scales, and this has led ecologists to define various scale-dependent varieties of diversity (Whittaker 1972). At the local scale, alpha (α) diversity refers to the number of species observed at a single point or within a single (small) sample. This is a tally of species, an inventory. At a larger scale, gamma (γ) diversity refers to the inventory of species observed to occur at a regional to subcontinental scale. In between—at the scale of landscapes— is beta (β) diversity, which refers to the variation in alpha diversity within the context of a bounding or regional gamma diversity (Ricklefs 1987). By contrast to the scale-dependent inventories of alpha and gamma diversities, beta is an index of the differentiation of diversity among sites (Jurasinski et al. 2009). If alpha diversity is the grist of community ecology and gamma diversity of biogeography, it seems obvious that beta diversity should be in the domain of landscape ecology. This work is emphasized here because it focuses explicitly on assemblages of patches or locations and aims to discover aggregate properties of the collections—i.e., landscapes.

7.3

Perspectives on Metacommunities

Beta diversity invites questions about differences in diversity among samples (habitat patches or discrete sample locations) over landscapes. But such general questions can lead to very different specific questions and analytic methods used to answer

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Perspectives on Metacommunities

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these questions. There is a wide range of approaches to this general theme, and they differ in their aims and their methods. Before delving into these perspectives, it will be useful to frame the discussion more broadly.

7.3.1

A General Framing

As context, let us begin by acknowledging that many different factors might contribute to community structure and patterns in local biodiversity within landscapes. Broadly writ, ecology is about the relationships between organisms and their abiotic (biophysical) and biotic (i.e., among themselves) environment. This spans all of community ecology and much of ecology in general, and it is by no measure a monolithic, unified discipline. At the simplest level, spatial heterogeneity in the physical template of landscapes provides suitable habitat for different species at different locations. For plants, this would include the sorting of species along abiotic gradients in temperature, moisture, and fertility (Chaps 1 and 2). For animals, this might be the same (e.g., for ectothermic species that respond to the environment physically). Other animals (birds, mammals) might respond to vegetation structure or composition as potential habitat, with the vegetation itself reflecting the underlying abiotic gradients. In general, the focus here is environmental filtering or sorting, and this invokes niche theory and other perspectives on how species relate to or partition their shared environment (recall MacArthur’s work with birds featured in Chap. 4, Sect. 4.2.1). In terms of analytic approaches, a focal-species perspective would resort to species distribution models (SDMs) or other models of species-environment relationships. The community-level approach has long been to relate trends in species composition to environmental factors, and the general tool is ordination (recall Fig. 1.1, but the tools have evolved substantially over time!). Environmental filtering, as gradient response in vegetation, implicitly or explicitly invokes interspecific competition as a biotic interaction that mediates speciesenvironment relationships (Chap. 2, Sect. 2.4). At the community level, such interactions might also include trophic relationships (e.g., predator-prey relations) or positive interactions such as facilitation (where the presence of one species creates a more favorable environment for another species) or mutualism (where interactions between species are positive in a direct way, not mediated by the physical environment). If discrete locations across the landscape are coupled by dispersal, then there might be a spatial signal in species-environment relationships beyond that induced by the spatial structure of environmental factors. In particular, the effects of local dispersal might manifest as spatial structure in species composition that is evident even after accounting for local environmental effects (Chap. 2, Sect. 2.5). That is, there might be a stronger species-environment correlation because this is amplified by local dispersal; or this correlation might be weakened because dispersal is limited

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(and so species adapted to a site might not be able to get to it) or because species not well adapted to the site are present because of a dispersal subsidy from nearby (a mass effect, Sect. 2.5, or source/sink dynamics, Sect. 6.2.3). It should be underscored here that these processes—competitive sorting along gradients, perhaps amplified by local dispersal—are the processes that we considered in Chap. 2 as biotic agents of pattern. It is exactly these same processes that mediate species response to pattern. The distinction (and it is an arbitrary one!) is that as agents of pattern, we were concerned with the evolution of rather macroscopic aspects of pattern—the stuff we see in the distance while looking out a window. This typically applies to steep gradients and species response that manifests as banding or zonation in vegetation. At a finer grain and more subtly, these same processes govern local composition and structure of communities, at a level that might not be visible from afar but which manifests readily in studies of community composition. The preceding applies to continuous gradients over landscapes, as represented by sample locations stratified over the gradients. But most landscapes are not intact but rather are fragmented by local conversions of natural habitat into other land covers and land uses. This adds another level of pattern to this discussion. In particular, fragmentation results in remnant patches of natural or semi-natural vegetation separated by other land cover types. This means that each patch will represent a limited sample of the underlying environmental gradients, which sample will depend on patch size as well as location along the gradient(s) (e.g., upland versus bottomland). Similarly, dispersal or other spatial processes will depend on distance but also the nature of the intervening matrix. And species interactions might be among species in the same or similar habitat patches, or these might involve species from different habitats put in proximity because of habitat fragmentation. Finally, ecological processes are often stochastic, and so there is an element of chance to many observed patterns. In explanatory models (e.g., regressions), this chance element is typically relegated to the residual error term: it is variation that is not explained by the other main effects in the model (e.g., environmental factors or spatial factors). But ecologically, this is not “error”: stochastic events are valid contributors to ecological outcomes. To sum up, community ecology at the landscape scale invokes, in the simplest case of a semi-natural landscape, an explanatory model that includes environmental filtering, spatial process (especially dispersal), biotic interactions, and chance. In a landscape shaped by human land uses, we might add patch-level factors such as area or geometry (including edge effects) and perhaps some additional nuance in dispersal (Fig. 7.4).

7.3.2

Inferences and Limits to Inference

Because there are several factors that might contribute to community structure or patterns of diversity at the landscape scale, the question is not, “Does this factor matter?,” but rather, “What is the relative importance of these factors?.” This

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Perspectives on Metacommunities

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Fig. 7.4 A conceptual framing for metacommunities, in terms of the processes that define them Top panel: An environmental gradient defined by topography and soils. Forest communities (here, as tree species of various shapes and colors) sort along that gradient in terms of, e.g., relative soil moisture. The interactions are indicated by arrows: browns, environmental constraints on species; green, interspecific interactions (e.g., competition); solid gray, local dispersal; and dashed gray, longer-distance dispersal Bottom panel: The same, but with the vegetation patches fragmented by other land covers. The same arrows apply, but we now add the effects of patches on the sampling subsets of the gradient and the related area effects, plus possible edge effects (orange), and perhaps some additional influences on dispersal (gray)

becomes a sort of multiple regression problem, and the inferential approaches (there are several) share some basic elements. Details of the various approaches are considered later. The importance of environmental constraints is typically estimated by using environmental factors to predict (in a regression sense) the distribution of one or more species. For single species, one approach is species distribution models; for multiple species at once, these become joint species distribution models. Another approach is to use ordinations, which summarize patterns of association among species. If the ordination is constrained to be expressed in terms of environmental variables, then the solution estimates the explanatory power of the environmental variables to account for observed species distributions. In either case, the variability in species distribution not attributable to environmental factors includes some due to chance. It is possible (even likely) that the residual variation in species distribution that cannot be attributed to the environment is itself spatially structured or autocorrelated. That would be evidence of a spatial process such as dispersal at work, beyond the effects of the environment (which is also spatially structured). But as much as we

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might like to attribute that residual spatial signal to dispersal, that is only one of the alternatives. The residual spatial structure could be due to an important but unmeasured environmental factor (also spatially structured). Or it could be due to shared (but unobserved) history, such as a prior disturbance event (e.g., fire or contagious pest or disease). In practice, we cannot attribute the spatial signal unless the underlying factor is measured. Similar inferential difficulties emerge with interspecific interactions. What we observe is positive or negative associations or covariances between pairs of species. These could be due to positive interactions (mutualism, facilitation) or negative interactions (predation, competition). These also could be due to joint species response to the same environmental factors (positive or negative). If the effects of environmental factors are controlled (e.g., via partial regression), then any residual covariation among species could be the expression of interspecific interactions. But these could also be due to joint species response to an unmeasured environmental factor. In short, we cannot make inferences about factors that we have not measured. As we cannot measure everything, this might lead to some frustration because of the uncertain nature of inferences we can make. This invites two responses. The first is to rely on multiple lines of evidence in applications, to seek consensus or complementary insights. The second is to be patient and to invest in the process of discovery. This implies a sequential or recursive approach that focuses on identifying the scale(s) of residual spatial signal in the system, once the measured factors have been accounted. This approach provides a great deal of leverage in trying to interpret communities. Following the logic of McIntire and Fajardo (2009), this approach makes it easier to ascribe observed patterns to known (measured) factors and to identify the scale(s) and relative importance of unknown factors. This then invites new hypotheses about the unknown factors, which might lead to new field measurements that would help resolve the uncertainties (Dray et al. 2012). This approach, in turn, is perfectly consistent with the advice of Levin (1992) in his seminal lecture on how we should think about scale and pattern.

7.4

Approaches and Lines of Evidence

Our conceptual model for communities invokes several nonexclusive explanatory factors or processes. Nobody in ecology attends all of these factors at once. Everybody in ecology attends some of these factors. The challenge in community ecology is to try to determine the relative importance of these factors. And because nobody currently addresses all of them at once, that means that we must rely on inferences from multiple, complementary approaches. The various approaches to community ecology on landscapes can be roughly categorized relative to how they deal with the processes or mechanisms implied by the arrows in Fig. 7.1 (Table 7.1). There are several bodies of work on this general

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Approaches and Lines of Evidence

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Table 7.1 A catalog of various approaches or traditions in community ecology Focus on SPP × . . . Geometry SPP (geometry) SPP SPP, ENV (chance) ENV, space (chance) SPP, ENV, space, chance ENV (chance) ENV, SPP (chance) ENV, SPP, space (chance) Space (chance) ENV, space (chance)

Approach (targeted processes) Island biogeography (IBT) (area vs. isolation) (IBT) Incidence functions/assembly rules SPP ordination SPP ordination constrained with ENV SPP ordination with ENV + spatial predictors Various metacommunity models (focus varies) Species distribution models (SDMs, single species) Joint SDM (multiple species) Joint SDM with ENV + spatial predictors Landscape genetics (neutral markers) Landscape genomics (neutral, selected markers)

Abbreviations are explained below (in text)

theme. These are not exclusive approaches but will serve to add heft and detail to the general outline we have framed. In the following sections, we touch briefly on several disciplinary approaches, emphasizing the process(es) each addresses. We will delve a bit more deeply into an approach based on ordinations—in part, to pick up a thread begun in Chap. 1 and also to illustrate the evolution of this approach to its current practice. We close by collecting terms and recommending a general strategy for managing communities distributed over landscapes. In the table, all applications are concerned with patterns among species (SPP). ENV refers to environmental factors associated with species distributions (i.e., SPP × ENV). SPP refers to among-species patterns (i.e., a focus on SPP × SPP). Geometry refers to area, isolation, or edge effects (mostly from island biogeographic theory and follow-on approaches). Space refers to explicit focus on locational or distance effects. Chance refers to unassignable, random processes. Factors in parentheses indicate that the effect is estimated indirectly (e.g., as residuals from a regression model). For example, most regressions attribute unstructured residual variation (model error) to chance. The various approaches are summarized and illustrated in the next few sections. Additional details are provided in Supplement S7.1.

7.4.1

The Incidence Matrix and Community Assembly

In the same monographic chapter in which Diamond (1975a) introduced incidence functions, he posed a set of community assembly rules. Diamond noted that on his sets of islands, there were fewer observed combinations of species co-occurrences than might be expected. He posited that these combinations were resistant to invasion by other species that would render them “forbidden combinations.” Similarly, he observed that some pairs of bird species might be common but rarely

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occurred together. The presumption was that competition prevented the species from co-occurring, with the implication that patterns of species occurrence would then manifest as “checkerboards” indicated by the presence of one or the other species but not both. The checkerboard would be evident in a tally of species presence/absence (1/0) per site (island), in an incidence matrix. His incidence functions also played into assembly rules, expressing likelihoods of species occurrence in terms of species number (or equivalently, island size). Forbidden combinations and checkerboards invoke competition or other interspecific interactions as underlying mechanisms, but these patterns are purely observational; the processes are not observed directly. Diamond’s initial analysis has launched an enormous literature (reviewed by Gotelli 1999, 2000; Gotelli and McCabe 2002; see also Gotelli and Graves 1996 and Weiher and Keddy 1999). There were two main threads to the argument: What patterns might we expect, and why? And in terms of mechanics: How might we best test these predictions? What is the null model? Research on assembly rules continues today but has come to focus on a few key patterns, the elements of metacommunity structure (Liebold and Mikkelson 2002) (see Supplement S7.1.1). Gotelli and McCabe (2002) performed a meta-analysis of 96 datasets to evaluate the weight of evidence for Diamond’s assembly rules. They focused on forbidden combinations and checkerboards, as well as an index of checkerboards integrated over all species. They found that observational studies supported assembly rules: there were fewer species combinations observed than expected and more checkerboards (and the synthetic integration of checkerboards) than expected by chance. Effects were larger for homeotherms (and ants!) and for vascular plants. It should be emphasized here that metacommunities cannot be interpreted based solely on observed patterns. A focus on process complements this interpretation. And it is also important to note that space itself (i.e., geography or spatial process) is not explicit in the patterns posed as assembly rules. The spatial perspective is more explicit in the perspectives of generative metacommunity models and in partitioning beta diversity (below).

7.4.2

Metacommunity Models: Variations on a Theme

By contrast to assembly rules that focus on empirical patterns, metacommunity theory has mostly focused more on generative processes. This focus defines recent efforts in metacommunity ecology, but its roots extend well back into ecology to include seminal explorations of the role of patchiness or dispersal in mediating predator-prey or competitive interactions. Theory and empirical applications have been reviewed by Schmida and Wilson (1985), Liebold et al. (2004), Holyoak et al. (2005), and Logue et al. (2011); Liebold and Chase (2017) have provided an in-depth synthesis. Liebold et al. (2022) have recently attempted to generalize this approach in terms of included processes, following the synthesis provided by Vellend (2010, 2016).

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ce s valen Equi g Specie n Amo Neutral Theory Patch Dynamics Mass Effects Environmental Sorting

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Fig. 7.5 Locations of four themes in metacommunity research, in terms of their relative emphasis of habitat heterogeneity, dispersal, and the equivalence of species. (Redrawn with permission from Elsevier, from Logue et al. (2011))

While metapopulations in theory might encompass all aspects of metapopulation dynamics plus interspecific interactions, in practice there have been a few approaches that put more or less emphasis on different mechanisms. One natural division in this variety of approaches depends on the definition of community and the interspecific interactions considered. In some instances, communities are vertically integrated and include trophic interactions (especially predator-prey relations); the analytic framework is food webs. In other cases, the community is more horizontal, and the dominant interaction is competition (e.g., among forest birds). The former, as it deals in the currencies of energy and biomass, is more strongly aligned with ecosystems ecology, and we will revisit this in Chap. 8. There are multiple threads of work on metacommunity themes. Liebold et al. (2004) categorized these into four thematic approaches: (1) patch dynamics, (2) species sorting or environmental filtering, (3) mass effects, and (4) neutral theory (see Supplement S7.1.2 for details). Logue et al. (2011) characterized these four modeling approaches as domains within a space defined by habitat heterogeneity, dispersal capacity, and equivalence among species (Fig. 7.5). Winegardner et al. (2013) emphasized that three of these are variations on the same theme—the interaction between dispersal and environmental heterogeneity—while neutral theory is distinguished by its assumption of functional equivalence of species. Thus, in cases where species differ in their competitive ability under varying environmental conditions and habitat patches vary in terms of environment, environmental filtering and mass effects are

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distinguished by the relative strength of dispersal. Liebold and Chase (2017) used the terms dispersal constraint, sufficiency, and surplus to emphasize this relationship, with species sorting requiring sufficient dispersal and mass effects emerging where there is surplus dispersal. Where patches are rather equivalent environmentally, local extinctions and recolonizations (i.e., patch dynamics) rule. In principle, these alternative models could be competed, using field observations to arbitrate among the models. Liebold and Chase (2017) have synthesized evidence from observational studies and manipulative experiments. They found at least some empirical support for each of the models, for taxa ranging from protists to plants to vertebrates. But in reality the models are not exclusive, as they differ in the relative importance of the same underlying processes or mechanisms. So the proper question is not one of model selection—Which model fits best?—but rather: What is the relative importance of these mechanisms? This is the perspective of partial regression in general, to which we now turn with two particular and complementary approaches.

7.4.3

Species Distribution Models

Species distribution modeling (SDM) is a fundamental task in accounting for the distribution of a focal species, and the tools of the trade are very well developed (Guisan and Zimmerman 2000; Elith et al. 2006; Elith and Leathwick 2009; Franklin 2010; Pearson 2010; Guisan et al. 2013) (see Supplement S7.1.3). In the context of metacommunities, this task amounts to dissecting the relationship between species distributions and a set of environmental variables—a particular perspective on environmental filtering. Although the details depend on the specific technique, one general result of fitting an SDM is the summary estimate of the explanatory power of the model. This is essentially an estimate of the strength of environmental filtering for the focal species. Variation not explained by the environmental predictors is model error and typically ascribed to chance (but see below). In many landscape-scale applications, an SDM is based on geospatial environmental predictors and so can be mapped explicitly (i.e., in a GIS). This provides a visual means of interpreting spatial patterns in predicted habitat due to the spatial structure of the environmental variables. For example, the effects of elevation or topography would be evident in the map of predicted “habitat.” Overlaid with known locations of the focal species, this approach can also reveal sites that are predicted to be habitat but where the species has not been observed (false positives), as well as sites where the species was observed but which were not predicted to be habitat (false negatives) (Pearson 2010). These misclassifications are model errors—but they also are cases that are interesting in their own right. A false positive could be the result of dispersal limitation (habitat unoccupied because of isolation). A false negative could be the result of a strong dispersal subsidy from a nearby source habitat as predicted by Pulliam’s (1988) source-sink metapopulation

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model (Chap. 6, Sect. 6.2.3), a mass effect. That is, this approach can provide insight not only into the role of the environment but also of spatial process. SDMs that can be mapped can also provide some insight into the influence of unmeasured environmental predictors. For example, if model errors can be visually associated with topographic features (hilltops, stream channels), this might suggest factors that could be added to the model to improve its performance. SDMs clearly aim at interpreting the environmental effect on species distribution. There are some challenges in capturing the role of local interspecific interactions on species distributions modeled at the regional scale (Wisz et al. 2013). But SDMs can be extended to address, at least indirectly, interspecific interactions and spatial structure. SDMs have been modified to incorporate spatial structure, but this typically has been to account for relatively local autocorrelation in the distribution of a species rather than spatial processes such as dispersal. Keitt et al. (2002) reviewed several approaches and found that adding spatial structure generally improved model performance—with the qualitative addition of space itself more important than the details of how spatial structure is implemented.

7.4.3.1

Joint Species Distribution Models

Species distribution models can be extended to consider multiple species at once, a joint SDM (JSDM; Clark et al. 2014, 2017; Pollock et al. 2014; Warton et al. 2015; Ovaskainen et al. 2016, 2017, 2019). In a JSDM, multiple species are fitted simultaneously while explicitly attending to between-species covariation. It would be really satisfying if JSDMs could actually estimate interspecific interactions; but these models are based on covariation or correlation and so can only reveal patterns of joint occurrence or abundance (or lack thereof). Still, JSDMs can provide rich insights into community patterns. In particular, when applied to communities of species, JSDMs tend to perform better than a collection of “stacked” single-species SDMs (which tend to overpredict species richness). Clark et al. (2020) extended their JSDM to include time series observations. This allows the discovery of interspecific interactions mediated by the environment, such as competitors whose interaction is amplified under drought. In terms of logical inference, time series data offer an important bit of leverage: the role of antecedent conditions. In this, a change in the response of one species after the change in another species—while controlling for environmental factors—provides stronger inference about interspecific interactions. JSDMs can also be estimated using explicitly spatial predictor variables (e.g., Ovaskainen et al. 2016, 2019). The technical details can be a bit daunting, and we defer this to the following section. It might be noted here, however, that a joint SDM with environmental and spatial predictors as well as time-varying species abundances would provide the strongest inferential leverage—short of manipulative experiments—on separating environmental constraints, species interactions, and spatial signals. This model does not yet exist (but it almost certainly will soon!).

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Multivariate Approaches to Partitioning Beta Diversity

Another approach to beta diversity is to try to explain it in terms of the relative explanatory power of predictive factors, a partitioning. In this, the primary aim is to separate the effects of environmental constraints on species as compared to spatial processes such as dispersal. That is, this is another statistical approach to the same elements that are the focus of assembly rules, metacommunity models, and joint species distribution models. This can be set up as a regression problem, initially. We are interested in predicting species abundances and have a set of environmental variables as predictors. The aim is to add spatial processes as additional predictors. The difference here is that the approach is based on many measured variables— multiple species, multiple environmental variables, and spatial predictors. There are two analytic approaches.

7.4.4.1

Partitioning on Distance Matrices: Mantel Tests

One way to introduce space into a regression framework is to convert the data into the form of distance or dissimilarity matrices. This converts a dataset with N samples (rows) into an NxN matrix of pairwise dissimilarities between samples. For example, from geographic sample locations, it is straightforward to construct a matrix of Euclidean distances between samples; more nuanced distances also could be used (e.g., least-cost path distances: Sect. 6.4, Fig. 6.6). Similarly, there are many options to compute indices of ecological dissimilarity from species compositional or environmental variables (reviewed by McCune and Grace 2002; Legendre and Legendre 2012). Mantel’s test (Mantel 1967; Legendre and Fortin 1989) is a correlation between two distance or dissimilarity matrices. This is the basis, for example, for the “distance decay of similarity” (Nekola and White 1999; Soininen et al. 2007) in which samples located at increasing distance from a reference site are decreasingly similar ecologically. This also yields the “isolation by distance” effect as used in landscape genetics (Wright 1943, Sect. 6.5.2). This test can be extended to multiple distance matrices using partial correlation or regression (Smouse et al. 1986). In this, the partial effect of one dissimilarity matrix is estimated as its explanatory power in a correlation with the residuals of a regression on another matrix. For example, Urban et al. (2002) used partial Mantel tests to distinguish environmental variables from (residual) spatial structure for forests of the southern Sierra Nevada in California (the system featured as a running example in Chaps 1, 2, and 3, and see below). Their results suggested that residual spatial effects were stronger than environmental effects in that system. Mantel tests have some limitations. Nonlinearities can degrade the correlations, a problem that can be partially addressed by truncating (Ferrier et al. 2007) or ranktransforming the distances (Goslee and Urban 2007). Mantel tests are also averaged over all distances, which means that they cannot resolve the particular scale(s) of any

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relationships between the matrices. This problem can be solved by using a Mantel correlogram, in which the correlations are evaluated within discrete distance classes; partial Mantel correlograms are also available (Goslee and Urban 2007). A more significant problem with the Mantel test is that it tends to have a lower power relative to other analytic approaches (Legendre and Borcard 2005; Legendre and Fortin 2010; Legendre et al. 2015). This problem cannot be solved easily, and so Mantel tests are no longer the preferred approach to partitioning beta diversity (but see Somers and Jackson 2022).

7.4.4.2

Partitioning Using Constrained Ordinations and Spatial Predictors

The consensus approach to partitioning beta diversity currently is to use a constrained ordination with “pure spatial” predictors derived from a geographic distance matrix. The ordination component is relatively familiar territory for community ecologists: this has been a fundamental tool for many, many decades. Here we begin with the early versions of ordinations of species and then layer on the environmental and spatial elements. An ordination is a multivariate statistical tool used to reduce the dimensionality of a multivariate dataset, extracting the main trends while reducing noise (Gauch 1982; McCune and Grace 2002; Legendre and Legendre 2012). We began this book with an early example (Fig. 1.1), which was a direct ordination assembled subjectively by the investigator (Whittaker 1960) to relate species to the environment. Many alternative approaches are available now (Supplement S7.1.4). In this discussion, we focus on ordinations of species data, where the data comprise tallies of species occurrence or abundance over a set of sample locations. It will be useful here to develop ordinations in layers of complexity. A convenient starting point is an indirect ordination of the species data. In this, the ordination is used to summarize the main trends in the species data. The result of an ordination is a set of new, synthetic variables—the ordination axes—that are derived from the original species data and which capture the main trends in composition in just a few axes. This also suppresses the noise in the data, by relegating that to minor ordination axes (which are typically discarded). To be clear, an ordination of species data summarizes patterns of association among species. As with a joint SDM, this focuses on multiple species simultaneously but cannot prove direct interactions among species (though it should capture the result of these). In a constrained ordination, the ordination axes are forced to be expressed in terms of ancillary environmental variables measured at the same locations as the species tallies. Although the details vary among techniques, the basic approach is to predict species abundances, by regression, from the environmental variables and then ordinate the predicted values. The result is a summary of those compositional patterns that can be attributed to the measured environmental variables. Again, this is familiar territory for community ecologists. Relative to our discussion, this is an effort to account for environmental filtering in a compact way.

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The protocol for incorporating space into a constrained ordination is newer and evolving (Borcard et al. 1992; Borcard and Legendre 2002; Dray et al. 2006; PerosNeto and Legendre 2010). The general approach now is based on Moran eigenvector maps (MEMs: Peres-Neto and Legendre 2010; Dray et al. 2012; Borcard et al. 2018). MEMs are “pure spatial” variables extracted by multivariate reduction (ordination) of a (typically sparse) matrix of pairwise distances between samples. In most applications, these distances are computed as Euclidean (there is no reason why more nuanced estimates of functional distance could not be used). At this point, the details of the analysis become unavoidably complicated. To begin, the MEMs are extracted by principal component analysis (see Supplement S7.1.4) of the between-sample distance matrix. The principal components of a distance matrix are a bit difficult to grasp intuitively, but these components are orthogonal (linearly independent) variables that are purely spatial, representing the main sources of variation in “distances apart” among the samples. In the special case of regularly spaced samples along a transect, the MEMs manifest as sinusoidal variables of decreasing wavelengths or scales. For other sampling designs, they are less straightforward but still represent different scales. For a distance matrix of N samples, there are N MEMs, which for typical datasets is a lot of spatial information. And while the MEMs are linearly independent, there might be MEMs that are very similar in scale but differing in location or position relative to the samples (Legendre and Legendre 2012). The logic of variance partitioning is important because it has a huge impact on the task at hand, to partition the explanatory power of several environmental variables— each spatially structured at some scale(s)—and a set of “pure spatial” predictors (MEMs), which probably express spatial structure at some of the same scales. In applications, the approach is to perform a constrained ordination of the species data, using a set of environmental as well spatial predictors. To be clear: this is a multivariate regression problem using multiple response variables (species) and two sets of predictor variables (environment and space). The aim is to conduct the regression and summarize it as a constrained ordination. One approach to this task is to use forward-selection model-fitting techniques to identify all of the MEMs that are related to species composition and to compete these with the environmental variables in model selection (Dray et al. 2012). In model fitting, the forward-selection logic would include useful environmental variables (and hence their spatial structure), and MEMs would be included as needed to account for spatial structure in species composition that cannot be attributed to the environmental variables. In the end, the full model includes relevant environmental factors as well as spatial predictors, at scale(s), as needed to generate a model with spatially independent residuals (the aim of any regression, Borcard et al. 1992; Dray et al. 2006; Peres-Neto and Legendre 2010; Wagner 2013). We will explore an example of this application shortly, but (especially if these technical details are a bit daunting!) it might suffice to say here that in such applications, there is typically a substantial level of spatial information in species datasets that cannot be attributed to the measured environmental variables.

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It should also be noted here that MEMs can be used in joint species distribution models as a means of partitioning the explanatory power of the environment as compared to spatial residuals (Ovaskainen et al. 2016, 2017, 2019). The approaches are compatible and complementary.

7.4.5

Lines of Evidence and Complementary Analyses

Perhaps somewhat frustratingly, none of the analytic approaches just described can provide all of the insight we might like: assembly rules can evaluate patterns and test these against expectations from chance. Metacommunity models can pose expectations, but these are nonexclusive. Constrained ordinations or joint SDMs with spatial predictors can distinguish environmental effects from spatial structure unrelated to the environment but cannot capture interspecific interactions beyond any implicit in compositional trends or covariances among species. Inferences about interspecific interactions based on co-occurrences remain problematic (Blanchet et al. 2020). But these approaches are not competing, but rather complementary, and so they can provide richer insights when applied in combination. Cottenie (2005) used variance partitioning (partial redundancy analysis) in an analysis of 158 datasets from a variety of ecosystem types. He mapped the relative importance of the variance components to the archetypal metacommunity models: species sorting (environmental filtering) implies a significant effect of the environment controlling for space, while significant effects of the environment as well as space controlling for the environment would suggest species sorting and mass effects are both important. The neutral model and patch dynamics models are not readily distinguished in this approach, as both imply nonsignificant environmental effects and a significant spatial signal controlling for the environment. Cottenie found that nearly half (48%) of the variance was accounted by a combination of the environment and space. In terms of metacommunity models, the species sorting model was the “best fit” in 44% of the cases, while a combination of species sorting and mass effects was indicated in 29% of cases. While the neutral or patch dynamics models implied by pure spatial effects were indicated as the “best fit” model in only 8% of cases, these spatial effects were significant in 37% of the studies and thus should not be ignored in applications. Meynard et al. (2013) used variance partitioning as well as incidence-matrix approaches to examine grasslands in the French Alps. They emphasized the complementarity of the approaches; in particular, that variance partitioning can indicate the relative importance of environmental filtering, while the analyses of the incidence matrix can dissect how filtering occurs. The incidence matrix can provide richer insights into filtering patterns but cannot address the role of dispersal or other pure spatial effects. Variance partitioning addresses space explicitly but cannot provide insights into mechanism. The two approaches are nicely complementary. Legendre (2014) coupled variance partitioning to the elements of metacommunity structure (see Supplement S7.1.1), specifically isolating the

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elements of turnover (species replacement) as compared to differences in species richness (and possibly nestedness). The analyses proceed from dissimilarity indices that focus on species that are replaced between sites as compared to the richness difference between pairs of sites, with the observation that these components sum up to total dissimilarity (and see Baselga 2010; Podani and Schmera 2011; Legendre and De Cáceres 2013). Ovaskainen et al. (2019) used an agent-based model to simulate a large number of metacommunities which varied in terms of habitat (patchiness, quality, and temporal dynamics) and species traits (habitat affinities and specialization, dispersal capacity). They then virtually sampled the simulated communities to extract “community data” (species presence/absence, habitat variables, and location) and analyzed the data using a set of common approaches including beta diversity indices, variance partitioning, distance-based redundancy analysis, and a joint species distribution model with environmental as well as spatial predictors. Their results shed useful light on how much can be inferred from observational data. They found that the JSDM performed better than the other analytic approaches in recovering the simulated patterns but underscored that none of the approaches was perfect and that the most information was gained by combining approaches. In the previous chapter, we looked at landscape genetics and genomics as a promising means of separating metapopulation structure due to dispersal as compared to environmental constraints (Sect. 6.5.2). In this, neutral markers reveal the long-term integration of successful dispersal, while markers correlated with environmental factors suggest the action of selection (Manel et al. 2003). With metacommunities, these same genetic tools might provide additional empirical evidence in distinguishing environmental filtering from spatial processes. Thus, although we do not yet have an analytic framework that integrates all of the processes or factors we believe are important to metacommunities, recent advances in theory and empirical analysis are promising.

7.5

Illustration: Sierran Forests

We can explore metacommunity structure and beta diversity by revisiting the Sierran system that we used to illustrate agents of pattern (Sects. 1.4.1, 2.4.3 and 3.2.1). The community data comprise abundance measures (as basal area, m2 ha-1) for 11 common tree species. There are 99 georeferenced sample plots, and a set of environmental variables was measured at the same locations. The data are described in more detail in Urban et al. (2002). The samples are arrayed in clusters of three or four plots randomly located within ~100 m of the cluster centroid; the clusters themselves are stratified over a long elevation gradient (~3000 m relief) (Fig. 7.6). At each sample location, environmental variables were measured to quantify topographic position, soil texture and depth, and surface conditions. In the following sections, we will view highlights of a larger analysis documented separately (Urban et al., unpublished).

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Illustration: Sierran Forests

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Unknown Ponderosa pine White fir Red fir Lodgepole pine Xeric conifer Subalpine conifer Foothills conifer/grass Foothills chaparral Mid-elevation hardwood Montane chaparral Meadow Rock/barren Other (water) Sequoia groves

Fig. 7.6 Locations of 99 sample plots distributed along an elevation gradient in Sequoia National Park in the southern Sierra Nevada, CA, USA. Inset is colored on elevation using a rainbow shadeset so that low elevations are hot colors (reds) and high elevations are cool colors (blues); elevation ranges ~800–3300 m. The larger pattern follows roads and major trails

7.5.1

The Perspective of Ordination and Gradient Analysis

In general, the tree species show a nonlinear relationship with the elevation gradient (not shown, but a pattern similar to Fig. 2.9). In the spirit of gradient analysis, the community can be viewed as an ordination summarizing trends in species composition. In this case, the species were ordinated with nonmetric multidimensional scaling (NMS, Supplement S7.1.4), yielding a two-axis summary that accounts for 86% of the variation in the compositional dissimilarities used in the ordination. Note that NMS is an indirect ordination; it is based solely on species data and includes no environmental constraints. In the ordination, samples are positioned so that samples that are compositionally similar are near each other in NMS space, while samples that are far apart are also compositionally dissimilar. To complement this gradient perspective, samples were classified into discrete communities by partitioning around medoids, a nonhierarchical pooling technique (Kaufman and Rousseeuw 1990). The analysis is based on the same compositional

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NMS 2 Fig. 7.7 Nonmetric multidimensional scaling ordination of 99 samples and 11 tree species, from Sequoia National Park in California, USA. Samples are colored by six classified community types, themselves identified by species that reach their maximum abundances in those types (i.e., the same color). Correlation vectors indicate correlations between the environmental variables and the NMS axes (e.g., elevation is strongly positive with NMS1). Species codes are plotted at their weightedaverage position on each NMS axis. Species codes: ABco Abies concolor (white fir), ABma Abies magnifica (red fir), CAde Calocedrus decurrens (incense cedar), COnu Cornus nuttallii (Pacific dogwood), PIco Pinus contorta (lodgepole pine), PIje P. jeffreyi (Jeffrey pine), PIla P. lambertiana (sugar pine), PImo P. monticola (western white pine), PIpo P. ponderosa (ponderosa pine), QUke Quercus kelloggii (California black oak), and SEgi Sequoiadendron giganteum (giant sequoia). Variable xDepth is mean soil depth; xLitter, mean litter depth; ECEC, effective cation exchange capacity; C.N, carbon:nitrogen ratio

dissimilarities as the NMS ordination and so can readily be incorporated into the ordination. In the ordination diagram (Fig. 7.7), sample plots are color-coded by community type, and species codes are colored by the community in which they reach their maximum abundance. The species codes are plotted at their weightedaverage positions on each of the two NMS axes.

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Illustration: Sierran Forests

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Correlations were computed between the NMS axes and the environmental variables and plotted as vectors in the ordination diagram (Fig. 7.7). Vector direction indicates correlation with each of the axes (a perfect positive correlation would parallel the axis), with vector lengths indicating the magnitude of the correlation. Only significant (P < 0.01) correlation vectors are drawn. This figure was constructed using the ecodist (Goslee and Urban 2007), vegan (Oksanen et al. 2019), and cluster (Maechler et al. 2021) packages in R (R core team 2019). The ordination is graphed with the first axis drawn vertically, in deference to a long tradition of gradient analyses featuring elevation gradients this way. The ordination emphasizes a strong elevation gradient (R2 on NMS1 is 75%); along this gradient is a sequence of dominance by lower-elevation ponderosa pine, white fir and its associates (the mixed-conifer zone), red fir, and the subalpine conifers western white pine and lodgepole pine. The second axis separates mixed-conifer samples characterized by Jeffrey pine from sites dominated by white fir, sugar pine, and giant sequoia; NMS2 also separates western white pine from lodgepole pine at higher elevations. In general, the ordination suggests a community strongly patterned by the elevation gradient complex but with substantial variation within lower elevation zones. This is a low-diversity forest, so some of the community types are nearly monospecific.

7.5.2

Partitioning Beta Diversity

An ordination-based partitioning analysis was conducted with redundancy analysis (RDA), using R packages ade4 and its dependencies (Dray and Dufour 2007; R Core Team 2019). The analyses followed the recommendations of Dray et al. (2012), Bauman et al. (2018), and especially Dray (2020). Spatial predictors were generated via principal coordinate analysis of a distance matrix processed to emphasize between-sample distances of less than 3000 m, based on Mantel correlations. Mantel correlations showed species composition to be spatially structured to distances up to 3000 m and environment autocorrelated to just over 2000 m (both P < 0.001). (Elevation itself, being a gradient, is not autocorrelated at a characteristic scale; recall Sect. 4.3.2.) In this example, the explanatory model was constructed by first fitting the environmental variables in RDA and then fitting the MEMs to the residuals on the environment. This approach allowed the environmental signal to be captured, with the MEMs capturing any spatial signal not explained by the environment. This model retained five RDA axes. Elevation, as expected, was the most significant environmental variable (P = 0.001), with lesser effects from mean soil depth, soil C:N ratio, slope, mean litter depth, and soil pH. Eight MEMs were highly significant (P < 0.001) in the final model, with nine more of lesser significance (P < 0.05). The highly significant MEMs are somewhat difficult to interpret visually but suggest spatial signals at a range of coarse, intermediate, and fine scales. Given

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familiarity with the data, these might be interpreted further (but with substantial uncertainty). Relative to the NMS ordination (Fig. 7.7), both axes are significantly correlated with at least a few spatial variables (Fig. 7.8), suggesting that there is a spatial signal, even in this strong elevation gradient, that cannot be explained with the measured environmental variables. Using these same analyses, an aggregate variance partition summarized the partial explanatory power of the environmental variables, the spatial predictors, and their correlations. This analysis used vegan function varpart, which itself uses RDA (Okasen et al. 2019). This variance partitioning suggests a slightly smaller environmental signal (25% of the variance in species composition) relative to the spatial signal (30% of the variance) and with some shared information (10%, which is estimated by differencing).

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It is important to remind ourselves that the effects of “space” can represent many different things. In this Sierran example, two possibilities warrant consideration. First, while the environmental variables were selected based on a wealth of accumulated experience in the study area (Vankat 1982; Stephenson 1988, 1990; Graber et al. 1993; Stephenson and Parsons 1993; Halpin 1995; Urban et al. 2002), it is still possible that some important environmental factors were missed. For example, cold air drainage is known to have an influence in some parts of the Park, but no measure of this was included in this study. Another spatial factor in this system is fire, a contagious disturbance. While the Park has comparatively rich data on recent fires, no measures of fire occurrence or fire history were developed for this analysis. A logical follow-up to the analyses shown here would be to revisit the scale(s) and locations of spatial signals in the data, to pose further hypotheses about explanatory factors that might be tested empirically.

7.6

Managing Metacommunities

Metacommunity processes—environmental filtering, dispersal, species interactions, and stochasticity—are relevant to landscape management and biodiversity conservation because it matters how communities are structured. It is perhaps disappointing that analytic approaches cannot simply resolve causal processes from observational data. But even without a definitive analysis of these processes for any given landscape or application, appreciating the possible role of these processes can inform our expectations from management, restoration, or forecasting community response to global change. A long tradition in wildlife management has presumed that environmental factors are what govern wildlife species: habitat management is a foundation of wildlife management (e.g., Leopold 1933). With the exception of cases where wildlife is protected by the removal of predators or direct competitors, interspecific interactions have not been a huge focus in wildlife conservation. By contrast, much of our understanding of plant communities is founded on the assumption that interspecific competition has a direct effect on species distribution (recall Sect. 2.4.2). While we need not immediately resolve the debate about the role of competition in structuring communities (which debate is as old as ecology itself!), we do need to consider biotic interactions that might be acting in our system and respond accordingly. As a case in point, species distribution models are perhaps the fundamental analytic tool in wildlife management and biodiversity conservation. SDMs are used to infer which environmental factors are most important in defining “habitat,” and they are used to forecast species response to habitat management or environmental change. The vast majority of these applications model species individually. That is, they are applied without any information about covariance among species. Joint species distribution models should help substantially in this; even though these models cannot demonstrate interactions directly, they often do a better job modeling

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Management options Manage habitat: Protect? Restore?

Candidates? native? exotic/invasive?

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Communities and Patterns of Biodiversity

Manage matrix: Connect or not?

Source? same patch? connected patch?

Manage species: Which species?

Fig. 7.9 Model template for considering metacommunities in management application. The process begins by evaluating potential explanatory factors (left panel) and proceeds through decision points for factors (middle) to management implications. The implications might be practical actions to alter the situation (e.g., increasing connectivity), marshaling further research as management experiments, or simply adjusting expectations for the system

individual species (i.e., extracting single species from the joint solution) than a collection of single-species models done separately. Similarly, invasive species management and restoration interventions typically focus on a single species, even though most sites are invaded by more than one species (Kuebbing et al. 2013). Interactions are typically ignored, even though they are common (Kuebbing and Nunez 2015). The single-species approach often leads to reinvasion (Pearson et al. 2016). In this, suppression or eradication of a dominant invader results in the expression of dominance by a second invader that was outcompeted by the first dominant. Again, the conclusion must be that we should pay more attention to interspecific associations. Spatial processes, especially dispersal, feature prominently in most but not all metacommunity models. The consideration of spatial structure can add substantially to the inferences we might draw from field data—but “space” can also be misleading because of all it might encompass: dispersal, contagious disturbances, pests, diseases, or, indeed, the historical legacies of these—or from unmeasured but spatially structured environmental factors. Useful forecasts about environmental change will require that we resolve uncertainties about what “space” means in any application. Anticipating species response to climate change is perhaps the biggest challenge facing us today. This will require us to attend environmental constraints (including those beyond climate), connectivity for directed dispersal or migration, and possible interactions among species. We return to climate change in Chap. 10. A model template for communities would invite the user to consider the main effects: the environment, spatial processes, and other species (Fig. 7.9). A focus on habitat variability and connectivity inherits from metapopulations (left panel), while communities add an explicit consideration of interspecific interactions (center panel). The role of chance is not included because it is typically assessed as that variation not attributable to the other factors. (It is worth keeping in mind that in variance partitioning studies, a substantial proportion of the variance is often unattributed.)

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217

Decision points vary substantially across these main factors. In the case of habitat variability, it might be important to distinguish spatial variation (e.g., as along gradients) from variability in time (e.g., post-disturbance successional dynamics). With respect to connectivity, the distinctions among constrained, sufficient, or surplus dispersal matter because these suggest the extent to which environmental filtering can manifest, as compared to isolation effects or mass effects that can mask or bias environmental affinities. In the case of biotic interactions, the process includes a canvassing of likely candidates, but this might play out differently for native as compared to exotic or invasive species. In real landscapes, species interactions might arise locally (within the same habitat patch), from nearby (connected) patches of similar habitat, or with species inhabiting and moving from nearby patches of different habitat types. The management implications of these decision points (right panel) likewise vary across factors. For habitat variability, we might manage to improve habitat or attempt to conserve or protect a variety of biophysical sites to support focal species or a higher biodiversity. If the habitat variety varies substantially over time (e.g., as post-disturbance succession), then efforts might focus on maintaining a stable distribution of age classes or seral stages (i.e., Watt’s unit pattern, Sect. 2.2). Evidence of limited dispersal might invite efforts to improve connectivity; but in cases where dispersal is sufficient or even surplus, the management response might be more a matter of managing expectations. A possible exception might be the case of invasive species, where a management option would be to disconnect the system. In this, the same geospatial tools that underpin connectivity conservation (Sect. 6.5) might be used to advantage. Responses to decisions about biotic interactions similarly might range from very targeted actions (e.g., removing an exotic competitor) to accepting the interactions and managing expectations. In many cases, the evidence will be inadequate, and so management experiments can provide crucial data to resolve uncertainties (and we have considered many ways that such data might be analyzed!).

7.7

Summary and Conclusions

Community ecology is concerned broadly with the role of environmental constraints (niche differentiation through habitat selection) and interspecific interactions (competition, trophic relations) in governing species assemblages. Over landscapes, these processes are mediated by large-scale heterogeneity in abiotic factors as well as the juxtaposition of habitats that support different species. Dispersal among sites adds a new dimension to community ecology, generating metacommunities. In one sense, landscape ecology as a discipline was founded on early efforts to extend community ecology to landscapes. Many aspects of community ecology have been extended readily to metacommunities, by applying approaches over a larger extent (and so incorporating more spatial heterogeneity) or by embracing space explicitly. The main lineages

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include the exploration of assembly rules, process-based metacommunity models, species distribution modeling, and statistical approaches to partitioning beta diversity. The approaches represent different and complementary perspectives on communities, and they use different and complementary analytic tools. Collectively, these approaches offer insights into patterns of species co-occurrence and the structure of communities, the relative importance of generative processes in shaping communities, and, especially, an appreciation for the relative importance of environmental as compared to purely spatial factors in explaining community structure. An appreciation of the several abiotic (environmental filtering) and biotic (interactions, dispersal, demographic stochasticity) processes that govern metacommunity structure and patterns of beta diversity is crucial to understanding and forecasting the potential response of communities to management, restoration, and global change. New, hybrid analytic approaches that combine the strengths of complementary perspectives can provide richer insights into community assembly and more useful guidance to landscape-scale applications.

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Chapter 8

Implications of Pattern for Ecosystems

8.1

Introduction

The link between spatial heterogeneity and ecosystem processes is so tightly coupled that it is difficult to distinguish cause from effect. Ecosystem processes—especially productivity and nutrient cycling—are governed by temperature and moisture and so are tightly coupled to the physical template of landscapes. Of course, these processes are also tightly coupled to the biological components of ecosystems and so reflect biotic processes as well. In many instances, ecosystem processes tend to reinforce or amplify biophysical and biotic patterns. For example, the accumulation of soil organic matter and moisture at lower slope positions creates conditions favorable to plant growth, which in turn generates more soil organic matter and higher waterholding capacity at these slope positions: a positive feedback. This chapter begins with a review of biophysical agents of pattern (especially the interaction of climate and landform) and explores the role of ecosystem processes in amplifying pattern via positive feedbacks. Ecosystem processes mediated by soil tend to be slow, which leads to legacy effects on landscapes—long-term echoes of past actions. But ecosystem processes can also escalate through positive feedbacks, leading to potentially rapid changes over a large spatial extent. The interplay of “fast” and “slow” ecosystem processes is key to our discussion here. As was the case with metapopulations and metacommunities, landscapes comprise a heterogeneous mosaic of sites with different biophysical characteristics, connected to varying degree based on their location. With populations and communities, the connections are via dispersal of individuals or propagules. With ecosystems, the connections are via transfers of materials, nutrients, energy, and information, and these might be mediated by hydrology or wind or gravity (topography) as well as dispersal by plants and animals (which themselves might be viewed as discrete packages of materials, nutrients, and energy). These fluxes or transfers occur in natural or seminatural landscapes, which feature terrestrial ecosystems as well as embedded freshwater systems (lakes, streams), or at © Springer Nature Switzerland AG 2023 D. L. Urban, Agents and Implications of Landscape Pattern, https://doi.org/10.1007/978-3-031-40254-8_8

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coasts, adjacent marine systems. Especially in landscapes influenced by humans, the juxtaposition of differing land uses or ecosystem types leads to edge effects, a topic as old as ecology itself but one that is still very relevant on landscapes. The juxtaposition of disparate systems also admits the likelihood that these systems exchange materials, nutrients, and energy and thus function as systems of systems: meta-ecosystems. Meta-ecosystems are the larger-scale generalization of more localized edge effects, and landscape ecology can benefit by adopting the larger-scale perspective on these fluxes.

8.2

Spatial Heterogeneity and Ecosystems

While some seminal writings on landscape ecology (e.g., Risser et al. 1984) emphasized ecosystem processes as a key focus of the discipline, there was a time lag before the field embraced ecosystem processes such as primary production and nutrient cycling as these generate and are affected by spatial heterogeneity at landscape scales. In part, the lack of attention to heterogeneity reflected a dominant modeling paradigm in ecosystems ecology. In this, ecosystems are represented as “boxes” of components or element pools, coupled by arrows denoting fluxes or transfers among these compartments (Fig. 8.1). Typically, it is assumed that the boxes are homogeneous and well mixed (i.e., they can be represented by single

Carbon Cycle

Nitrogen Cycle Atm CO2 Photosynthesis

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External

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(slow) Denitrification N Deposition

Plant Assimilation Respiration

Litterfall and Mortality

Litter and Coarse Woody Debris

Soil Mineral N

N Fixation

Decomposition Mineralization

Soil Organic Matter

N Leaching

Fig. 8.1 Compartments and flows of a coupled carbon and nitrogen cycle. (Redrawn from US DOE 2008)

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parameters). Fluxes among components are mostly vertical, i.e., as part of the soilplant-atmosphere continuum. Empirically, this perspective typically reflects a rather small-scale version of an ecosystem—one sufficiently small that the components can be managed logistically. Since the early 2000s more ecosystem scientists have addressed spatial heterogeneity (and scaling) deliberately (e.g., Turner and Carpenter 1999; Reiners and Driese 2001; Burke and Lauenroth 2002; Lovett et al. 2005; Turner and Chapin 2005).

8.2.1

Spatial Heterogeneity in the Physical Template

Before delving into explicitly spatial aspects of ecosystem processes, we should review the main patterns we expect to observe in the physical template as these influence ecosystem processes. We considered these in some depth in Chap. 1, and what follows here is intended as a reminder; indeed, all of Chap. 1 might be reviewed here as a reminder. Biophysical processes depend on temperature and moisture, as well as characteristics of soils. This implies that even a nonspatial model of ecosystem processes (e.g., as in Fig. 8.1) will generate system dynamics that vary with these drivers as distributed over landscapes, because the physical template itself is spatially structured (Sect. 4.3.2; Peters et al. 2004a). Temperature varies primarily with elevation and hillslopes as these interact with climate (Chap. 1, Sect. 1.4.1). Along elevation gradients, temperature decreases in a nearly linear fashion with increasing elevation, a lapse rate. Local topography influences temperature via radiation loading (a function of slope angle and azimuth, Sect. 1.4.2), as well as via the moderating influence of air moisture (e.g., distance to water bodies). Cold air pooling can be important in some topographic settings, and wind can influence temperature via convective heat loss. Soil moisture varies with the interaction between evaporative demand and water supply, the water balance. As we dissected the water balance (Sect. 1.3), we identified a large set of proximate factors that contribute to demand, supply, or both (Fig. 1.2). These factors include elevation, slope angle and azimuth, distance to water bodies, and cold air pooling as these affect demand. Water supply is influenced by precipitation (including the balance of rain and snow and any redistribution of snow by wind Sect. 1.4.3), local topographic drainage as affected by hillslope position, and soils (texture, organic matter content, and the distribution of these over the depth of the soil). Soil itself varies spatially in response to hillslope processes (the catena model, Sect. 1.4.4, Fig. 1.6). All of this implies a significant level of spatial heterogeneity in the main drivers of ecosystems processes, aligned in gradient complexes at the scales of elevation and hillslopes but also reflecting substantial fine-scale variation in soils (Fig. 4.9). Of course, many of these processes are mediated by microbes and so respond also at still finer scales! These patterns are themselves nested within larger-scale patterns driven by gradients in temperature (with latitude) and precipitation (with longitude or

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relative to mountain ranges and airmass dynamics). Again, we will expect to observe corresponding spatial heterogeneity in ecosystem states (biomass, carbon, nutrient pools) and rates (productivity, decomposition). The response of ecosystem productivity can be inferred readily from the pattern of vegetation as it drapes over gradients in temperature, soil moisture, and edaphic features: the banding of vegetation zones along montane elevation gradients, and vegetation contrasts between north- and south-facing exposures or between ridges and coves. That is, the agents of pattern that we considered in Chaps. 1 and 2 also reflect the responses of ecosystem processes to this pattern. But this heterogeneity is local and site specific; it does not reflect lateral fluxes (considered next), nor does it consider how positive feedbacks can reinforce or alter ecosystem processes locally.

8.2.2

Lateral Fluxes on Landscapes

As with metapopulations and metacommunities, landscape heterogeneity implies the likelihood that sites might be coupled by lateral fluxes, transfers, or interactions. In the case of ecosystem processes, there is a daunting variety of such fluxes. Reiners and Driese (2001) offered a conceptual framing for these, in an effort to codify the variety of fluxes while emphasizing their overall similarity—an early model template (and to which we return). They further developed this framework elsewhere (Reiners and Driese 2003, 2004; Reiners 2005), and what follows is based largely on their seminal efforts. Reiners and Driese were careful to adopt neutral language in their classification of lateral connections, which they termed propagations, choosing to avoid more specific terms (transfer, interaction, flux) that might apply to particular cases. It is worth delving into their conceptual model because it underscores the sheer variety and pervasiveness of these lateral transfers. Their far-ranging classification also has the benefit that the sheer variety of cases forces us to be precise about particular cases. Reiners and Driese (2001) traced the evolution of ecosystem science to embrace spatial complexity and scale. Their main focus was on the propagation of materials, energy, and information across heterogeneous landscapes. They abstracted this process into four general elements: (1) an initiating event or condition, (2) the vector of transfer or propagation, (3) the entity being transferred, and (4) the consequence of this at the target or recipient site (Fig. 8.2). Each of these elements includes a range of particulars that collectively cover an enormous variety of empirical cases. As an example, the redistribution of snow by wind is a common feature of many landscapes and a case that was illustrated and modeled in some detail by Reiners and Driese. In this, topography and vegetation mediate the action of wind to redistribute snow substantially; some windward slopes are swept free of snow, while sites leeward to slopes or vegetation patches can accumulate meters of snow. Here, the initiating condition is the original distribution of snow and the relative vulnerability

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Transport vector Entity transported

Event or condition

Deposition or consequence

Fig. 8.2 Entities that might be propagated across heterogeneous landscapes, streamscapes, or seascapes. Most transfers of ecological importance occur at the intersections of energy, matter, and information (information, in particular, can only be transferred via energy or matter). (Redrawn with permission from Annual Reviews, Inc., from Reiners and Driese (2003); permission conveyed through Copyright Clearance Center, Inc.)

of sites to wind. Wind is the vector, and snow is the entity being moved (along, of course, with anything contained in the snow). Local topography and vegetation can modify the routing relative to the prevailing (regional) wind direction. The consequences of this redistribution are changes in available moisture during the growing season because of the changes in snow meltwater (some sites drier, some sites wetter) but also changes in the phenology of the growing season (sites with deeper snowpack experience a shorter growing season). This intuitive example invites a much broader set of particulars. Reiners and Driese cataloged several variations on the initiating conditions. For example, the initiating conditions might be discrete events (i.e., disturbances) or chronic conditions. A landslide is a discrete event that moves mass downslope; but a large outcrop might also be a chronic source of colluvium. These events might be episodic and essentially random, or they might be seasonal or periodic (e.g., tidal flushes or spring floods); this variation in frequency might be associated with some variation in duration as well. Each condition or event might be spatially scaled in a particular manner. Some events might be abiotic in origin (windstorms, springs), while others are biotic (movement of organisms); some might be biotic but with abiotic implications (e.g., eutrophication resulting from waterfowl concentrations). All of these might vary for terrestrial, freshwater, or marine systems. And all might be modified by human activities, or new fluxes or transfers might be introduced by humans. The entities being propagated were cataloged by Reiners and Driese into three main classes: matter, energy, and information. Energy might be represented in various forms: sensible heat, latent heat (e.g., in water), kinetic energy or momentum of mass movement, and so on. Matter might include nonreactive inorganic compounds that are essentially passive in the ecosystem, or reactive (reduced)

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compounds such as those stored in biomass. Information transfer would include communication signals (light or sound) as well as biochemically coded information (e.g., pheromones) and including genetic information. Reiners and Driese emphasized that while any of these entities might be transferred, the significance of any transfer depends on the consequences at the target or recipient site—and part of this is defined by the interests of the researcher for a particular application. This is an instance of model specification and the decision about what to include or exclude from an application (Sect. 4.2.1). Importantly, Reiners and Driese noted that many ecologically relevant transfers occur at the intersection of these types of entities. For example, movement of water carries latent and sensible heat, momentum, dissolved solutes, and perhaps information (e.g., about nearby microclimates). Movement of an herbivore is simultaneously a transfer of energy and matter (and perhaps information). Which of these entities is interesting depends on the application; the key is to choose and declare the focus. Reiners and Driese noted that, in an ultimate sense, all vectors of transfer depend on solar energy or gravity. But this generality is not very useful, and so they cataloged a more proximal set of 11 vectors. These range from molecular diffusion (which happens everywhere but over very short distances) to fluvial or colluvial transport, sedimentation, tidal or nontidal currents, wind, sound, electromagnetic radiation (sensible or visible), and animal locomotion. Some of these occur only in instances of specific entities being transferred (e.g., the information content of firefly signals), while others encompass a wider range of entities that can be propagated (e.g., water and wind move many entities in many ways). The propagation of entities over landscape, by whatever vectors, often results in that propagation being modified by intervening spatial heterogeneity between the site of origin or initiation and the target or donor site. Flows of wind and water are influenced by local topography and vegetation, and the propagation of information via light or sound also would be affected by such local interference. Reiners (2005) used the phrase “reciprocal cause and effect” to underscore this feature of transport processes over heterogeneous landscapes—a perspective that resonates nicely with our dual emphasis on agents and implications of pattern. At the recipient site or location, any of these transfers might maintain current levels of heterogeneity, modify these, or override the underlying pattern. In the case of redistributed snowfall, the consequences might be a substantially different pattern in growing-season soil moisture as compared to that expected from topography and soils interacting with a more homogeneous input of precipitation.

8.2.3

Landform and Landscape Processes

In an early and insightful perspective on landscapes and ecosystems, Swanson et al. (1988) anticipated many of the points we have just considered but broadened the scope of the preceding discussion. Their focus was on landforms, which are specific instances of more general cases we have framed in terms of elevation gradients and

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local topography. For example, hillslopes shaped by landslides are particular landforms, as are alluvial gravel bars in stream or river systems, or talus slopes in the mountains, ridges or outcrops defined by erosion-resistant geologic formations, and so on. They identified four classes of effects of landform on ecosystems: 1. Landform influences environmental gradients in temperature, moisture, and soils. This would include temperature gradients as a function of elevation, soil moisture gradients generated by hillslope processes, and spatial heterogeneity in edaphic factors (perhaps also varying with elevation or hillslope position). We have already considered these in some detail in Chap. 1 and revisited these in Sect. 8.2.1. 2. Landform influences ecosystem fluxes. These would include gravitational (colluvial) and waterborne (alluvial) fluxes, as well as fluxes mediated by topographic flowpaths (colluvial or alluvial), geomorphic barriers to fluxes (e.g., ridges), or natural corridors for movement of materials or species (e.g., valley bottoms). The general scheme of Reiners and Driese (Sect. 8.2.2) covers these cases. For example, the specific case of redistribution of snow by wind, interacting with topography, would illustrate this class of cases. 3. Landform influences disturbances. This pertains especially to disturbances mediated by wind or water or animal routing influenced by terrain (e.g., grazing pressure). Fires, windstorms, floods, and many other disturbances would be included in this category. Mass wasting events such as landslides tend to be associated, for example, with concave hillslope configurations. This links landform and ecosystem processes explicitly to disturbance regimes (Chap. 3). 4. Landform influences geomorphic processes. While in most cases we tend to think of landform as essentially constant relative to the timescales of ecological processes, this is not always the case. Sometimes landform changes so slowly that it can be considered constant, but in other cases geomorphic events (e.g., landslides, river meanders) occur with sufficient frequency or are sufficiently fast that ecological (succession) and ecosystem (productivity, nutrient cycling) processes occur on the same timescales as the geomorphological change. The first two classes of effects are consistent with what we have already considered; and the third links this framework to disturbance as an agent of pattern that itself responds to pattern. The fourth class invites a more general consideration of the reciprocal relationships between agents and implications of pattern. If geomorphic processes are slow relative to ecology, then landform is a boundary condition or constraint on ecological processes (as in classes 1–3). If, however, geomorphic processes are relatively faster, they become agents of pattern themselves and influence ecological responses on ecological timescales. An appreciation for the abiotic heterogeneity of landscapes—the physical template and heterogeneity induced by biotic processes and disturbances—is necessary but not quite sufficient to understand the spatial heterogeneity of ecosystem processes. Lateral fluxes and propagation of energy, matter, and information occur in various ways, and these couplings are pervasive. The patterns generated by these

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patterns and processes can also be iterated sequentially (e.g., a transfer to a new location can then propagate another transfer from that location). These processes also can reinforce themselves via positive feedbacks.

8.2.4

Ecosystem Processes and Positive Feedbacks

Ecosystem processes respond to biophysical pattern but are themselves agents of pattern: the reciprocity of the pattern-process paradigm (Chap. 2, Sect. 2.2) is especially relevant here. Importantly, these processes can interact with pattern to amplify patterns over time, via positive feedbacks. For example, in the semiarid system considered as a scaling exercise in Chap. 4 (Sect. 4.2.1), spatial heterogeneity induced by plant-interplant differences develops over time to generate resource islands that impart substantial spatial heterogeneity to this system over small extent (Fig. 8.3). At a larger scale, interactions between soil moisture and plant processes mediated by topography (i.e., the hillslope processes of erosion and deposition, recall Fig. 1.6) amplify these same spatial patterns over time. In each case, the local accumulation of soil particles and organic matter improves the water-holding capacity and nutrient status of the soil locally, which supports more plant production, which provides more organic matter, and so on. This positive feedback can reinforce and amplify spatial heterogeneity (Fig. 8.4). A key insight from this body of work is that such positive feedbacks can lead to emergent patterns over landscapes, sometimes resulting in rapid and large-scale change. These are sometimes dramatic large-scale events that begin with smallerscale processes that escalate. For example, the between-plant erosion that leads to resource islands can evolve to the extent that highly connected eroded surfaces can interact with local weather (via albedo, wind routing, convection, and precipitation). In an extreme example, this sort of escalation contributed to the Dust Bowl in the southwestern United States (Peters et al. 2004b). Similar feedbacks contribute to regional and global patterns of desertification (Peters et al. 2004b). To be clear, such

Hummock Under

Bare

Fig. 8.3 Plant-interplant differences in aboveground biomass, fine roots, and soil organic matter result in a positive feedback of accumulation/erosion that amplifies local resource islands. (From Burke et al. 1999)

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A

Climate

Dynamic Controls

Topography Soil Microclimate C Vegetation D Soil Texture

B

Net N Mineralization

Soil Pools

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Fig. 8.4 Feedbacks among climate, landform, and vegetation in the semiarid ecosystems of Wyoming. Arrows A and D represent “fast” controls: A is snow and its redistribution; D is spatial and seasonal variation soil microclimate. Arrows B, C, and E represent “slow” controls: B is longterm tendency for plant productivity governing soil organic matter; C is long-term erosional and depositional processes; E is the result of A, B, and C—the tendency for downslope and leeward positions to have a higher N mineralization. (Redrawn with permission from John Wiley & Sons, from Burke (1989); permission conveyed through Copyright Clearance Center, Inc.)

large-scale events also involve other factors at regional or larger scales (in the case of the Dust Bowl, regional drought and agricultural practices and federal agricultural policy). We considered positive feedbacks previously in the context of small-scale or low-intensity processes that can escalate into large-scale disturbances (Sect. 3.2.3), but such feedbacks are common with ecosystem processes. This topic of emergent behaviors mediated in part by positive feedbacks is an important area of research, as the ability to forecast such events is integral to system resilience and long-term sustainability (Cash et al. 2006). We will return to the theme of rapid ecological change in Chap. 10 when we consider landscape resilience and adaptation to climate change.

8.2.5

Ecosystems Are both Fast and Slow

The controls on ecosystem processes illustrated in Fig. 8.4 underscore a key scaling characteristic of ecosystem processes: they include some fast processes, which are dynamic during the course of a growing season and often vary in response to weather events (i.e., over the course of days). But they also are mediated by soil processes that play out over hundreds of years or even longer timescales.

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In Fig. 8.4, soil microclimate and nitrogen mineralization are processes that track weather and biophysical processes during a growing season. By contrast, changes in vegetation stature and soil pools of carbon and nitrogen change much more slowly— over decades or longer. Soil texture changes even more slowly (perhaps over centuries), and topography evolves so slowly that most of us consider it as essentially constant. This separation of timescales can be illustrated conveniently with the CENTURY model of soil processes (Parton et al. 1987, 1988). This model separates soil carbon into a series of pools defined by their turnover times. Active soil carbon comprises materials that turn over on timescales on the order of 1–5 years. This component can be separated further into a metabolic fraction that turns over on faster timescales (within-year) and slightly slower structural components (1–5 years). By contrast, a slow carbon pool is modeled as physically protected and hence not as actively metabolized; this fraction turns over on timescales on the order of 20–40 years. On a much slower timescale, recalcitrant carbon fractions are so bound to physical soils that they are essentially not available to microbes; this fraction turns over very, very slowly—on the order of 200–1500 years. The combination of fast and slow dynamics helps us understand the surprises that can happen when typically slow processes erupt as a result of positive feedbacks (above). The slow processes also lead to persistent effects that linger for a very long time: landscape legacies.

8.3

Ecosystems and Landscape Legacies

Soils are the foundation of ecosystem processes. Soil scientists recognize five soilforming factors: parent material, climate, topography, biota, and time (Jenny 1941, and, e.g., Brady and Weil 2008). The slow pace of mineral weathering of parent material imparts long timescales to soil processes and hence to ecosystem processes governed by soils. This becomes especially apparent in cases where humans, through their impact on soils via various land uses, create legacies that persist for very long times. We have already touched on the theme of legacies when we considered the long memory of anomalies in Watt’s (1947) unit pattern (Sect. 2.2) and Sprugel’s (1991) illustrations of long transients in presumably primeval landscapes (Sect. 3.5.3). We also have noted the legacy effects of many disturbances on landscapes as seen in vegetation pattern (Sect. 3.2.4). Legacies from human land uses are a general and important aspect of ecosystem processes on landscapes. Foster et al. (2003) provide an insightful overview of land-use legacies in a variety of landscapes. They noted several factors contributing to the increased attention on legacies. Primarily, at the spatial extent of landscapes, it would be difficult to not encounter the influences of human activities—even in “natural” areas. Thus, as ecological studies scale up, we see more of humans and their impacts. Foster et al. emphasized the remarkable persistence of these legacies and argued that appreciating landscape history helps us understand modern landscape structure and function and so can help us anticipate and manage for future conditions.

Ecosystems and Landscape Legacies

Fig. 8.5 Dynamics of soil organic matter and nutrient supply in response to cultivation and its recovery after the abandonment of agriculture and return to grassland. (Redrawn with permission from John Wiley & Sons, from Burke et al. (1995); permission conveyed through Copyright Clearance Center, Inc.)

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Humans impact landscape legacies primarily through four activities: forestry, agriculture, modifying natural disturbance regimes, and manipulating animal populations (Foster et al. 2003). The legacies of deforestation and reforestation are widespread globally, though the particulars vary regionally. In the United States, the westward expansion of logging to fuel the Industrial Revolution resulted in landscapes with homogenized age classes of forests that have regrown, which in turn has exacerbated contagious disturbances such as fire and insect pests whose impacts depend in part of age-related susceptibility. Johnstone et al. (2016) have reviewed disturbance legacies more generally. Similarly, agriculture has left its imprint on many landscapes globally, with regional variations to the storyline. In the semiarid grasslands of the North American Great Plains, the effects of past plowing and fertilization are evident many decades after the practices ceased; these losses of soil organic matter might not be recovered for centuries (Fig. 8.5, Burke et al. 1995). In the southeastern United States, the history of forest clearing, agricultural intensification, and then abandonment of farming has left a legacy that is particularly rich (Trimble 1974). Over much of the Piedmont, agricultural practices were highly erosive, resulting in the loss of as much as a foot (30 cm) of topsoil from the eroded slopes. That history is manifest today in vegetation pattern and composition (Taverna et al. 2005), the loss of nutrients from the topsoil (Richter et al. 2000), the burying of old surfaces by the redistribution of locally eroded sediments (Richter et al. 2020; Wade et al. 2020; Fig. 8.6), and even topography itself (e.g., the “Little Grand Canyon” of the southeast, Providence Canyon in Georgia; Sutter 2015). Land use legacies on vegetation are especially well documented for the northeastern United States (e.g., Foster 1992, 2002; Foster et al. 1998; Motzgin et al. 1999). What is perhaps surprising about the legacies of prior land use (i.e., forest clearing for agriculture) is that they persist through subsequent changes in land use and subsequent disturbances. That is, changes in land use do not completely overwrite the older legacies.

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Fig. 8.6 An example of a landscape legacy in the southeastern United States. The sediments in the background were deposited over the past 100–150 years; the tree stump in the foreground has been dated to the 1700s and was exposed by erosion of the overlying sediments. (Photo courtesy Anna Wade)

Human influences on disturbance regimes are especially well documented in the case of fire. Through fire suppression policies in the middle of the twentieth century, many of the forests of the western United States support high fuel loads that make them particularly vulnerable to fires, leading to larger and hotter fires when these occur. It is impossible to understand current fire behavior in these systems as influenced by recent droughts, without also considering their management history. Human impacts of landscapes via introduced animals are familiar in the case of livestock, which leave reminders of their grazing and consequent redistribution of biomass and nutrients. Some of our understanding of these impacts is garnered by comparing livestock effects to those of native species (e.g., the American bison, Bison bison: Collins et al. 1998). Conversely, humans have affected some of the same large herbivores by reducing or eliminating natural predators from some landscapes. The removal and later reintroduction of wolves in Yellowstone is one illustration (Sect. 2.6.2, Ripple et al. 2014). The impacts of human introductions are also well documented for many invasive species, including insect pests as well as diseases such as blights. Other introductions might be less obvious but with profound impacts; the spread of introduced

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earthworms facilitated by agricultural practices is one example (Callaham and Blair 1999). Most landscapes are subject to more than one of these human-mediated disturbances and their resulting legacies, as we considered in Chap. 3 (Sect. 3.2.4). While some human action (e.g., plowing) or disturbances (e.g., mass wasting events) affect soils directly, many others have an indirect on soils through the action of changes in vegetation (e.g., grazing, diseases). Some disturbances such as fire have direct (heating) as well as indirect effects on soil (via litter, vegetation). In every case, once the soil changes, ecosystem processes also are changed, and these changes might persist for a very long time. One human influence on ecosystems—and one with very long-term implications—is the broad-scale conversion to developed land use and urbanization. We consider this in Chap. 9 where we delve into urban landscapes. An appreciation of the prevalence and persistence of landscape legacies reinforces the image of landscapes as palimpsests: modern pictures that still show the ghost images of previous states. Landscapes remember their histories, and we who study or hope to manage landscapes must remember these histories as well.

8.4

Patch Juxtaposition and Edge Effects

The juxtaposition of different ecosystem types creates edges (or ecotones) and edge effects have been a fundamental issue in ecology and landscape management for a very long time. In the United States and elsewhere, a major focus of game management was the deliberate creation and maintenance of forest openings and field-forest edges, because many popular small game species have affinities for edges (e.g., Leopold 1933). Somewhat ironically, as wildlife management widened its focus to include nongame species (especially passerine birds), this emphasis on edge habitat seemed to backfire, as edges have been shown to be very poor habitat (even ecological traps) for at least some species (recall Sect. 7.2.1). But edges are also important for many other processes, including ecosystem processes.

8.4.1

Edge Effects, Revisited

From a biophysical perspective, nearly everything shows steep gradients at a fieldforest edge: temperature, light, humidity, wind speed, and soil moisture all change within meters to tens of meters of the edge. In response these biophysical factors, vegetation structure is denser and more fully vertically stratified at the edge (Ranney et al. 1981). In response to this habitat structure and the increased productivity at the edge, species diversity of many taxa is also higher at the edge than in either forests or fields, though, often, this is due in part to species that favor the edge itself and also to the overlap of forest and field species spilling into the edge from either side.

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Edges are also subject to high rates of invasion by exotic species, in part because of the source area presented by adjacent or nearby nonforest habitats. Conversely, edges can create a less permeable boundary that might hinder dispersal by species that use forest or field habitats (Wiens et al. 1985). In such cases, the width and contrast of the edge can contribute substantially to its permeability. Finally, edges can mediate disturbance regimes by affecting the intensity of disturbances or their rate of spread. For example, forest edges can retard fire spread because of their higher humidity and moisture levels in the forest as compared to adjacent fields.

8.4.1.1

Uncertainty over Edge Effects

Despite an enormous interest in edges over the past several decades (e.g., Wiens et al. 1985; Saunders et al. 1991; Paton 1994; Murcia 1995; Cadenasso et al. 2003; Ries et al. 2004), a strong consensus on edge effects remains surprisingly elusive. Part of this might be because edges themselves are highly variable in terms of origin, structure, function, and temporal dynamics (Strayer et al. 2003). Murcia (1995) conducted a meta-analysis of studies of edge effects. She considered abiotic factors; vegetation density and structure; bird density; ecological processes such as seed dispersal, herbivory, and nest predation; and plant species richness and composition. She found what might be a surprising lack of consensus not only on the distances over which effects were found, but in many cases, in the sign of the effect. In the case of abiotic factors (air moisture, vapor pressure deficit, air temperature, light, soil moisture, and chemistry), in only one case was the edge effect unambiguous. In other categories of responses (vegetation structure composition, animal densities, biotic processes such as invasion or predation), there were documented instances of positive, negative, and no effects at edges. Ries et al. (2004) offered a general conceptual model of edge responses that focused on four mechanisms that effect organismal abundance patterns at edges: (1) ecological flows of energy, materials, or organisms; (2) access to spatially separated resources; (3) mapping of organisms onto particular resources; and (4) interactions between species. The first mechanism, ecological flows, essentially captures cases where such flows alter the biophysical environment or habitat quality at edges. Access to different habitat types, the second mechanism, is easy to visualize for species that use different kinds of habitat during their daily (e.g., foraging, resting) or seasonal activities (i.e., wintering versus breeding-season habitat). Resource mapping includes passive association of species with resources (environmental filtering) as well as active habitat selection. Predator-prey relationships are well studied species interactions at edges, along with brood parasitism in forest birds. Ries et al. argued that these mechanisms can explain much of the variation in patterns of species abundances at edges and can help resolve some of the lack of consensus about edge effects. To be fair, some of the complexity of edge effects is because all of these mechanisms might act collectively, with potential feedbacks among the mechanisms.

8.4

Patch Juxtaposition and Edge Effects

8.4.1.2

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Edge Effects in a Larger Context

Part of the confusion about edge effects might be due to the convention typically used to measure such effects. In most cases, edge effects are expressed in terms of “distance-to-edge” (i.e., from a sampling location in forest habitat). Such studies have been instrumental in raising our awareness of edge effects. For example, field measurements of nesting success by birds near forest edges were crucial to our appreciating the confounded influences of area, edge, and isolation in early studies of forest bird response to habitat fragmentation (e.g., Gates and Gysel 1978; Whitcomb et al. 1981; Brittingham and Temple 1983; Wilcove 1985; Temple and Cary 1988). In the case of forest birds and the edge effects of nest predation and brood parasitism, Donovan et al. (1997) used field studies in highly, moderately, and unfragmented landscapes to show that landscape context mediates the expression of edge effects. Similarly, Lahti (2001) highlighted the lack of consensus among studies of nest predation and argued that specific information of landscape configuration and which predators are present provided more useful explanations of edge effects than simple distance-to-edge (and see Chalfoun et al. 2002). Part of the confusion in using distance-to-edge is that such a simple measure (typically, as linear distance to the nearest edge) cannot capture the nuances of a larger landscape context. For example, Ries et al. (2004) pointed out the common instance that a point in the “corner” of a forest patch could be quite near two edges and subject to twice the effect; but this would not be accounted in most studies because only the closer distance would be tallied. Similarly, there are numerous studies that document the higher incidence of invasive plant species near forest edges; this is a result, in part, of the higher light levels near the edge and the proximity of seed sources from nearby lawns and agricultural fields. But this approach does not really capture the propagule pressure from these adjacent fields. MacDonald and Urban (2006) modeled the abundance of invasive species in terms of the total connected area of nonforest habitats incident to a sampled edge. Their best models included biophysical site conditions as well as an aggregate estimate of propagule pressure from adjacent fields. These studies that attend neighborhood or regional pressures on edges—rather than simple distance-to-edge—suggest that we might gain a more nuanced and context-sensitive understanding of edge effects if we were to deliberately attend the details of the operative mechanisms and the larger-scale context of edges.

8.4.1.3

Edges and Ecosystem Processes: Forest Carbon

As so many biophysical variables show edge effects, it seems clear that edges would have substantial impact on the landscape-scale integration of ecosystem processes. The specific example of estimating large-scale carbon flux illustrates this nicely. Carbon flux for a forest is largely the net balance of primary production (gains) and ecosystem respiration (losses); see Chen et al. (2014) for a review from a landscape perspective. Studies that have focused on edge effects on these processes suggest the complexities of extrapolating forest-level estimates to landscape-level estimates.

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Smithwick et al. (2003) used a detailed forest process model to explore edge effects in the forests of the Pacific Northwest of the United States. In their simulations, edges resulted in a higher productivity, primarily via the augmented light environment at the edge. At the same time, tree mortality increased in forest edges because of increased exposure to wind. Because of the spatial interactions at edges, they cautioned that landscape-scale estimates of carbon fluxes should not be simply extrapolated as the additive result of stand-level estimates. In the Piedmont of the southeastern United States, McDonald and Urban (2004) studied tree growth rates at forest edges. They cored trees to estimate growth rates and related these rates to canopy closure, several soil variables, and terrain-based indices. They found that growth rates were higher for some but not all species near edges; the edge effect was more pronounced for shade-intolerant species. Edaphic and topographic variables had as substantial or stronger effects than the edge effect. They did not attempt to integrate a landscape-scale implication of these effects on growth rates, but their results suggest that the edge effect itself, while important, also interacts with other edaphic factors and with plant life history traits. Reinmann et al. (2020) measured tree growth rates and soil respiration along gradients from edges to interior forest in urban (Boston) and rural landscapes in Massachusetts, USA. They found substantial enhancements in tree growth rates near edges—enhancements that were not offset by increases in soil respiration. Tree growth rates, however, were also affected by heat stress in exposed edges, and these effects were dramatically higher in urban as compared to rural landscapes. They cautioned that projections of carbon balances for landscapes should attend not only edge effects but also temperature effects as mediated by urbanization; this interaction will become increasingly important in a warming climate. These three studies underscore the reality that edge effects on ecosystem processes depend on species- and site-specific details as well as regional context—just like edge effects more generally.

8.4.1.4

The Pervasiveness of Edges

It is important that ecologists come to a better understanding of edge effects, because edges are increasingly everywhere. From percolation theory (Sect. 5.4.1), we know that under a random fragmentation scenario, when 50% of an initially intact landscape is cleared or converted (e.g., from forest to other land covers), that essentially all of the remaining forest is edge. Riitters et al. (2002) mapped the prevalence of intact forest cover for the conterminous United States, using 30 m resolution land cover data. They then mapped the incidence of forest aggregates (“interior forest”) of a range of sizes. While there is still substantial forest cover in many parts of the United States (itself regionally aggregated, Fig. 8.7a), there is dramatically less area of interior forest (Fig. 8.7b). Similarly, in the North Carolina Piedmont, although the landscape is roughly 60% forest, nearly 50% of forested pixels are within 100 m of a nonforest land cover (Fig. 8.8). Most biophysical edge effects (temperature, humidity, light) would fall within a 1-pixel edge (10% of the forested cells), while other

8.4

Patch Juxtaposition and Edge Effects

241

Fig. 8.7 Prevalence of forest (a, top) and interior forest (b, bottom), with interior defined aggregates 7 ha in size or larger, as classified from 30 m land cover data. (Reproduced with permission from Springer Nature, from Riitters et al. (2002); permission conveyed through Copyright Clearnace Center, Inc.) In the top figure, percent forest in 56.25 km2 aggregates is shaded from low (red) to high (green). The bottom panel displays percent “interior” forest (intact 7 ha aggregates) for those aggregates with more than 60% forest

processes such as weedy invasion, predation, and brood parasitism likely would extend beyond this distance. The pervasiveness of edge effects suggests that the juxtaposition of different ecosystem types is a general feature of most landscapes. Further, while the study of

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Fig. 8.8 Distances to nonforest edge in the Triangle region of North Carolina, based on classified 30 m imagery. Legend categories are deciles, so half the pixels are within 100 m of an edge. (Gray is nonforest land covers.) The lower inset is the same data averaged to a 1-km neighborhood

edges has focused largely on forests and adjacent fields, real landscapes include a wider variety of ecosystem types, in close enough proximity that we might expect them to interact. This invites the exploration of meta-ecosystems.

8.5

Ecosystems and Meta-ecosystems

The notion of meta-ecosystems is, intuitively, a natural extension of metapopulations (patches of differing habitat quality for a single species, coupled by dispersal) and metacommunities (patches of differing gradient position or habitat quality for

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multiple interacting species, coupled by dispersal). Following these examples, we might expect meta-ecosystems to be discrete patches of the same ecosystem type, coupled by fluxes of materials or energy. But the implementation of the meta-ecosystem concept has been not as natural as we might have expected. A few issues have contributed to the rather slow application of meta-ecosystem concepts in landscape ecology. One issue is a weak connection between theoretical and empirical applications. The original definition of metaecosystems (Loreau et al. 2003) was largely theoretical, emphasizing the implications of couplings between food web compartments across space. On the other hand, field ecologists were heavily invested in documenting the transfers of materials and species between adjacent ecosystem types—especially resource subsidies from one system to another (e.g., inputs to aquatic systems from terrestrial), studies of which date to the early 1960s. These two approaches are quite compatible but failed to connect, perhaps, because of the vantage points of the researchers. A second issue was that the connections between systems represented in theory did not map easily onto the kinds of fluxes that field ecologists were observing. In particular, there were many different kinds of movements or fluxes between systems on real landscapes, while theory tended to represent these rather generically in the abstract. Finally, the nature of the fluxes tended to confuse applications (Massol et al. 2011). For example, in cases where the fluxes involved organisms of different species but which species interact in the sense of community ecology, these applications fall naturally into the framework of metacommunities. In this, the dominant interaction among species is competition, and the community is arrayed horizontally in the sense of a food web (i.e., the interactions are among species that share the same tropic position, either as primary producers (e.g., plant communities) or consumers (e.g., bird communities). By contrast, if the fluxes of species are of predators or prey, then the interactions tend to wander from traditional community ecology (and metacommunities) to food web ecology, which is more aligned with ecosystems ecology. In this, the communities are vertically integrated (i.e., primary producers, herbivores, carnivores). Perhaps only in the instance of material transfers of detritus or inorganic nutrients are the fluxes unambiguously in the domain of ecosystems ecology. For our purposes, we will adopt two conventions to facilitate the discussion of meta-ecosystems. The first is to be explicit about what the fluxes are, that is, what is being transferred between systems. The second is to be explicit about how the transfers occur, especially the timescales of these transfers. Being explicit about these details does not compromise the generality of more theoretical approaches and might make it easier to connect empirical field studies with developing theory. This precision and attention to detail are as Reiners and Driese (2001, 2003, Reiners 2005) recommend (Sect. 8.2.1). This represents a disaggregation from the more generalized and abstract models of meta-ecosystems in theory, but this should make it easier to reconcile the concepts and to generalize across systems (and see below).

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Couplings Between Systems

A long tradition of field studies documents transfers of materials or species between different and adjacent ecosystems. Many of these studies focus on resource subsidies across systems, such as inputs of terrestrial materials into aquatic systems (e.g., Carpenter et al. 2005). Polis et al. (1997) synthesized a large number of these studies into a framework that focused on the transfers of materials (nutrients or detritus), prey, or consumers. They reviewed cases of couplings between aquatic or marine and other aquatic or marine systems (including transfers between pelagic and nearshore locations), transfers from land to water, from water to land, and between different locations on land (Table 8.1). Of the many transfers cataloged, transfers of detritus or materials were often passive (e.g., windblown loess or detritus), but sometimes the transfers were biotic (e.g., via the bodies of insects emerging from water but dying on nearby land). Similarly, transfers of prey might be passive (windblown) or via active and directed dispersal. Likewise, movements of consumers vary considerably among the examples they reviewed. The examples emphasize the broad variety of transfers and the ubiquity with which these occur: they are the norm in ecosystems, not the exception. A few examples will suffice to illustrate the kinds of couplings that occur and their consequences. These will serve to frame a more general discussion to follow.

8.5.1.1

Example: Marine to Terrestrial Subsidies

Helfied and Naiman (2001, 2002) used stable isotopes to document the importance of nutrient transfers from marine to terrestrial systems. In this, they took advantage Table 8.1 A catalog of pairwise couplings between ecosystems Transfer Nutrients and detritus Water-water Land-water Water-land Land-land Prey Water-water Land-water Water-land Land-land Consumers Water-water Water-land Land-land

Examples Upwelling, pelagic fallout Aeolian transfers, sedimentation, roosting in swamps Overwash deposition, shore wrack Aeolian systems, grazer/roost redistributions Diel vertical migration, downstream flow Insects blown/falling into water Emerging aquatic insects, anadromous fish Windblown arthropods (snowfields, other barrens) Anadromous fish, krill migration, aggregation at upwellings Coastal seabirds and mammals Animals tracking seasonal or localized resources

Scheme and examples from Polis et al. (1997)

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of the natural signal in marine systems, in the form of a concentration of the heavy isotope of nitrogen (measured as δ15N). The biology of this system is reasonably straightforward: anadromous salmon are born in rivers and then move to the ocean. There, they accumulate proteins into their biomass that are biased toward the marine nitrogen isotope. When the fish return to the rivers to spawn as adults, they are a primary food source for bears, and natural mortality further contributes to local nutrient transfer to inland terrestrial systems. Helfield and Naiman (2001) estimated that ~25% of the nitrogen in woody vegetation in these sites was of marine origin. This marine-biased nitrogen signal is discernible in tree tissues and is correlated with tree growth rates in all local trees except the nitrogen-fixing alder (Alnus) (Fig. 8.9).

Basal Area Growth (mm2/yr)

6000

Spawning Sites Reference Sites

5000 4000 3000 2000 1000 0 -8

-6

-4

-2

0

2

4

6

Foliar δ N Basal Area Growth (m2•ha-1•yr-1)

15

0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00 Spawning Sites

Reference Sites

Fig. 8.9 Nutrient subsidies from marine to terrestrial systems mediated by anadromous salmon. In this system, marine-biased nitrogen is discernible in trees that grow in terrestrial systems adjacent to spawning streams. The added nitrogen boosts forest growth in all species (Sitka spruce, Picea sitchensis, shown below) except alder (which is itself nitrogen-fixing). (Redrawn with permission of John Wiley & Sons, from Helfield and Naiman (2001); permission conveyed through Copyright Clearance Center, Inc.)

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8

Example: Aquatic and Terrestrial Couplings

Connections between aquatic systems (ponds or streams) and terrestrial systems are well studied (Polis et al. 1997; Richardson and Sato 2015). Knight et al. (2005) provided a tidy illustration of the implications of these couplings, based on a seminatural experiment. In their system in Florida, they surveyed a series of ponds, some of which supported fish while others did not. The food web implications of fish are indirect, mediated by an interaction pathway: dragonflies (Odonata) begin their lives as aquatic nymphs, which emerge as adults into the terrestrial system. As dragonflies, they prey on a variety of insects including pollinators. Depredation of pollinators has a direct effect on pollination success of terrestrial plants, which has implications for the persistence of those plant populations. The presence of fish in a pond leads to substantial reduction of aquatic nymphs, which leads to a reduction in terrestrial dragonflies, which decreases predation on pollinators and thus has a positive effect on the plant population. The dragonfly effect on pollinators is exacerbated by a change in the behavior of pollinators when dragonflies are present: they spend more time avoiding predation and less time pollinating. Note that the sign of the indirect effects is the product of the signs of the direct effects, so that the overall effect of fish is positive, mediated by a sequence of negative, positive, negative, and positive effects (Fig. 8.10).

Dragonfly

Pollinator

+ + + Larval Dragonfly

+ Fish

Aquatic Habitat

Terrestrial Habitat

Fig. 8.10 Trophic interactions across aquatic and terrestrial ecosystems, mediated by fish predation of larval dragonflies. The terrestrial dragonflies are predators of plant pollinators. Solid arrows are direct effects; dashed arrows are cumulative indirect effects (the sign of the indirect effect is the product of the signs of the direct effects along the path). (Reproduced with permission from Springer Nature, from Knight et al. (2005); permission conveyed through Copyright Clearance Center, Inc.)

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Litterfall

Waste, DOC, POM POM, DOC Fish, Prey

Flood Overwash

Emerging insects

Flood

Fig. 8.11 Schematic of couplings between aquatic and terrestrial ecosystems (redrawn from Richardson and Sato 2015). Transfers include abiotic and biotic elements, via passive (gravity) and more active (foraging) modes of transfer

Richardson and Sato (2015) summarized cross-system subsidies between terrestrial and freshwater systems. They argued that these subsidies are so pervasive and substantial that we should consider them explicitly in studies of resilience and stability and also incorporate these elements into conservation planning (Fig. 8.11).

8.5.2

Meta-ecosystems, Revisited

Gounand et al. (2018) revisited the meta-ecosystem concept to focus on the types of movements underlying transfers between systems. Like Polis et al. (1997), they distinguished between transfers of resources, primary producers, and consumers (herbivores). Further, Gounand et al. (2018) distinguished among various movements or behaviors that effected the transfers. These included frequent (and rather local) movements associated with foraging behaviors, seasonal migrations, movements between systems associated with life-stage changes (e.g., the emergence of aquatic nymphs onto land), and dispersal associated with natal dispersal and settling into new habitats (vagility). These four kinds of movements scale generally from frequent (daily foraging), to seasonal but repeating, to periodic mass events that happen only once in an organism’s lifetime, to singular events by individuals (but perhaps by many individuals).

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In combination, the organizational schemes of Reiners and Driese (2001, 2003), Polis et al. (1997), and Gounand et al. (2018) cover a broad range of cases and applications of the meta-ecosystem concept. While the approach of Reiners and Driese (2001, 2003), Reiners (2005) was rather abstract and deductive by design (i.e., to catalog the possibilities), the reviews by Polis et al. (1997) and Gounand et al. (2018) were generalized from many empirical examples. This approach might also make it easier to reconcile field studies with more theoretical treatments of the concept. This invites a model template (Fig. 8.12) that is disaggregated from broad generalizations to account for the many details that matter: very much in the spirit of the disturbance model offered by Peters et al. (2011, and recall Fig. 3.6). In this template, the assessment begins with an inventory of which patches or locations are of interest, the ecosystem types represented by these patches (e.g., forest, ponds, streams, agricultural fields), and the locations that determine the likelihood or rate of transfers between patches. The key step is to disaggregate the transfers, as suggested by Reiners and Driese (Fig. 8.2) and Gounand et al. (2018) to specify the details of the transfer: What exactly is being transferred (nutrients? whole organisms)? How do the transfers happen (e.g., passive fluxes of abiotic materials, foraging behavior, insect emergence, migration)? How much material is being transferred? And what is the timing (rate, frequency) of these transfers?

Patches

Types, Geometry, Locations

Transfers

Consequences

What?

Ecosystem (NPP, C, N, ...)

How? Amount?

Metapopns, Communities

Timing?

Fig. 8.12 A model template for meta-ecosystems (adapted from Gounand et al. 2018, after Peters et al. 2011). The combination of various patch types and locations, and the variety of possible transfers, allows for a potentially daunting complexity. For many applications, only a few of the transfers are likely to be important, but it is important to consider the possibilities before articulating the meta-ecosystem model. Note that because many transfers are via organisms, meta-ecosystems are also coupled to metapopulation and metacommunity dynamics

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These transfers have obvious consequences for ecosystem processes (energetics, productivity, C, and nutrient budgets). Because many of the transfers involve actual organisms, these fluxes also might have consequences for metapopulation dynamics via dispersal subsidies, as well community structure via interspecific interactions. That is, meta-ecosystems cannot be decoupled empirically from metapopulations and metacommunities.

8.5.3

Implications of Meta-ecosystem Structure

From a systems perspective as represented in food webs, there are significant implications of local couplings in meta-ecosystems. First, we might note that all of these couplings are donor-controlled (the recipient patches have no real control over what transfers come to them) and that the transfers are typically asymmetric. In the case of nutrient subsidies, these transfers can allow the development of entire food webs onto a resource base that is not locally derived or that is substantially augmented from elsewhere. In some systems (snowfields, barren lands), this subsidy might support a food web that otherwise has few or no basal resources. When the transfers are of limiting nutrients, the net result might be enhanced primary production and, consequently, elevated populations of herbivores and, perhaps, carnivores. In marine systems, local upwellings are a well-documented example of this bottomup support of a food web. Studies in other systems suggest that this local augmentation or supplementation of the resource base is a more general phenomenon. Of course, while bottom-up support of a local food web might be a good thing for a fishery, the same dynamic can lead to eutrophication and less positive results in other aquatic systems. In cases where the transfer is of prey species (e.g., herbivores), an intriguing implication is that the negative feedback between predator and prey densities typical of local food webs is bypassed: the local subsidy essentially decouples predator densities from prey densities so that unnaturally high predator densities can be supported via the subsidy. In some cases, this might lead to unnaturally high predator densities in otherwise marginal habitat, these densities maintained by the prey subsidy. Field studies suggest that augmented predator densities might depress local prey species as predators forage beyond the site of local subsidies (Polis et al. 1997). It might be useful to consider invasive species in this context. Invasive plants represent transfers as resources, while animals are transfers of consumers; in either case, these also then contribute their biomass and nutrients and so might alter community structure and biogeochemical processes where they encroach. Spatial context is important here, as proximity is crucial to the invasion dynamic. It is worth emphasizing that these implications are often quite obvious from theoretical models of meta-ecosystems, but the same effects have not been as well documented by empirical studies. This might reflect the early emphasis in field studies to document the transfers or subsidies themselves rather than their longer-

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Fig. 8.13 Schematic of meta-ecosystems that incorporate elements of metapopulations and metacommunities. Metapopulations are comprised of a single species with discrete habitats of the same or similar type (e.g., forests), coupled by dispersal. Metacommunities are defined by multiple interacting species in patches coupled by dispersal. Meta-ecosystems are coupled instances of different habitat types (e.g., forest to field, or forest to water). The combination of these juxtapositions and couplings imply that every landscape is unique (after Gounand et al. 2018)

term implications. Conversely, more theoretical studies have tended to focus on the longer-term implications without attending the details of the transfers. Going forward, a shared conceptual framework might make it easier to reconcile these perspectives. It might be obvious from this discussion, but it is worth emphasizing here: metaecosystems, when they involve transfers of organisms that represent trophic roles or potential competitors, incorporate (at least implicitly) metacommunities into metaecosystem dynamics. And metacommunities, by definition, incorporate metapopulations of different species. All of these “metas” depend on spatial heterogeneity in the physical template and habitat quality, and all depend on distancedependent couplings between sites of similar or different types (Fig. 8.13). We might emphasize again that spatial heterogeneity and location-dependent couplings are the hallmarks of landscapes. That is, an alternative and more familiar word for “meta-ecosystem” is “landscape.” The deliberate attention to the details of the spatial heterogeneity and couplings underscores that each and every landscape is unique, even though they all function according to the same general principles.

8.6

Summary and Conclusions

Ecosystem processes map closely onto landscape-scale environmental gradients in temperature, moisture, and soils. But feedbacks between ecosystem processes (productivity, nutrient cycling) and the physical template of landscapes mean that knowledge of the physical template is necessary but not sufficient to understand ecosystem processes at the landscape scale.

References

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Ecosystems can be both slow and fast. Because most ecosystem processes are mediated by soils, ecosystems are slow and have long memories; the soil integrates everything that happens over time. But positive feedbacks can escalate in ecosystems, resulting in larger-scale manifestations of small-scale dynamics. In extremes, these feedbacks can result in dramatic and abrupt changes in system structure: so-called tipping points. Landscape heterogeneity puts patches of differing type into juxtaposition, resulting in edge effects that are as idiosyncratic as they are pervasive. The nuances of particular edge effects do not summarize neatly in terms of simple metrics such as distance-to-edge but rather require attention to the mechanisms underlying the responses and the larger-scale context of the landscape. Interactions among patches of differing type lead naturally to the concept of metaecosystems. Applications of this concept have been hampered by a mismatch between theoretical studies and field-based studies that focus on what is being transferred between locations (especially, resource subsidies) and the ecological processes that mediate those transfers. This conceptual model will benefit as more studies are couched in this framework and the implications of these couplings are better documented. The juxtaposition of different types of patches in all landscapes means that what we observe of any landscape is context-dependent and peculiar to that particular landscape. That is, every landscape is unique, but they all work according to the same general principles governing the agents and implications of landscape pattern. Thus, we should be able to understand any landscape by viewing it through this lens. In particular, we should be able to tackle the huge challenges that face us today: landscape ecology in the Anthropocene. In the next two chapters, we turn to two of these challenges: urban landscapes and landscapes under global climate change.

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Chapter 9

Urban Landscapes

9.1

Introduction

Most of the world’s population now lives in cities (UN DESA 2018), and so it is timely to explore these settings explicitly as landscapes. Urban ecology emerged as a discipline rather recently, and its evolution is well documented in conceptual perspectives (e.g., Pickett et al. 1997; Collins et al. 2000; Grimm et al. 2000; Alberti et al. 2003; Shochat et al. 2006; Pickett and Grove 2009; McHale et al. 2015; Pataki 2015; McPhearson et al. 2016; Pickett et al. 2016; Alberti 2017; Groffman et al. 2017; Zhou et al. 2021), synthetic reviews (e.g., Pickett et al. 2001, 2011), and books (e.g., McDonnell and Pickett 1997; Alberti 2008; Marzluff et al. 2008; Elmqvist et al. 2015; McDonald 2015; Kabisch et al. 2017; Pickett et al. 2019). Here we explore urban systems by comparing them to the seminatural landscapes that have been the focus of most of this book. In this, we adopt the framing developed in previous chapters—of agents and implications of pattern—and ask whether this ecological framing is useful for human-dominated landscapes. Virtually all landscapes are modified by human activities. Indeed, much of the attention to habitat fragmentation and indexing landscape pattern has been focused not on natural landscapes but rather on landscapes with high levels of conversion to human land uses, especially agriculture and forestry. Urban landscapes are the end-member in this gradient of human land use intensity: landscapes in which built infrastructure1 is a predominant land cover type. We begin with an overview of urban ecology, to provide context and to recognize the human elements of urban landscapes. We then revisit these landscapes from the perspective developed in this book and highlight the special issues that arise in urban settings. Along the way, we will delve into two areas where urban landscapes can serve as especially useful models for landscape ecology. First, we take advantage of 1

For a rather sobering perspective on this, estimates by Elhacham et al. (2021) suggest that by 2040, there will be as much mass of concrete on the earth’s surface as all biomass combined.

© Springer Nature Switzerland AG 2023 D. L. Urban, Agents and Implications of Landscape Pattern, https://doi.org/10.1007/978-3-031-40254-8_9

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the physical reality that streams spatially integrate everything that happens upstream in their watersheds, which makes urban streams ideal study systems in which to explore the effects of landscape pattern on ecosystem processes. The so-called urban stream syndrome provides a compelling illustration. Second, we look at urban landscapes as mesocosms in which to explore the implications of global change. Urban landscapes are already warmer due to the urban heat island effect; cities also experience higher levels of carbon dioxide and other greenhouse gases, along with a host of other symptoms of global change. Cities are useful mesocosms because for urban landscapes, the future is already here.

9.2

Social-Environmental Systems

Urban ecology has deep roots as a discipline but has undergone major transformations over the past few decades. Pickett et al. (2016) summarized this trajectory as an evolution from ecology in cities, to ecology of cities, to ecology for cities (and see also McPhearson et al. 2016). Ecology in cities refers to conventional ecology that happens to be done in cities. For example, a forest ecologist might study bird communities in urban forest patches, perhaps comparing these communities to those from more intact or extensive rural forests. While these differences might be interpreted in terms of factors such as proximity of urban features (roads, built infrastructure), the conceptual model is largely “normal” ecology, and the landscape is parsed as “natural” or “anthropogenic”—essentially a binary classification. By contrast, ecology of cities embraces the entirety of the urban setting: the presence of built infrastructure as structural elements of the landscape and, especially, the presence of humans and their institutions as actors in the system. This perspective has emerged under several rubrics: coupled natural and human systems (CNH), socio-ecological or social-environmental systems (SES), and social-environmental-technological systems (SETS). Each of these rubrics emphasizes the dual and sometimes parallel structure of natural systems and human systems, as well as the many interactions and feedbacks among these components (Fig. 9.1). (While there are nuances to these various perspectives, in this chapter we will refer to them interchangeably.) The SES framework emphasizes that both social and ecological systems by themselves have structures and behaviors and that their integration generates new patterns and processes that are influenced by both the social and ecological elements. This model template2 (Fig. 9.1) is a high-level construct that becomes real when it is implemented using detailed elements and interactions—and data—from a particular system.

2

This is the template, indeed, that inspired the other model templates scattered throughout this book. I am grateful to Steward Pickett for his thoughtful insights into the value of these templates.

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257

External Political & Economic Conditions

Social Patterns & Processes

Integrated Social-Ecological System

Ecological Patterns & Processes

Demography Technology Economy Institutions Culture Information

Interactions Land use Land cover Production Consumption Disposal

Primary productivity Populations Organic matter Nutrients Disturbance

External Biogeophysical Conditions

Fig. 9.1 Model template for a social-ecological system. Patterns and processes on the left are social, while the right side is ecological; their integration comprises the coupled system. (Adapted with permission of Elsevier, from Pickett et al. (2011); permission conveyed through Copyright Clearance Center, Inc.)

As Pickett et al. (2016) emphasized, the in and of perspectives are not exclusive. Ecological studies in cities inform studies of cities by elaborating the natural side of things and how these interact with the human or built environment. In particular, studies of whole cities as systems are accomplished by aggregating a substantial amount of ecology in cities while also incorporating the social-science aspects of the coupled system. A more recent evolution of urban ecology is that for cities. This perspective is not really new, of course: Ian McHarg’s iconic Design with Nature was published in 1969. The perspective’s newer incarnation is motivated by emerging issues of sustainability and resilience and is more relational and dynamic than McHarg’s earlier approach. Compared to the in and of models, the for approach embraces researchers, stakeholders, and decision-makers as active participants in the enterprise, that is, the intent is that these actors collectively can shape the ecology of cities to provide more resilient (sensu Walker et al. 2004), sustainable, and equitable futures for cities (Childers et al. 2015; Rademacher et al. 2019; see also Pickett et al. 2021). Adaptive feedbacks to human institutions are a key part of this integration (Biggs et al. 2010). McGrath and Pickett (2011) used the term metacity to emphasize the deliberate integration of urban ecology, with all its spatiotemporal fluxes and feedbacks, to these ends. Pickett et al. (2020) have traced the Baltimore Ecosystem Study (a Long-Term Ecological Research program) from the perspective of conceptual models and theoretical underpinnings as this LTER site has evolved from an ecological study to an SES to a program very much invested in ecology for that city.

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Very many cities are now embracing this perspective as they develop adaptation plans in preparation for climate change and its symptoms (e.g., Kabish et al. 2017; Boswell et al. 2019; McDonald and Beatley 2021).

9.2.1

Approaches to Studying Cities

The perspectives of ecology in, of, and for cities intersect with empirical approaches to studying urban systems. One approach might be tagged “samples in cities,” while an alternative approach would be “cities as samples.” The former is a typical approach to ecology in cities, in which samples are distributed within cities and inferences are drawn from the heterogeneity among these samples. Examples would include studies of bird communities in urban forest patches (e.g., Minor and Urban 2010; Shanahan et al. 2011; Kand et al. 2015) or nitrogen cycling in lawns subject to various homeowner behaviors (irrigation and fertilization, horticultural practices; e.g., Law et al. 2004; Golubiewski 2006). In the latter approach, the city itself is a sample, and measures are aggregated to the city level. Comparisons or inferences are then drawn from a collection of cities (e.g., McDonnell and Hahs 2009, 2013). Whole-city energy or material budgets use this approach, as do ecological footprint studies (Wackernagle et al. 2006). These are studies of cities. Again, these two approaches are complementary; while some data might only be collated at the city level, other city-level empirical estimates are aggregated from samples within the city. A third empirical approach is synthetic and attempts to construct a real or hypothetical gradient of the intensity of urbanization, for example, as a transect from a highly developed urban center, through less intense development (e.g., mixed-use or suburban neighborhoods), to sparsely developed exurbia and a seminatural or natural (rural) endpoint (e.g., McDonnell and Hahs 2008; Kaminski et al. 2021). Often, this would be synthesized from a collection of spatially disjunct samples-in-cities stratified over levels of development intensity (e.g., Pataki et al. 2007); but the gradient also might be a literal one (e.g., a straight-line transect from the urban center out into the country, e.g., Rao et al. 2014). The gradient approach—and a samples-in-cities design for that—is perhaps most consistent with the way many now think about urban landscapes. In this, the city is part of a functional urban area that encompasses the city and its commuting area and which naturally includes an intensity gradient from the city itself into its suburban and exurban surroundings. It is important to point out these empirical approaches because the way that data are collected in urban landscapes has a direct effect on how readily urban ecology can be compared to more conventional ecological studies. In particular, the nature and distribution of samples-in-cities has implications for highlighting the scaling of urban ecology (and see below).

9.3

Agents and Implications of Pattern

9.3

259

Agents and Implications of Pattern

We begin this section by exploring the agents of pattern for urban landscapes, revisiting the physical template, biotic processes, and disturbance regimes. We then turn to the implications of these patterns for populations, communities, and ecosystem processes. Pickett et al. (2011) provided an extensive, in-depth review on many of these topics (reprising and extending their earlier review from the previous decade, Pickett et al. 2001); what follows relies heavily on their synthesis. The intent here is not to review urban ecology but rather to gauge the extent to which the framing developed in the rest of this book might be applied to urban systems.

9.3.1

Agents of Pattern

Cities experience a very different physical template than more rural areas and not simply because of the addition of concrete and steel. Cities capture a restricted sample of the physical template in any geographic setting. For example, cities in wet locales would tend to be located on the drier sites locally, while cities in drier climates might be concentrated near rivers or lakes. (Globally, cities tend to be along rivers and coasts.) Despite these starting points, Steele et al. (2014) suggested that humans modify surface hydrology—by creating surface waters in drier sites and draining them in wetter sites—so that cities tend to converge in terms of surface hydrography. It is intriguing to wonder whether this applies to other aspects of our cities. Relevant to the physical template of cities is the process and spatial pattern of development and the role of history in shaping that trajectory. Trimble (1974) provided an in-depth illustration focusing on the Piedmont of the southeastern United States. Trimble scoured old land use records to assemble a generalized trajectory of how forests were cleared for agriculture by European settlers. In this, the most arable lands were cleared first, mostly in bottomlands (but not too much in the flood zone); clearing then progressed uphill, farther from water, until it stopped when settlers encountered slopes that were too steep to plow or with clay content that could not be farmed. As lands became degraded by erosive agricultural practices, lands were abandoned in essentially the reverse of this order. Taverna et al. (2005) explored this trajectory as a hypothesis that might explain the distribution of forest cover types in the modern landscape. They found that residual hardwood forests (i.e., those that had never been cleared) occupied very wet sites adjacent to streams as well as spatially disjunct sites on very steep slopes or on sites characterized by clay soils with high plasticity (shrink-swell potential). Pine forests, which were primarily postagricultural, occupied sites on intermediate slope positions and soil types; presumably, lands still in agriculture are on sites that are the most arable (Taverna et al. 2005).

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This example suggests that land use legacies might often play a role in the location of human development locally, with this layered onto more macroscopic and geographic constraints on the locations of cities.

9.3.1.1

The Urban Heat Island Effect

The primary gradients defining the physical template of terrestrial landscapes are temperature and moisture, and both of these are highly modified in urban settings. Perhaps the best known of these is the urban heat island effect (Oke 1982). Urban heat islands are local temperature anomalies that cause cities to be warmer (especially at night) than rural settings with intact vegetation cover. This effect reflects a variety of forcing factors: waste heat (e.g., from industry and automobiles), the heatholding capacity of concrete, the low albedo of built structures (especially asphalt roads), the trapping of re-radiation by tall buildings in “urban canyons,” the reduced evaporative cooling due to the lower vegetation cover, and so on (Bonan 2008; Pickett et al. 2011; Wilson 2011). Because of these varied forcings, within-city temperature anomalies are quite spatially heterogeneous (Fig. 9.2). Many studies of the urban heat island have used a cities-as-samples approach, focusing on the relationship between city size or configuration and the heat island and emphasizing the downwind propagation of the effect. More recently, studies have adopted a samples-in-cities approach to highlight the extreme local variability Surface Temperature (Night) Air Temperature (Night)

Temperature

Surface Temperature (Day) Air Temperature (Day)

Rural

Suburban Pond

Warehouse or Industrial

Urban Residential

Downtown

Urban Park Residential

Suburban

Rural

Fig. 9.2 The urban heat island effect along a transect across a hypothetical city (US EPA n.d.). The transect represents the aggregate effect as well as its internal heterogeneity

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Agents and Implications of Pattern

261

in heat island effects (highlighted in Fig. 9.2). This has been enabled by the availability of remotely sensed data products with a high spatial resolution (Voogt and Oke 2003), such as the Landsat Thematic Mapper’s thermal band (typically resampled down from 120 m). Such imagery illustrates the dramatic local variation in surface temperature—as much as 10–50 °C. Note that these are temperatures at the top of the surface land cover (i.e., “skin temperature”), not near-ground air temperatures, which are lower and less extreme. In the Piedmont of North Carolina, unpublished data suggest that larger forest patches are a few degrees cooler, on average, than nearby nonforest areas; this temperature varies with distance to the forest edge (interior forests are cooler than edges) and with the amount of built (impervious) surface area within a 500-m buffer around the smaller forest patches.

9.3.1.2

Precipitation

Moisture varies across cities due in part to spatial trends in precipitation. One forcing factor is the feedback between evapotranspiration and precipitation: if evapotranspiration is reduced because of less vegetation cover, then precipitation can also be reduced. Precipitation also is affected by surface roughness of the city (i.e., the heterogeneity of the urban height profile in Fig. 9.2) as this affects wind speed and convection. This results in less precipitation over cities, with this effect displaced spatially to downwind of the city itself. As with the urban heat island effect, precipitation anomalies can be spatially heterogeneous within cities as well.

9.3.1.3

Other Abiotic Factors

Available moisture, the result of the interaction of water supply and water demand (Chap. 1, Sect. 1.3), is influenced by temperature (demand) as compared to precipitation, local runoff, and storage in the soil (all supply terms). Runoff and infiltration capacity are influenced enormously by land cover: impervious surfaces route runoff to streams or stormwater infrastructure with very little infiltration, and even residual soils might have reduced infiltration capacity due to the lower vegetation cover and local soil compaction. Soils might be residual and seminatural, or they might be highly modified by humans. For example, consider the vast amounts of fill material trucked in to level the topography of built areas: this fill is not surface soil with a high organic matter and biological activity; it might not be soil at all (Pickett et al. 2011). As a result, the water cycle in urban systems tends to be dramatically different than in a natural (e.g., forested) system (Fig. 9.3). In cities, surface runoff is much greater relative to infiltration. We return to this below, when we explore the urban stream syndrome.

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Urban Landscapes

75-100% Impervious Surface 30% Evapotranspiration

40% Evapotranspiration

55% runoff

10% runoff

25% shallow infiltration

10% shallow infiltration 25% deep infiltration

5% deep infiltration

Fig. 9.3 The water cycle in urban as compared to a natural system, emphasizing differences in surface runoff and shallow and deep infiltration. (Redrawn after FSRWG 1998)

9.3.1.4

Biotic Agents of Pattern in Urban Settings

As in Chap. 2, when we consider biotic agents of pattern, we focus on the causes of broad-scale, macroscopic patterns, and we will reserve more subtle variation in the local structure and composition of biotic communities as implications or responses to pattern. From this perspective, the most flagrant agents of biotic pattern are the actions of humans to alter communities or vegetation and to introduce new elements. The biotic elements of urban landscape pattern take on various forms, but several schemes organize these into just a few categories. Remnant vegetation patches are residual and at least somewhat natural (but probably with some exotic or invasive elements). Managed or restored types are remnant but persist subject to substantial and sustained human intervention or maintenance; parks and cemeteries are illustrations. Many forests in urban settings are not remnant but rather emergent and have developed as second growth on the sites of former agriculture or other land uses. Other elements are purely of anthropogenic origin, such as planted lawns or gardens. As with hydrography mentioned previously, humans tend to move biotic elements toward the middle: we plant vegetation in sparse landscapes, and we clear more densely vegetated sites. The interspersion of these patches with built elements (roads, buildings) provides for a very high-contrast landscape that can emphasize the stark differences between human and seminatural patches while masking the heterogeneity among patches of similar type. Cadenasso et al. (2006) emphasized the interplay of ecological and social drivers of this heterogeneity.

9.3.1.5

Disturbance Regimes

Disturbance can be a confusing topic in urban systems because it is intuitive to treat land conversion in urbanization as a disturbance event. But conversion at the scale of the event itself (e.g., for a building) is hard to reconcile with the conventional notion of disturbance as a discrete event that causes a disruption in the system (Pickett and

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White 1985, Chap. 3). While the perturbation is obvious enough, the awkward bit is that the converted site does not then undergo some sort of succession or recovery; conversion is typically permanent, and hence the event has no ending. It might be tempting to consider urbanization a persistent or chronic stress instead of a discrete event, but this is not very satisfying either. The problem with disturbance and urban systems is that this means too many things! Grimm et al. (2017) provided an insightful reconciliation of traditional notions of disturbance and urban systems. They used the conceptual model of Peters et al. (2011, and recall Sect. 3.3.1), which disaggregates disturbance to focus on the initial state of the system, the biophysical mechanisms by which the disturbance has its effects on the system, and the response of the system to the disturbance—including any legacies or changes to the state of the system that might in turn influence future disturbances. Grimm et al. (2017) emphasized three themes in considering urban systems: they focused on disturbance as a process, they translated disturbance notions to socialenvironmental-technical systems, and they were careful to specify the system in space and time. They considered both short-term, abrupt events (pulses) and longerterm, more chronic stressors (presses) (Collins et al. 2011). As Peters et al. (2011) had emphasized, Grimm et al. recognized that many disturbance events act via multiple mechanisms. For example, a hurricane causes damages via wind, a storm pulse (e.g., a wave), and prolonged flooding. Further, in socio-environmental systems there will be ecological responses and legacies as well as social responses and legacies. For example, social responses to extreme flooding might include behavioral responses (people relocating to higher ground) as well as institutional responses (changes in zoning or other regulatory policies). Importantly, Grimm et al. emphasized that there are interactions between natural and social responses to disturbances, with social responses perhaps on a different time scale than natural responses. They found the Peters et al. model to be effective in applications to heat waves, fires, and floods in cities, land conversion (development itself as well as reforesting via deliberate plantings), and humaninduced socioeconomic disturbance (a recession, Fig. 9.4). The review and illustrations by Grimm et al. (2017) suggest that ecological notions of disturbance and disturbance regimes can be applied readily to urban systems, so long as the important details are disaggregated and incorporated into the model. This approach requires that the system be defined at an appropriate scale.

9.3.2

Scale and Pattern

We have already explored the natural scaling of ecological patterns and processes in Chap. 4. In many landscapes, this scaling can be modified by the actions of people and their physical infrastructure. For example, fragmenting intact forests into discrete patches with often substantial edge effects can alter the natural scaling of forests due to heterogeneity in soils, topography, or microclimate. Jenerette et al.

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Disturbance Event Drivers

Drivers

Available colonist pool Dispersal, colonization Release of management

Housing “Bubble” Dist Type

Internal Processes

Economic Downturn

Resource Dynamics, Competition

Dist Mechs

Foreclosure, Abandonment

Disturbance Impact Disturbance

System Properties

Rapid housing construction Speculation Highly mobile and growing population

Human migration Loss of Management System Properties Change

Dist Recovery/Succession/ Reorganization Changing System

New State of System

Vacant and unmanaged properties New species colonists

Loss of vegetation Altered species composition

Fig. 9.4 Economic recession as a disturbance to a socio-environmental technical system, using the disaggregated model of Peters et al. (2011). (Redrawn from Grimm et al. 2017)

(2006) found different patterns of local heterogeneity in biogeochemistry at the patch, cover type, and regional scale in the Phoenix area, southwestern USA. Similarly, natural processes such as hydrologic fluxes or dispersal by species in urban settings can be modified in ways that we attend in the following sections. What is new to the scaling of social-environmental systems is the characteristic scaling of human behaviors and institutions. Land use itself is an inherently spatial process: development has a characteristic grain dictated by parcel sizes, and urbanization is a contagious process by which development begets subsequent development nearby (e.g., McDonald and Urban 2006). But human institutions are also scaled by social and economic interactions. Pickett et al. (2011) framed this as a space-time diagram (Fig. 9.5, and recall Fig. 4). In this, the ownership parcel (e.g., a house on a lot) is the basic spatial unit, and these are nested within neighborhoods, larger administrative units (e.g., counties or metropolitan areas), and so on. Time scales range from human behaviors that unfold over months to the longer-term dynamics of the evolution of transportation systems and land use policies. Socio-environmental technical systems (SETS) are further complicated by interactions that might not be strictly spatial and certainly not in a nested pattern. For example, institutions related to professional, religious, and lifestyle identities might be spatially distributed heterogeneously over areas much larger than a neighborhood

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GLOBE

COUNTRY Employment opportunities; living costs; urban amenities; climate, and other Public natural services, features infrastructure, local policies

METRO

Space

REGION

COUNTY

Economic restructuring

Transportation and communication costs

Socioeconomic characteristics; urban amenities; natural amenities; zoning; access to employment, shopping, recreation, parks, other destinations

NEIGHBORHOOD

Household wealth

Structural features, public utilities, land parcel, neighboring houses

HOUSE

Time MONTH

QUARTER

YEAR

DECADE

CENTURY

Fig. 9.5 Scaling of human components of a social-environmental system. The fundamental unit is the household, at the scale of a parcel, in the context of surrounding neighborhood and larger-scale and longer-term constructs. (Redrawn with permission from Elsevier, from Pickett et al. (2011); permission conveyed through Copyright Clearance Center, Inc.)

or a city. And economic connections, even for small towns, are routinely much larger than the city and increasingly global. Seto et al. (2012) characterized these teleconnections in terms of whether the connections mapped one:one, many:one, or one:many between cities and distal locations; they also considered direct connections among cities. Finally, SETS can be complicated by the reality that the spatial boundaries of natural systems often do not correspond to human boundaries. A watershed that spans political boundaries is a familiar example that can confound water resources management. Wilson et al. (2015) cataloged the many ways in which the timescaling of human and natural systems might be mismatched. They emphasized the natural time-scaling of policy and institutional learning as compared to the ecological scaling of issues such as water quality, fire, and invasive species management.

9.3.3

Implications of Pattern

Metapopulations, community patterns, and biogeochemistry and hydrology are increasingly well studied in urban landscapes. These include a mix of empirical approaches, but most such studies adopt a samples-in-cities approach or a gradient model constructed from samples in cities and nearby exurban or rural locations.

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Urban Metapopulations, Communities, and Patterns of Biodiversity

The relatively discrete nature of residual or second-growth habitat patches in urban settings would seem to invite applications of metapopulation theory. Many such studies have been conducted in habitat patches in urbanizing landscapes, but the focus has often been on exurban landscapes fragmented by nearby development pressure. Kand et al. (2015) focused more deliberately on urban settings, and Lepczyk et al. (2017) have reviewed applications related to biodiversity in cities, with an aim to marshal further research on understudied issues including connectivity. It remains, however, that a quick search for papers on metapopulations in cities reveals a preponderance of studies of epidemiology in cities: the role of connectivity and metapopulation structure in mediating the dynamics of infectious disease (e.g., LaDeau et al. 2015). Tremblay and St. Claire (2011) used translocation experiments to explore the effect of habitat permeability on the movement of forest birds in urban settings. They found species-specific behavioral differences in how birds responded to forest gaps and roads and suggested that cumulative barriers were more important than individual structures. Their focus on dispersal behavior and functional distances echoes these themes in metapopulation ecology as discussed in Chap. 6 (Sect. 6.5.1). By contrast, a very large literature addresses patterns of biodiversity and community assembly in urban landscapes. For example, Marzluff and Rodewald (2008, and further reviewed by Pickett et al. 2011) posed general trends in species richness along an urbanization gradient that reflected an increase in invader species with increasing urbanization intensity, a loss of avoider species sensitive to urbanization, and a peak in adapter species at intermediate levels of urbanization. The net result, over the landscape, is a peak in total species richness at intermediate levels of urbanization. Michael McKinney (2002, 2004, 2005, 2006, 2008; McKinney and Lockwood 1999) has summarized a huge volume of literature on human impacts on biodiversity, coining the term biotic homogenization to describe the loss of biodiversity and increasing compositional similarity of urbanized environments. In a large review (McKinney 2008), he found that both invertebrates and vertebrates most commonly showed the highest diversity in sites in the lowest category of urbanization, while the most highly urbanized sites showed the lowest diversity. By contrast, plant diversity was the highest at intermediate levels of urbanization; this effect was driven largely by invasive species and consistent with the gradient described by Marzluff and Rodewald (2008). Kinzig et al. (2005) underscored the links between urban biodiversity and human cultural and socioeconomic factors. Williams et al. (2009) disaggregated the urbanization effect into the “four filters” hypothesis. They posed that urbanization comprises four mechanisms that influence plant biodiversity: habitat conversion (change in type), habitat fragmentation, the abiotic environment of urban settings (i.e., temperature, moisture, and

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Fig. 9.6 The “four filters” hypothesis on how urbanization influences plant diversity in urban settings. The filters are habitat transformation, fragmentation, the abiotic environment, and human preferences. Conceptual (latent) variables are drawn as ovals in the style of a structural equation model, each measured by empirical indicator variables (rectangles). The abiotic environment is drawn as a composite variable (hexagon) aggregated from multiple (additive) indicators. Directed arrows are causal, while bidirectional arrows are correlational. Black lines are positive effects; red, negative. (Redrawn with permission of John Wiley & Sons, from Lopez et al. (2018a); permission conveyed through Copyright Clearance Center, Inc.)

chemistry), and direct human influences and preferences (e.g., horticultural choices). Lopez et al. (2018a) recast this hypothesis as a general path model (Fig. 9.6) and used structural equation models (Grace 2006; Grace et al. 2010, 2012) to explore the relative importance of the four factors on taxonomic, phylogenetic, and functional trait diversity of urban plant communities. This approach invites further assessment as a model template for biodiversity in urban landscapes. This plant-centric model might need some modification in application to wildlife species, where response to urbanization is often behavioral (Lowry et al. 2013). Metacommunity concepts, using the formalisms we considered in Chap. 7, have not been explored so much in cities, although Andrade et al. (2021) have provided some recent guidance on how to apply metacommunity models (Sect. 7.4.2) in urban systems. Sattler et al. (2010) adopted the method of variance partitioning, used in metacommunity ecology (Sect. 7.4.4), to assess the relative importance of environmental controls as compared to spatial processes in explaining patterns of diversity in spiders, bees, and birds in three European cities. They found environmental effects to be much stronger than “pure” spatial effects, in contrast to studies of more natural systems where the spatial signal is much stronger—often stronger than the environmental effect. They suggested that urbanization might disrupt spatial processes such as dispersal. Their results are especially intriguing in that so many species common in cities are generalists or cosmopolitan species with rather loose environmental affiliations.

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Fig. 9.7 Human-mediated filtering of urban biodiversity, emphasizing the relative importance of human selection (e.g., choices about pets, garden plants) and dispersal (e.g., via deliberate movement). (Redrawn from Avolio et al. 2021)

Lopez et al. (2018b) used variance partitioning to compare local environmental conditions and alternative models of connectivity (based on Euclidean distances, least-cost paths penalizing urban land covers, and stream-based corridors) for riparian plant communities. They found both connectivity and environmental effects to be important, with the relative importance varying according to dispersal mode and for native as compared to exotic (introduced, nonnative) species. Avolio et al. (2021) reviewed conceptual models for urban biodiversity, linking these to community ecology more generally (e.g., Vellend 2016). In this, they focused on human actions and behaviors that influence patterns of environmental filtering and dispersal (Fig. 9.7). Key to this was the identification of two species pools that are filtered in urban communities: a regional pool and a pool provided by humans (e.g., via horticulture) that is increasingly global. They further argued that urban landscapes are a heterogeneous mix of communities that vary in the intensity of management, from essentially unmanaged sites (e.g., abandoned properties) that are colonized naturally and filtered in place to sites that are so intensively managed such that the community is essentially controlled by human behaviors. Their framework offers useful guidance on developing a more nuanced and predictive understanding of how ecological communities are assembled in urban landscapes and underscores the wide range of community-level heterogeneity we might expect based on the relative importance of human influences on assembly processes.

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Agents and Implications of Pattern

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Ecosystem Processes

Ecosystem processes are rather well studied in cities. These include cities-as-samples studies that document whole-city element or energy budgets. As an example of this approach, ecological footprint studies (Wackernagle et al. 2006) emphasize the large subsidies to urban budgets from distal sources (by contrast to the frequent assumption that ecological ecosystem budgets represent closed systems). Pickett et al. (2011) reviewed and critiqued footprint studies. More interesting here are samples-in-cities approaches that focus on local or neighborhood-scale ecosystem processes, especially studies of human influences on element budgets and biogeochemistry (e.g., via lawn fertilization). Pickett et al. (2011) reviewed several such studies. These studies focus on the profound spatial heterogeneity in urban systems, consistent with our emphasis in all aspects of the implications of pattern (Chaps. 6, 7, and 8). In cities, this heterogeneity often maps onto patterns in socioeconomic status and cultural preferences (e.g., Law et al. 2004; Kinzig et al. 2005; Golubiewski 2006). Kaye et al. (2006) reviewed energy and material fluxes among the atmosphere, land, surface waters, and groundwater in urban ecosystems. They underscored the reality that, of all the possible pairwise fluxes between these components, most fluxes are mediated to some extent by human activities. Urban systems readily lend themselves to the meta-ecosystem concept promoted in Chap. 8 (Sect. 8.4.2, Gounand et al. 2018). This framework emphasizes the diversity of exchanges among similar ecosystem types (e.g., forest patches) as well as the many and varied subsidies among adjacent systems of different type. In Chap. 8, we focused on subsidies between seminatural systems such as adjacent aquatic and terrestrial systems. In urban settings, there are a number of additional examples including exchanges between planted (horticultural) gardens or lawns and more natural vegetation. Additionally, there are many instances where developed infrastructure contributes directly to ecosystem behavior; examples include nitrogen deposition and other atmospheric effects as well as pollutant inputs to terrestrial and aquatic systems (e.g., Lovett et al. 2000; Rao et al. 2014). For example, Wade et al. (2021) found spatially heterogeneous patterns of lead concentrations in urban soils, a legacy of inputs from leaded paint on buildings and leaded gasoline near roads (and see Pouyat and McDonnell 1991; Schwarz et al. 2016). These legacy patterns are pronounced despite the abandonment of leaded paint and gasoline many decades ago. Finally, consistent with the meta-ecosystem conceptualization of Gounand et al. (2018), the couplings among elements vary enormously in terms of actual mechanism, spatial distance, and timing.

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Revisiting the Agents-and-Implications Framing

Our main concern in the preceding sections was not to document all of the agents and implications of pattern in urban landscapes but rather to ask whether that framing could be applied usefully to urban settings. In general, the framing seems useful. It is reassuring that the ecological paradigm of reciprocal pattern-process interactions and feedbacks seems sufficiently general to encompass urban systems. Likewise, issues of spatial and temporal scaling are equally crucial in socialenvironmental systems. Importantly, the fundamental issues of spatial heterogeneity and connectivity—and how these vary over time—are shared by urban landscapes as well as more natural settings (Cadenasso et al. 2006; Pickett et al. 2017). This framework does require some important extensions for urban landscapes. While we have emphasized the generation and consequences of spatial heterogeneity and local interactions, urban systems are more open and often feature inputs or exports that are far removed from the city itself. Global economic teleconnections are an extreme but common case of these interactions. Similarly, the spatial and temporal scaling of social systems might be rather different from ecological systems, with social systems again featuring interaction networks that might be far removed from the city. Scaling mismatches between human and natural systems, including differential lags or response times, can be complicating as well. Importantly, these invite extensions to the agents-and-implications framework— not an entirely new conceptual model. Perhaps the most pressing extension is to include humans as self-aware and directed actors in the system, which is a necessary step if we are to design sustainable and resilient cities. Ecologists will need help from social scientists to fully embrace this approach. Our understanding of socioenvironmental systems will be enriched especially if studies merge the approaches of ecology and social science to embrace novel questions and approaches.

9.4

Urban Landscapes as Laboratories

Urban landscapes offer themselves as compelling laboratories in many ways, often in a quasi-experimental way. In this, recent or historical changes in land cover or land use are used to make inferences about pattern-process relationships. These are before/ after inferential designs, but typically without proper experimental controls. Here we delve into two examples. The first, on urban streams, takes advantage of the huge local variability in landscape pattern in urban settings and the empirical convenience that streams integrate this variability spatially. The second example focuses on climate change and takes advantage of the reality that cities already experience most of the changes we anticipate for the near-term future.

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The Urban Stream Syndrome

Seminatural or intact watersheds serve as a reference case for comparison with streams in urban landscapes. Urban streams have been studied extensively (Paul and Meyer 2001), and the differences between urban and more natural reference streams are sufficiently profound that these are recognized as the urban steam syndrome (USS, Walsh et al. 2005). The USS is a complicated tangled web of symptoms but has a succinct explanation: urban streams are over-connected to their catchments and under-connected to their riparian zones. In urban systems, development creates impervious surfaces such as roads and rooftops, as well as other infrastructure such as holding ponds and sewerage pipes. Development redirects or relocates natural hydrologic flows, by channelizing streams or burying them in culverts. These modifications profoundly influence the flow regime of streams, including the magnitude, frequency, duration, timing, and rate of change of high-flow conditions (Karr 1991; Poff et al. 1997; Meyer et al. 2005; Walsh et al. 2005; Booth et al. 2016). Urban streams tend to be “flashy,” with higher peak flows soon after storms and lower baseflows between precipitation events. The higher peak flows stem from rapid routing of precipitation to streams via impervious surfaces and pipes. Because of this rapid routing, there is less infiltration into the soil and less water recharging the stream after precipitation events, resulting in lower baseflows. These hydrologic alterations, in turn, affect stream ecosystems by influencing the physical habitat of streams, energy sources, resources (i.e., carbon and nutrients), and contaminant loadings. These influence the stream biota and ecosystem function in streams. Changes in stream hydraulics result in strong pulses in stormflow, which scour streambeds and can lead to deeply incised channels. Incision itself can change the energy supply to the stream, as deeply incised channels can be heavily shaded. The scouring can redistribute sediments substantially, which in turn has strong and periodic impacts on biota attached to or embedded in the sediments. Channel incision can disconnect urban streams from their riparian zones. This can result in less frequent overwash events during high flows, which short-circuits a normal mechanism for replenishing floodplain soils. Incision also can result in increased soil moisture dry-down at low flows, because the riparian zone is elevated higher above the baseflow water level. As urban stream hydrology becomes flashier, it creates elevated concentrations of nutrients and resources as these are routed into streams; at the same time, inputs of resources from the (disconnected) riparian zone might be reduced. The levels of contaminants or toxins increase because they are flushed into streams from roads and other human land uses, including chemicals (pharmaceuticals, cosmetics) flushed from households. During drier conditions, these solutes are increasingly concentrated in the lower water volumes at low flow. These dynamics lead to a pulse/press regime for stream systems (Collins et al. 2011; Blaszczak et al. 2019a). Urban streams are often in highly modified landscapes, and so land cover symptomatically affects streams. In particular, reduced canopy cover in riparian

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Fig. 9.8 Major paths that mediate the impacts of hydrology altered by development infrastructure (simplified from Walsh et al. 2005, and see Poff et al. 1997)

zones admits more solar radiation to streams, increasing their temperature while also favoring green algae that thrive under higher light conditions. Increased temperature influence all biophysical processes in streams while also affecting oxygen levels (which decrease with increasing temperature), further affecting stream biota. All of these factors can have a profound influence on stream biota. Some of these are readily observed, for example, changes in fish populations (e.g., Karr 1991, Roy et al. 2005). Others are apparent to trained observers; for example, aquatic macroinvertebrates respond so dramatically to changes in water quality that they are used as bioindicators (e.g., Allan 2004; Lenat and Crawford 1994; Lammert and Allan 1999; Moore and Palmer 2005; Violin et al. 2011). Some changes to the biota are less apparent (e.g., microbial composition) but have consequences for ecosystem functions such as carbon metabolism and denitrification. All of these symptoms can be collected into a few mediating pathways by which urbanization affects stream structure and function (Fig. 9.8). The task is to account for the relative importance of these mediating factors in urban landscapes of different configuration, under varying geology and climate conditions. That is, this is a model template than might be implemented and assessed in various real systems, toward a more general understanding of the USS. As Booth et al. (2016) noted, there is no reason to expect that the USS plays out similarly in all cases, and the differences among cases would help inform management decisions. This would require a set of studies carefully articulated to probe specific instances of the mediating pathways.

9.4.1.1

Watersheds as Samples

Streams are excellent systems for studies of the effect of pattern on process, because streams spatially integrate everything that happens in their catchments (Pickett et al. 1997). Hydrologists have a long history in monitoring streams with gauges at the pour point where streams exit a watershed (e.g., Bormann and Likens 1979; Swank and Crossley 2008). But the upstream spatial integration can be measured at any

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point along a stream. Streams are naturally nested, of course, and so this integration becomes less tidy as we look at larger (higher-order) streams: large streams might integrate very different conditions or processes in the catchments of each tributary and thus average or dilute the contributions from different catchments. For this reason, small or headwater streams are the most compelling study units: they spatially integrate a relatively small contributing area, and this area can be linked directly to in-stream processes. Hydrologists have studied urban streams using two common inferential designs. In the simplest case, urban streams are compared to “natural” reference streams—a comparison that typically (unsurprisingly) would find them different. Another common model is the gradient model of urbanization intensity, in which sample watersheds are arrayed along a gradient measured, for example, in terms of the proportion of the watershed in impervious surface cover. Gradient studies are often confounded by the extreme differences between the natural and intensively urbanized endpoints, which makes it hard to resolve subtle differences at intermediate levels of urbanization (Hassett et al. 2018). In particular, a strong gradient effect can mask the relative importance of the spatial configuration of development infrastructure as compared to its area. The effort to relate watershed pattern to stream processes, in a very precise sense, is the same area versus configuration debate that we confronted in Chap. 5 (Sect. 5. 5.3). In the previous instance, we wanted to improve the functioning of landscapes for species by optimizing the configuration of habitat to mitigate for the loss of habitat: we want to maximize the impact of a given amount of habitat area. Here, the application is the same but in mirror image: we would like to improve watershed function by mitigating the impact of impervious surfaces and development infrastructure by managing its configuration—we want to minimize the impact of a given amount of developed area. The task, then, is to find ways to arrange impervious surfaces and development infrastructure to minimize its impact for a given level of development. Recall from Chap. 5 that most measures of landscape pattern or configuration vary with area as p, the proportion of the landscape occupied by the focal cover type. In previous applications, we were concerned with habitat cover; here, we are interested in impervious surface area, but the principle is the same. In particular, we can only compare configurations for landscapes that have a similar amount of cover, similar values of p (Gardner and Urban 2007). That means that we must contrast watersheds that vary in their configuration while holding developed surface areas relatively constant. Emily Bernhardt and her colleagues have studied streams in a series of field studies in an urban landscape of the Triangle region of the North Carolina Piedmont. They have focused on small, headwater streams where the link between land cover and streams should be most direct. Over time, their approach has evolved from comparative, to gradient, and now to a more nuanced sampling design that varies development configuration while holding developed land cover constant (Fig. 9.9). Somers et al. (2013) used small watersheds as sample units to explore thermal pulses in urban streams in the Triangle region of the North Carolina Piedmont.

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Fig. 9.9 Sampling approach to separate the effects of developed area from its configuration (E. Bernhardt and D. Urban, unpublished). In the left-most panel is a binary approach to sampling, contrasting urban and nonurban (reference) streams. In the center panel, a regression model is invoked, and samples are distributed along a gradient of urbanization intensity. In the right panel, a narrow range of development intensity is selected, and samples are arrayed over a range of spatial configurations at that level of development. Only this last case allows us to make clear inferences about spatial configuration or pattern

Somers delineated sample watersheds from readily available geospatial datasets on hydrography (the National Hydrography Dataset, NHD+, McKay et al. 2012) and land cover (the National Land Cover Dataset, NLCD, Homer et al. 2004). Candidate sample watersheds were stratified in terms of the intensity of development, estimated in terms of the percentage of each watershed in developed land covers. Candidate watersheds were “air-truthed” using high-resolution aerial imagery, and a final set of samples was selected. Somers instrumented each sample stream with temperature data-loggers and used the temperature time-series data to characterize thermal pulses to each stream in the aftermath of precipitation events. She used structural equation models (SEMs) to estimate the relative importance of various aspects of development to the thermal regime of the streams (i.e., focusing on the energy path “heat/ light” in Fig. 9.8). Somers found that variables measured at the stream reach (channel width, canopy closure overhead) were more important in explaining baseflow temperatures, while watershed-scale variables (especially percent developed) were more important in explaining stormflow thermal pulses. This effort to relate more nuanced measures of watershed pattern to stream processes was confounded somewhat by the length and strength of the development gradient, which ranged from 90% developed land cover: with this strong a gradient, it was difficult to resolve much else. But we also can better appreciate now why it was difficult to separate developed area from other aspects of pattern within these watersheds: this is area versus configuration again, and again area confounds other correlated aspects of pattern. Bernhardt and colleagues have addressed this challenge in a series of field studies in an urban landscape of the Triangle region of the North Carolina Piedmont, extending their earlier work based on a development gradient (above). In this, they

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Fig. 9.10 Sample watersheds illustrating a design that contrasts aboveground surface area aggregation with belowground stormwater pipe density while holding developed area constant (K. Somers, unpublished)

revisited the full set of watersheds to select candidate sites within a narrow range of developed land cover (e.g., 20–30%). Within this subset of watersheds, they used FRAGSTATS (McGarigal et al. 2002, Sect. 5.3) to characterize the configuration of land cover. This approach allowed them to separate configuration from area effects (Fig. 9.10). Blaszczak et al. (2019b) used a subset of 24 of these sample watersheds, instrumented with continuous monitoring of streamflow, temperature, and conductivity along with bimonthly measures of solute chemistry, to explore the relationship between development configuration and “chemical flashiness” in urban streams. They found that subsurface piping (e.g., stormwater and sewerage infrastructure) mediated the relationship between roads and stream chemistry: in watersheds with high pipe density, ionic streamwater concentrations were lower at baseflow and higher and quite variable at peak flows. In watersheds with low pipe density, baseflow concentrations were higher and peak flow concentrations were lower and less variable. This approach to disentangling the urban stream syndrome illustrates two important points. First, inferences about the relative importance of development configuration as compared to developed area can be resolved most clearly if configuration is varied while holding area nearly constant. This is consistent with our conclusions

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more generally about inferences on pattern (Chap. 5), and it is at odds with the popular approach of using urbanization gradients as the basis for such inferences. And it should probably be emphasized here, again consistent with conclusions about area and configuration in Chap. 5, that the main effect in watersheds is still likely to be impervious area; but still, configuration can be managed to minimize impacts at a given level of development. Second, the general model of the USS (as a model template, Fig. 9.8) is one that can be dissected by carefully implemented field studies, and we expect that the details will vary substantially in different settings (Booth et al. 2016). Indeed, Blaszczak et al. (2019a, b) found that their urban streams behaved quite differently in watersheds according to underlying geology. Continued specification of this model template, adopted to a range of landscape settings, should improve our understanding of urban streams. This, in turn, would allow us to make better management decisions under scenarios of continued development pressure (Bernhardt et al. 2008). If we are going to develop cities anyway, we should learn how to do that while minimizing the impacts of development.

9.4.2

Cities as Mesocosms for Global Change

Urban heat islands naturally invite an analogy to future-climate scenarios. Several authors have suggested cities (e.g., Grimm et al. 2008) or urban-to-rural gradients (Carreiro and Tripler 2005; Rao et al. 2014) as analogs for climate change. The analogy is apt and extends well beyond warming. Cities experience warmer temperatures, to be sure, but they also see higher CO2 concentrations, altered precipitation regimes, increased frequencies of floods and droughts because of the urban stream syndrome, altered biogeochemical cycles because of atmospheric deposition and human inputs of nitrogen and other elements, and characteristic flora and fauna (i.e., through invasives and biotic homogenization) that are symptomatic of the future (Fig. 9.11). This is all on top of the more obvious changes in land cover and land use—itself another key aspect of global change. These correspondences make it easy to recommend the use of cities as mesocosms in which to explore the ecological and social-ecological implications of global change. In this, we would be adopting a space-for-time substitution (Chap. 2, Sect. 2.2) while recognizing that all such substitutions are imperfect. One obvious effect of urban heat islands is the likelihood that plant phenology would be disrupted (Neil and Wu 2006; Fisogni et al. 2020); Zipper et al. (2016) found a shift of about 5 days due to within-city heat island impacts, with this shift tempered by the local cooling effect of parks. Such changes have implications for plant-pollinator systems (Harrison and Winfree 2015). Phenological effects also have been documented for plant pests (e.g., Meineke et al. 2013; Youngsteadt et al. 2015).

9.4

Urban Landscapes as Laboratories

Fig. 9.11 Comparison of urban environments to symptoms expected of global climate change. (Redrawn with permission from the Royal Society (UK), after Lahr et al. (2018); permission conveyed through Copyright Clearance Center, Inc.)

Climate Change Expectation

higher temperature higher carbon dioxide more frequent heat waves more droughts and heavy rain events regionally higher ozone

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Local temperature anomalies can have measureable effects on species composition in urban settings. For example, Menke et al. (2011) documented compositional shifts in ant species composition in urban forests, mixed-use development, and industrial settings. They found that more open (developed) settings supported ant assemblages with species characteristic of warmer and drier climates of the American southwest. Other studies have documented the effects of urban environments on genetic drift (e.g., Miles et al. 2018) and evolutionary processes (Rivken et al. 2018). From the perspective of climate change, the relevant research questions are about how species respond to a rapidly changing climate: Do they adjust locally by modifying their behavior (diurnal or seasonal activity times, microhabitat use)? Can they move short distances to more suitable microclimates (e.g., to cooler topographic positions or habitat types)? What role might interactions with other species—especially invasives—play in this? Can species adapt in place, using standing genetic variation? Can they adapt fast enough in the face of changing selection pressures? We will consider these options when we delve into climate change and climate-resilient landscapes in Chap. 10, but these already are accessible questions in urban landscapes today. Many of these questions relevant to climate change adaptation can be framed in terms of current approaches in metacommunity and meta-ecosystems ecology. In particular, the relative importance of environmental filtering as compared to dispersal or species interaction is a focus of metacommunity ecology (Chap. 7, Sect. 7. 3.2), and these questions might be gainfully addressed in urban settings. Likewise,

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the roles of abiotic and especially biotic transfers of materials and trophic roles— among similar as well as dissimilar patch types—are emerging as a more empirically accessible version of meta-ecosystems theory (Gounand et al. 2018, Sect. 8.4.2).

9.4.2.1

Global Change, Spatial Heterogeneity, and Environmental Equity

The profound spatial heterogeneity of urban systems is widely recognized, and the correspondences between this heterogeneity and socioeconomic, racial, and ethnic indicators are increasingly obvious (e.g., Bolin et al. 2005; Mohai and Saha 2007; Uejio et al. 2011; Wolch et al. 2014). The case of exposure to extreme heat due to urban heat islands is particularly well studied (e.g., Hoffman et al. 2020), but disparities also exist in terms of air quality and access to recreational green spaces (reviewed by Wolch et al. 2014). Urban heat islands spawn increased likelihood of adverse health outcomes, either directly or through interactions with air quality (e.g., ozone). Some structural aspects of cities, of course, are related to multiple hazards or amenities: tree cover affects temperature, air quality, and recreational opportunities (though in some cities these are not straightforward relationships: Schwarz et al. 2018). And episodic events such as heat waves interact with other stressors and systemic disparities to amplify adverse health outcomes including disease, asthma, and obesity (e.g., Wilhelmi et al. 2021). This constellation of patterns is sufficiently established that they have been referred to as the urban health penalty (reviewed by McDonald and Beatley 2021). These symptoms invite an ecology for cities, and such concerns have indeed been a key motivation for this new perspective on urban ecology. If we want sustainable and livable cities, we will need to address the disparities in environmental amenities and stressors—especially those exacerbated by climate change and extreme climate variability. The issue of environmental disparities in cities mirrors—though not completely—equity issues at the global scale. While some global concerns such as the inundation of island nations do not have a general analog in cities (except, of course, some coastal cities!), the more general issue remains that climate change will most impact those who have the least capacity to adapt. Moreover, these vulnerable populations are, in general, not the principal actors responsible for climate change. Global change is a daunting and frustrating problem precisely because it is happening everywhere, and it is happening rapidly. Its solution, however, will stem from the widely distributed efforts of local actors. These actors are individuals but also part of institutions, organizations, and governments. Cities—as socialenvironmental systems—can serve as the laboratory and proving ground for these solutions.

References

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Summary and Conclusions

Urban landscapes are characterized by direct human actions that create or modify structural elements of the system. These elements, in turn, influence processes that occur on urban landscapes. Despite this apparent novelty, the agents-and-implications framework seems readily amenable to urban settings, so long as we attend the anthropogenic and social elements. Humans provide for interactions among novel patch types, as well as a fuller set of potential interactions between natural elements and social elements or institutions. Urban landscapes, as social-environmental systems, are further complicated because of the dual role of people as agents of change and responders to those changes—with the agents and responders perhaps decoupled in space and time. Urban watersheds, because of the tight coupling to and spatial integration of landscape pattern, can serve as natural laboratories in which we might a lot about stream ecosystems and pattern-process linkages more generally. This should give us better capacity to develop urban landscapes while minimizing the impacts of development. Cities are harbingers of global change in that they already experience many of the symptoms. This should allow us to explore ways to mitigate or adapt to these changes, essentially using cities as laboratories in which to develop solutions. This applies, perhaps especially, to problems of social equity and environmental justice.

References Alberti, M. 2008. Advances in urban ecology: Integrating humans and ecological processes in urban ecosystems. New York: Springer. ———. 2017. Grand challenges in urban science. Frontiers in Built Environment 3: 6. Alberti, M., J.M. Marzluff, E. Shulenberger, G. Bradley, C. Ryan, and C. Zumbrun-nen. 2003. Integrating humans into ecology: Opportunities and challenges for studying urban ecosystems. Bioscience 53: 1169–1179. Allan, J.D. 2004. Landscapes and riverscapes: The influence of land use on stream ecosystems. Annual Review of Ecology, Evolution, and Systematics 35: 257–284. Andrade, R., J. Franklin, K.L. Larson, C.M. Swan, S.B. Lerman, H.L. Bateman, P.S. Warren, and A. York. 2021. Predicting the assembly of novel communities in urban ecosystems. Landscape Ecology 36: 1–15. Avolio, M.L., C. Swan, D.E. Pataki, and G.D. Jenerette. 2021. Incorporating human behaviors into theories of urban community assembly and species coexistence. Oikos 130: 1849–1864. Bernhardt, E.S., L.E. Band, C.J. Walsh, and P.E. Berke. 2008. Understanding, managing, and minimizing urban impacts on surface water nitrogen loading. Annals of the New York Academy of Sciences 1134: 61–96. Somers, K.A., E.S. Bernhardt, J.B. Grace, B.A. Hassett, E.B. Sudduth, S. Wang, and D.L. Urban. 2013. Streams in the urban Island: Spatial and temporal variability in temperature. Freshwater Science 32: 309–326. Biggs, R., F.R. Westley, and S.R. Carpenter. 2010. Navigating the back loop: Fostering social innovation and transformation in ecosystem management. Ecology and Society 15: 9.

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Chapter 10

Climate Change: Adapting for Resilience

10.1

Introduction

Landscape pattern has had a profound impact as a driver of global climate change but also can play a significant role in mitigating change and adapting landscapes for resilience. Deforestation and land use practices (especially agriculture) have contributed substantially to increasing CO2 emissions into the atmosphere, but afforestation and changes in land use also could contribute substantially to climate mitigation by reducing emissions of greenhouse gases (GHGs) and sequestering carbon (IPCC 2019; Malhi et al. 2020). There is an enormous and authoritative literature on the topic of climate change, ranging in scale from global syntheses (e.g., IPCC 2014), to national summaries (e.g., US GCRP 2016, 2017, 2018), to more regional efforts and on down to state (e.g., Bedsworth et al. 2018) and local climate action plans (e.g., Boswell et al. 2019). There is also a growing body of evidence on ecological responses to climate change (e.g., Parmesan 2006; Chen et al. 2011, Foden et al. 2013; Pacifici et al. 2015, 2017) and the implications for conservation and natural resource management (e.g., Heller and Zavaleta 2009; Mawdsley et al. 2009; Watson et al. 2013; Stein et al. 2014). Our purpose here is not to reproduce nor even summarize this vast amount of information. For a general discussion of resilience, see Chambers et al. (2019), and for a broader perspective on global change biology, see Sage (2020). Rather, we will look at landscapes from an adaptive perspective: we will explore aspects of landscape pattern (and land use) that might contribute to landscape resilience under climate change and how we can manage deliberately for resilient landscapes. Our focus will be on seminatural resources and conservation applications, but this approach can be extended beyond conservation. The need to act deliberately and adaptively toward resilience is crucial, in part, because the climate system has so much inertia that even if we had the technical capacity and political will to reduce emissions dramatically and immediately, the climate will continue to change for decades if not centuries, and so we will need to adapt. © Springer Nature Switzerland AG 2023 D. L. Urban, Agents and Implications of Landscape Pattern, https://doi.org/10.1007/978-3-031-40254-8_10

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To be clear about word usage here: mitigation refers to actions to reduce greenhouse gas emissions and slow climate change; adaptation refers to actions to moderate the impacts of climate change. As we shall see, many of the actions taken to increase resilience under adaptation will also contribute to mitigation, and many actions toward adaptation to climate change are consistent with current conservation aims and practices. This overlap and opportunity for leverage will be welcome. In this chapter, we begin with a brief overview of the main elements of climate change and how these manifest regionally. We then turn to adaptation. In this, it is useful to frame adaptation as a problem in risk management: what are the elements of risk, and what can we do to reduce these risks? We will explore this by delving into a few illustrative efforts to estimate climate vulnerability for target species or ecosystem types, as a means to prioritize sites for adaptive management. We will also look at an example of a systematic approach to designing climate-resilient landscapes. Climate change is an issue where the stakes are global but all relevant action is local, that is, all local models are specific realizations of the general case.

10.2

Framing Adaptation

Framing any discussion on adaptation to climate change requires that we first specify what, exactly, we aim to adapt to and then define the scope of the discussion in terms of rationale and levels of activity. In this section we first outline the main issues represented by climate change and then adopt a risk-management perspective on adaptation options.

10.2.1

Components of Climate Change

The elements of climate change are well known and increasingly well documented empirically (e.g., IPCC 2014, 2019). Changes include a general warming, with increases amplified at higher latitudes. Warming is more pronounced in winter than in summer, and so patterns of warming also include changes in seasonality and phenology. Changes in precipitation are more uncertain than in temperature, in part because of the complexities arising from frontal as compared to convective storm systems but also because current patterns in precipitation are already quite variable: in some regions the natural variability in precipitation currently observed (i.e., over the past 30-year norms) is as large as the changes expected of future climates. A second component of climate change is an increase in the frequency and intensity of extreme events, such as floods and droughts. Some of this is simply physics tied to warming: as the air warms, it has a higher water-holding capacity, and so storms can generate more precipitation; likewise, high aridity leads to rapid diurnal warming. The increasing prevalence of droughts stems from increased evaporative demand as a function of temperature and more frequent incidences of

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reduced precipitation. The combination of more droughts and more floods is particularly difficult in some regions. The frequency of extreme events, in turn, can lead to increased climate-mediated disturbances (e.g., fire, pest outbreaks, landslides). In coastal regions, climate change includes changes in coastal processes. These include sea level rise (perhaps the most obvious issue) but also include changes in storm surges, wave energy, “sunny-day floods,” and saltwater intrusion into freshwater aquifers. It is worth reminding ourselves of these various aspects of climate change because they manifest very differently regionally and so imply different strategies for adaptation. North Carolina provides a useful illustration. The state includes parts of three ecoregions: the southern Blue Ridge Mountains, the Piedmont, and the Coastal Plain. In the mountains, warming is perhaps the most obvious threat under climate change. Species inhabiting higher elevations in the mountains risk being “warmed off the tops” of these mountains, and so a major concern is uphill migration (if space is available) or migration farther north; if farther north, the species will have to navigate intervening lower-elevation habitats that will become increasingly inhospitable in the future. Climate-sensitive connectivity emerges as a key aspect of adaptation. In the Piedmont there is an enormous amount of biodiversity within freshwater streams as compared to terrestrial habitats (terrestrial biodiversity is higher in the mountains and at the coast). Here, the increasing variability of floods and droughts poses a significant threat to this biodiversity—in part, because this freshwater biodiversity competes with humans for water. Agriculture and municipal water use will feel the pressure of more frequent droughts. Adaptation strategies here must be framed in terms of buffering capacity of the systems (i.e., maintaining minimum ecological flows in streams, moderating the impacts of floods and drought) and how to allocate competing demands for water. Finally, on the coast the concern is changes in shoreline processes, including sea level rise but also increases in the frequency and intensity of storm events and “sunny-day” flooding, and saltwater intrusion. These impacts are already evident from a recent spate of hurricanes, which produce more intense rainfall because of warmer waters and warmer air. Along the coast, adaptation strategies revolve around armored as compared to “green” solutions for resilient shorelines and adapting coastal infrastructure for rising sea levels.

10.2.1.1

Direct and Indirect Effects of Climate Change

Climate change has direct impacts on some species, mediated through temperature or moisture effects on plant or animal physiology. But perhaps even more important are indirect effects. These include the impacts of climate-mediated disturbances, such as fire, and impacts due to altered hydrology (droughts and floods, with droughts also contributing to fires). Indirect effects also include system-level changes due to altered predator-prey or trophic relationships, disruptions to pollinator systems, shifting competitive balances, and invasive species. We have already considered

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some of these impacts, as they are already attracting attention in cities (e.g., Lahr et al. 2018, and recall Cities as Mesocosms for Climate Change, Sect. 9.4.2 in Chap. 9). The high level of site- and species- or system-level heterogeneity in the impacts of climate change motivates the nature of adaptation. First, the most pressing aspects of climate change need to be identified and prioritized, and then we can focus on adaptive strategies. This invites a risk-management perspective.

10.2.2

The Perspective of Risk Management

Risk management is concerned generally with identifying and prioritizing risks and then acting to reduce the likelihood or impact of negative events. While risk management is widely applied in business and other sectors, in ecological applications, it is typically applied to natural disasters. As Thomalla et al. (2006) have noted, the parallels between natural disasters and climate change more broadly are rather obvious (and see NASEM 2016). Risk can be decomposed into a few basic elements: exposure, hazard, and vulnerability. Exposure and hazard are attributes of the event or threat (here, climate change), while vulnerability is an attribute of the affected systems or populations. Exposure is an estimate of who (or where) is affected by the threat, while hazard is an estimate of how severe the impact might be on someone (or somewhere) exposed. For example, a lightning strike has a very low exposure in terms of risk, though the hazard might be rather extreme to a person struck. By contrast, everyone in the world is exposed to increased CO2 levels, but the direct hazard of that exposure is (on average) quite low at the individual level. In terms of climate change, the risks must be parsed at the level of the various components of climate change (temperature, extreme events, coastal processes, etc.). For these components, both the exposure and the hazard are extremely variable at the regional and local scales. Vulnerability adds another layer of complexity to risk. Given the same exposure and hazard, different populations might have very different capacity to withstand the risk. In human health issues, we are accustomed to thinking about vulnerable populations, such as the greater vulnerability of the elderly, the very young, and those with compromised immune systems, when exposed to environmental stressors such as air pollution or extreme heat. In terms of natural systems, the emphasis is on different taxa and their relative sensitivity to climate change (e.g., amphibians as compared to birds) or to variation among species within taxa (e.g., among birds). Vulnerability often includes a consideration of the affected species or population’s capacity to adapt or respond to the stress. In many instances, this is framed in terms of predisposing factors, such as a system or population being stressed by multiple aspects of change (e.g., warming, drought, habitat fragmentation, invasives) or preexisting conditions.

10.2

Framing Adaptation

10.2.2.1

291

Exposure and Hazard: Analog Climates and Climate Velocity

In climate-change applications, one common convention is to combine exposure and hazard into a single measure. The measure is termed climate velocity (Loarie et al. 2009). The measure is developed from several pieces. First, it is based on an estimate of the magnitude of change expected at a particular location. For example, we might find that model projections suggest a 2.5° warming at a given location, between current climate and a projection for 2050 (i.e., 30 years into the future as this book is written). The second task is to project this warming into geographic terms. This relies on temperature lapse rates (recall Sect. 1.4.1), whereby temperature lapses (cools) at a rate of approximately 5° per 1000 m elevation or 1000 km latitude. In the northern hemisphere, that implies that the future analog climate for that location is either 500 m uphill and not far away horizontally (in the mountains), or 500 km north (on flat ground), or some combination of these (in most places). Given the timespan of the climate projection, this distance over the projected time interval yields a rate of change: climate velocity. Climate velocity invites the notion of a climate analog. We might ask, where are the future-climate conditions that match current conditions as recorded at a focal location? In the northern hemisphere, these (reverse) analog locations are to the south, and they suggest what we might expect of the future. Conversely we might ask, where will today’s climate at this site be similarly expressed in the future? These (forward) analogs might suggest how far north a species might need to migrate to find conditions similar to its current-climate distribution. Forward analogs are also used in estimating climate velocity. Estimates of climate similarity are more complicated than what is implied by average temperature lapse rates. Because climate encompasses various aspects of temperature, precipitation, and their interaction (e.g., drought), climate velocity is an inherently multivariate issue, and the analog climate is based on multivariate indices of climate similarity (Hamann et al. 2015; Dobrowski et al. 2021). At this writing, there are very helpful visualizations of reverse climate analogs available for the USA (Fitzpatrick and Dunn 2019) and the globe (Dobrowski et al. 2021). The Climate Analogues application of the Copernicus program, based in Europe, provides a similar approach globally (https://climate-analogues.climate.copernicus.eu/). If species response to climate change is mediated by complex terrain and intervening habitats between current locations and their future-climate analogs, the distances implied by climate analogs are further complicated (e.g., Dobrowski et al. 2013; Dobrowski and Parks 2016; Carroll et al. 2018; Parks et al. 2020). Estimates of climate velocity vary regionally, according to regional topography. Given the regional differences in projected climate change and regional differences in terrain, the level of spatial heterogeneity in climate velocity is quite remarkable even at the regional scale (Fig. 10.1). This spatial complexity arises in part because of the mountainous terrain: in the mountains, large temperature changes occur with elevation and so over comparatively small horizontal distances (hence low velocity),

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1 10 0.1 0

-10

Spatial gradient (°C km-1)

20

0.01

b

c

0.060

10

0.055 1 0.050

Speed (km yr-1)

Temporal gradient (°C yr1)

Mean annual temperaure (°C)

a

0.1 0.045 0.01 0.040

d

e

100km

Fig. 10.1 Climate velocity for part of California, USA: (a) mean annual temperature for 800 m grid cells; (b) the same, for the small rectangle in (a) covering California; (c) spatial change in temperature, based on ensembled climate scenarios; (d) temporal rate of change in temperature; and (e) climate velocity, as the quotient of (d) and (c), in km per year. (Reproduced with permission of Springer Nature, from Loarie et al. (2009); permission conveyed through Copyright Clearance Center, Inc.)

while on flat ground the implied horizontal distances lead to higher velocities. These differences are evident in the figure as a contrast between the Central Valley and the Sierra Nevada mountains (the valley is red in Fig. 10.1b and blue in Fig. 10.1e; the mountain range just to the east shows just the opposite).

10.2

Framing Adaptation

10.2.2.2

293

Vulnerability: Sensitivity and Adaptive Capacity

Most of us are familiar to the concept of differential vulnerability because we see this applied to issues of human health. The same concept applies more generally to climate change and its impacts on other species, although the specific factors that confer vulnerability vary more widely for nonhuman subjects. It is typical to separate vulnerability into two components: sensitivity and adaptive capacity. Sensitivity depends on life-history traits of the focal species, while adaptive capacity depends on certain species traits as well as other extrinsic factors (often related to landscape context) that predispose a species to risk or its ability to respond to risk. Sensitivity to climate change ranges from the direct physiological effects of heat or drought stress to the indirect effects due to climate-mediated changes in disturbance regimes (e.g., fire) or effects on interspecific interactions such as competition, predator/prey relations, or pollinator systems (Foden et al. 2013; Pacifici et al. 2015, 2017; Young et al. 2016). The capacity for a species to adjust or adapt to a rapidly changing environment depends on responses ranging from behavioral adjustments to evolution. This depends, in part, on phenotypic plasticity and the genetic capacity to respond through natural selection. The latter, in turn, depends on standing genetic variation in the population and generation time (i.e., how this compares to the rate of climate change). More immediately, behavioral traits and habitat associations can affect species sensitivity. These aspects of a focal species and its possible response to climate change invite a consideration of which options are available as an adaptive response.

10.2.3

Options for Response and Adaptation

To plan for resilience, it is helpful to think about the responses a species might adopt given rapid or extreme environmental change. The options are rather limited (Table 10.1).

Table 10.1 Options for species response to rapid environmental change Tactic Tolerate Adjust Adapt in place Move locally Migrate Go extinct

Note Depends on local site, species tolerance Change in behavior or activity patterns Depends on genetics and generation time Depends on local heterogeneity, permeability Depends on regional connectivity If all other options fail; invites direct intervention

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Tolerate A species might “hunker down” and hope to persist in place because its location is “good habitat,” and, chances are, it will remain good habitat in the future. In general, we might expect longer-lived species that have some natural capacity to withstand climate variability to be more able to hunker down. This tactic would be most appropriate in sites that expect low climate velocity. Adjust A species might adjust in place, behaviorally, by adjusting its activity daily or seasonally to mediate more extreme environmental conditions. For example, terrestrial salamanders might emerge from underground earlier in the season and retreat earlier during the summer, given warmer temperatures and lower groundlevel humidity. Similarly, individuals might adjust their activity patterns to earlier or later in the day. This suggests that species with some ability to adjust their behaviors daily or seasonally would be less vulnerable to climate change. Adapt in place A species might adapt locally, using standing local genetic variation or phenotypic plasticity. The rate of this response would vary substantially, depending on the degree of plasticity and the selection pressure on standing genetic variation. Adaptive capacity also depends on generation time of the species relative to the pace of environmental change. We would expect long-lived species and those with a low genetic variability to have trouble tracking rapid environmental change. Move locally A species might relocate locally, by selecting more favorable local microhabitats. For example, larger forested tracts can be several degrees cooler than small forest fragments, and local differences in slope aspect or proximity to water can impart similar levels of local variability in microclimate (recall Chap. 1, Sect. 1.4). These sites represent microrefugia from a changing climate (Dobrowski 2010; Davis et al. 2019). To take advantage of this local microhabitat variability, a species would need to be sufficiently mobile to be able to access nearby habitats, and the landscape would need to be sufficiently intact or permeable that the species could navigate local heterogeneity. Migrate Given more pronounced changes in climate, a species can undergo a directed migration to more suitable habitat. On flat ground, this implies a latitudinal adjustment, while in mountainous terrain the adjustment might be uphill and rather local. In complex terrain, the adjustment is a combination of elevation and latitude, mediated by intervening (lower-elevation) habitats. To be able to do this, a species would need to be mobile (either via direct movement such as by animals or via medium- to long-distance dispersal vectors for plants). And the intervening landscape would need to be navigable by the species, which would depend on regional land cover, land use, and local climate. Go extinct Failing in all of these, the species might go locally extinct. From this perspective, such species would be those with little or no capacity for the previous adaptive options. That is, the most vulnerable species would be those with high sensitivity to climate or climate-mediated disturbances, low genetic capacity for adaptation, low mobility, and limited dispersal range. In such cases, the remaining options would involve direct interventions such as translocation (e.g., to introduce better-adapted genotypes into a local population) or assisted migration (i.e., to move individuals of the species into a more favorable future-climate location).

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These options frame the possible responses in deliberate actions for adaptation toward resilience. The tasks are to identify the most vulnerable targets and adopt what tactics might best reduce the vulnerability and increase the resilience of those targets. There are several objectives.

10.2.4

Resilience Planning: The Tasks at Hand

Planning for resilience implies an assessment of relative risks and options and then deliberate actions to manage or mitigate those risks by implementing various management options. In this section we explore these options. We should be clear about what we mean by resilience. Given a perturbation, a system can be resistant or resilient to varying degree. A resistant system withstands the perturbation and is mostly unaffected (unaltered) by it. A resilient system is affected by the perturbation—perhaps altered substantially and irreversibly—but continues to function. In terms of climate change, a resistance approach would deny climate change, while the resilient approach would accept it and hope to function sustainably into the future even in an altered state. A more recent entry into this catalog of approaches is transformation: active management of a system (or a species) to facilitate its transition into a climate-adapted future. Peterson St. Laurent et al. (2021) reviewed the diversity of adaptation frameworks (there are very many!) and attempted to provide for more precision and objectivity in the way these are cataloged. Relative to the species perspective in Table 10.1, they adopted the perspective of management actions. To add precision, they coded the options on a scale from 1 (active resistance to change) to 6 (active assistance toward accelerated transformation) (Fig. 10.2). At the same time, yet another framing is emerging that emphasizes just three stages along this spectrum: the resist-accept-direct (RAD) framework (Schuurman et al. 2021, Williams 2022 and associated articles in a special feature in BioScience). The RAD framing is perhaps especially compelling in that it is being adopted by many agencies (e.g., US Geological Survey, US National Park Service, US Fish & Wildlife Service), and in this, the agencies are discarding previous notions of managing toward a known (or presumed) historical baseline and instead managing toward ecological processes into the future. In their review, Peterson St. Laurent et al. (2021) noted that there seems to be a trend away from resistance and toward more actively assisted transformation. In this chapter, we focus mostly on the midrange of these options—from resilience to autonomous transformation—as these are probably the most common approaches in practice today. Each of the population-level response options outlined above implies particular adaptive tactics. These are presented in the following sections, as guiding principles in adaptation toward resilience.

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Transformation

6

Accelerated Transformation Actions designed to more rapidly advance transition towards new structures and functions.

5

Directed Transformation Actions designed to drive transition towards new structures and functions.

4

Autonomous Transformation Actions designed to facilitate the autonomous transition to new structures and functions.

3

Resilience Actions designed to improve the capacity of a system to return to desired past or current structures and functions following a disturbance to the extent possible while recognizing some new elements are inevitable.

2

Passive Resistance Actions designed to passively maintain current/historical structures and functions.

1

Active Resistance Actions designed to actively maintain current/historical structures and functions.

Resistance Fig. 10.2 The R-R-T typology of adaptation approaches along a spectrum of resistance, resilience, and transformation. (Peterson St. Laurent et al. 2021)

10.3 Approaches to Adaptation Planning Heller and Zavaleta (2009) and Mawdsley et al. (2009) have reviewed adaptation strategies for conservation and natural resource management under climate change. Efforts vary widely, as might be expected of efforts that have been implemented at levels ranging from local land trusts to national assessments. Dawson et al. (2011) provided an insightful synthesis of species-level approaches in terms of climate exposure, sensitivity, and adaptation capacity.

10.3

Approaches to Adaptation Planning

10.3.1

297

Levels of Activity and Currency of Assessments

Pacifici et al. (2015) reviewed various approaches to assessing vulnerability to climate change. They categorized approaches in terms of temporal scale (past, present, future), spatial scale (local/site, region, global), and taxonomic focus (below species rank, species, multiple species). They also considered the currency of the assessment and methods or models used to do the assessment (Table 10.2). In the table, correlative approaches would include regressions of vulnerability on life-history traits based on historical or recent trends in species abundances or regression-based models that relate population trends to climate or habitat characteristics. In general, the data and model intensity of the approaches increase from the upper left to the lower right in the table. For example, trait-based assessments can be done by expert opinion with rather little data beyond knowledge of natural history, while population viability analysis to estimate extinction risk requires more intensive demographic data to parameterize a population model. Species distribution models (SDMs) are widely used to project potential range shifts for species under climate change. There is an enormous literature and essentially an entire industry devoted to the development and application of these models (e.g., Franklin 2010; and recall Chap. 7, Sect. 7.4.3 and S7.1.3). In climate-change applications, species distributions are modeled in terms of various climate variables (often, as well as predictors derived from land cover and terrain). The model fitted on current climate is then projected using future-climate variables, to predict range shifts. This is essentially a species-specific mapping of a climate analog. The SDM approach makes several key assumptions about species distributions, including that species are in equilibrium with current climate and that interspecific interactions are unimportant. We have considered the latter already (Sect. 7.3.4, on community structure) and noted the promise of joint species distribution models in this case (Clark et al. 2014; Pollock et al. 2014; Warton et al. 2015; Ovaskainen et al. 2016). The issue of equilibrium is more difficult, as it depends on species longevity and recent climate variability. In some cases, projected future climates are unlike any current climates, and there are uncertainties in forecasting species response to non-analog climates (Williams and Jackson 2007). We look at an example of SDMs applied to climate change below. Pacifici et al. (2015) note that vertebrates (especially birds and mammals) and some plants (e.g., trees) are better studied than other taxa (e.g., invertebrates). Also, in many cases the assessment does not cover the full geographic range of the species, so inferences about vulnerability are local. Table 10.2 Approaches to assessing species vulnerability. TVA is trait-based vulnerability assessment; SDMs are species distribution models; PVA is population viability analysis Currency/model Vulnerability Range shift Pop’n trend Viability

Expert opinion TVA

Abstracted from Pacifici et al. (2015)

Correlative (Regression) SDMs (Regression)

Mechanistic

PVA

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Some assessments are implemented at the level of communities or ecosystem types. These studies often use the same correlative methods as species-level assessments, such as species distribution models. While such assessments can be informative in an approximate sense, it should be noted that an abundance of paleoecological insight (e.g., Graham and Grimm 1990) suggests that communities do not move as entities: communities disaggregate as species respond to change individualistically to climate change and then reaggregate locally depending on which species are there, local environmental constraints, and community assembly processes (recall Chap. 7).

10.3.2

Elements of Adaptation

Given the need to adapt, there are several management options—but not as many as one might guess. This listing follows Schmitz et al. (2015), but the principles represent a reasonably broad consensus among practitioners (e.g., Heller and Zavaleta 2009; Mawdsley et al. 2009) and are echoed in many approaches including R-R-T and RAD (above). Their approach recommends actions on six fronts: (1) protect current biodiversity; (2) protect large, intact landscapes; (3) preserve geophysical settings; (4) maintain or restore connectivity; (5) identify and protect futureclimate habitats; and (6) identify and protect climate refugia. Specific actions in each of these areas would vary at the level of focal species, ecosystems, or landscapes.

10.3.2.1

Preserve Current Diversity

It should be intuitive that we would want to preserve or protect areas that currently support high levels of biodiversity or have a high conservation value. The value in this under a future-climate scenario is that we expect that such sites are intrinsically favorable habitat and likely will continue to support high levels of diversity. For example, Belote et al. (2017a) mapped conservation value in terms of ecological integrity (highly intact, low human impact), natural corridors among protected areas, representation in protected areas, and endemism; they later overlaid these areas with climate vulnerability to further prioritize their assessment (Belote et al. 2017b). In many approaches, this focus targets geophysical settings or land facets defined in terms on underlying geology or topographic positions. The argument here is to “preserve the stage” (Anderson and Ferree 2010; Lawler et al. 2015), the geophysical settings in which evolutionary and community assembly processes have played out favorably in the past and which (we assume) should function similarly in the future. In many applications, current biodiversity and geophysical settings are combined, by calibrating geophysical settings in terms of the biodiversity they support currently. For example, The Nature Conservancy has intersected known occurrences of species with geophysical land facets to assign a higher conservation value to facets that currently support high levels of biodiversity (Anderson et al. 2016, and see below). This element of resilience planning supports the “tolerate” response to climate change (Table 10.1) while also admitting future changes in local communities.

10.3

Approaches to Adaptation Planning

10.3.2.2

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Maintain Local Heterogeneity of Microsites and Microclimates

Areas with high levels of local heterogeneity provide buffering capacity under climate variability. The logic here is that local heterogeneity would give species opportunities to move to cooler (or warmer or wetter or drier) microsites in response to interannual variability in weather or to select incrementally more favorable sites under gradual environmental change. Local variability in topography, hydrography, and land cover can affect microclimate substantially (e.g., Geiger et al. 2009). For example, in exploring the physical template of landscapes (Sect. 1.4), we have already noted the tendency for sites near water bodies to be cooler and to have a lower diurnal range in temperature as compared to drier sites. Similarly, slope exposure can have substantial effects on temperature via radiation loading. In landscapes with mixed land cover, sites with closed forest canopies can be cooler than open sites. In particular, large tracts of forest tend to be substantially cooler than the surrounding landscape (often, because such forests tend to be near streams or other water bodies). Sites with a high topographic variability can provide microrefugia for species (Dobrowski 2010). The buffering capacity provided by local microsites supports the “adjust” or “relocate locally” option for species response (Table 10.1) and so might also allow a species to persist within the same general area (Suggitt et al. 2018).

10.3.2.3

Maximize Local Permeability

Local heterogeneity in microsites or microclimates is only useful if species can access them. While the local navigability of landscapes has been described in many terms, we will adopt permeability as the general term. Local permeability depends on local land cover, the contrast (or permeability) of edges or ecotones among patches of different land cover types, and natural or anthropogenic barriers to movement such as roads. Approaches to quantifying local permeability vary widely among applications. These range from integrators of human influence such as distance-to-road (e.g., Riitters et al. 2002; Theobald 2013; Hak and Comer 2017) to more nuanced indices based on the relative navigability of land covers as represented in a dispersal cost-surface such as used to compute least-cost paths across landscapes (Anderson et al. 2016). Local permeability is crucial to the “relocate locally” response mode and also contributes to long-distance migration or “directed migration” through its influence on the location of potential corridors.

10.3.2.4

Plan for Directed Connectivity to Future Climates and Refugia

In general, directed migration implies poleward movement (northward in the northern hemisphere) or movement to higher elevations in the mountains. When the distances implied by directed migration are large, the approach is to design corridors

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connecting current locations to locations with more favorable future climate. To do this, one needs to identify the target future sites. One way to do this is to use climate projections to locate another site with a future climate analogous to that of the focal site (i.e., its analog-climate site) as discussed previously. Potential climate refugia are sites or regions with a very low expected exposure to climate change, that is, a low climate velocity. Efforts to identify potential climate refugia have not received quite as much attention as identifying future-climate analogs (but see Morelli et al. 2020 et seq. in a special feature on refugia). Corridor design typically involves the generation of least-cost paths, but in this instance the cost-surface can be nuanced to attend intervening land cover (as with conventional corridor design) but also the intervening climate. In applications of climate connectivity, the corridor must traverse intervening habitats while also staying within a window of compatible climate. That window might be spatial (e.g., by following riverine corridors that tend to be cooler), or it might be in time (e.g., by traversing an area before it becomes too warm). For example, species that inhabit high-elevation sites in many mountain ranges in North America would need to more northward in the future, but to do so they will need to navigate the intervening valleys which might be inhospitably warm and dry. Phillips et al. (2008) provided an early example of optimizing connectivity under a changing climate. There are now multiple tools for exploring and designing climate connectivity corridors (e.g., Nuñez et al. 2013; Pelletier et al. 2014; Littlefield et al. 2017; Keeley et al. 2018a; Parks et al. 2020; Schloss et al. 2022), although implementing such plans is not a simple task (McGuire et al. 2016; Keeley et al. 2018b; Parks et al. 2020). Climate connectivity supports directed migration as a response. Climate refugia invite a “tolerate” or “move locally” response for species already living in those regions. But species in nearby regions with expected higher exposure might also need to be connected to refugia, and so these will also be involved in directed migration.

10.3.2.5

Caveats

Butt et al. (2016) reviewed applications in climate adaptation and offered four caveats concerning approaches: (1) They cautioned against applications that considered only exposure, but not sensitivity or adaptive capacity. (2) They underscored the importance of the variability in future climates, beyond the average trend. For example, we might expect the increasing frequency and intensity of extreme events (floods and droughts, heat waves) to be at least as stressful as the average climate. (3) They argued that framing applications in terms of a future climate ignores the threat posed by climate changes observed to date, over the past few decades. Many sites are already experiencing “future” climate. (4) They warned about focusing too much on the direct effects of climate change rather than attending interactions between climate and other stressors. These other stressors, such as the impacts of habitat fragmentation or invasive species, can affect the adaptive capacity of focal species or sites.

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301

Most applications in climate resilience are perhaps best considered as a bet-hedging strategy: we attempt to establish and support conditions that will enable adaptation, but we cannot really know how natural systems will react until we actually witness those responses.

10.3.3

A Template for Applications

We can gather up these pieces of climate-change adaptation and assemble them into a general template for applications (Fig. 10.3). In this, the process begins by identifying or prioritizing the aspects of climate change—direct and indirect—that are most relevant to the local application; these will vary substantially depending on geography. This process might entail estimating climate velocity or mapping potential climate analogs as ways to visualize or communicate these elements. After considering climate change itself, the process must focus by choosing a target species or ecosystem (Fig. 10.3, middle panel). This entails estimating the hazard to the target, in terms of the potential severity of the impacts and the vulnerability and adaptive capacity of the focal species or system. The available response options for the focal species or system (from Table 10.1) suggest the adaptive measures (from Sect. 10.3.2) that might be undertaken to reduce the risk and increase resilience. These range from essentially a “do nothing” response to, in the worst case, deliberate and challenging interventions such as translocation or assisted migrations (Fig. 10.3, right panel). That is, the situations experienced by the target species in the center panel correspond to the R-T-T spectrum of management responses cataloged by Peterson St. Laurent et al. (2021, Fig. 10.2). Drivers

Options

Climate Change: Variables? Means or extremes?

Impacts

Protect: Current hotspots Large/intact? Preserve the stage

Hazard for Target(s): Sensitivity? Adaptive capacity?

Connect: Local permeability Directed migration

Indirect effects: Disturbances? Stressors? Other species?

Risk: Exposure? Velocity? Analogs?

Responses: Ignore Adjust Adapt Migrate (none of these)

Anticipate: Climate refugia Future hotspots Climate corridors Intervene: Translocation Assisted migration

Fig. 10.3 A model template for climate adaptation applications. The process begins by identifying the aspects of climate change that are most relevant to the local application (left panel), proceeds to identify the hazard to a focal species or system and the response options (middle panel), and then matches these elements of risk to potential tactics to mitigate those risks (right panel)

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It should be underscored here that any given application would likely address a small subset of climate drivers and a restricted set of potential management options. That is, the overall approach would be realized only by aggregating very many local applications for a variety or drivers and focal species or systems. In the following section, a few applications illustrate how applications can be focused from the general (and daunting) to the local (and feasible).

10.4

Illustrations of Approaches

In this section we delve into a few representative examples of climate-change assessments. The selected examples are not exhaustive, but span a range of approaches being used currently. Although none of the examples attend every issue identified in reviews of adaptation strategies—which effort would be daunting!—they do collectively illustrate most of these issues. The examples also suggest that regional efforts can be usefully complementary.

10.4.1

NatureServe’s Habitat Climate-Change Vulnerability Index

NatureServe is an organization that stewards a vast amount of data on species and communities of conservation concern. As an organization, they have invested heavily in estimating the vulnerability of species to climate change (e.g., Young et al. 2016). They have been developing approaches to estimate vulnerability for more than a decade; their effort to categorize the climate vulnerability of communities in the western USA is a recent illustration of that effort (Comer et al. 2019). Their approach (Fig. 10.4) focused on a large number (50+) of natural communities, which they treat essentially as “species” for the assessment. They incorporated climate exposure and community resilience, with resilience partitioned into sensitivity and adaptive capacity. Climate exposure is indexed in terms of the change in climate suitability for each community and location, by estimating change of key climate variables against a twentieth-century baseline for the full natural distribution of each type, using random-forest species distribution models (Liaw and Wiener 2002). Future climate was modeled in terms of RCP 4.5 (a moderate emissions scenario, van Vuuren et al. 2011) for the years 2040–2070. They also looked at recent climate change, indexed in terms of historical climate data from 1948 to 2014. Beyond the average measured or projected climate, they also assessed climate typicality, indexed in terms of interannual deviations from the baseline (recent or future) means. They estimated sensitivity in terms of four predisposing factors at each location: 1. Landscape intactness (measured in terms of distance to development infrastructure) 2. Invasion severity (based on documented occurrences of invasive species)

10.4

Illustrations of Approaches

303 Exposure

Sensitivity Exposure Score

Resilience Score

Adaptive Capacity

Resilience

Exposure

“by area...today, or by mid-century”

Fig. 10.4 Schematic logic of NatureServe’s approach to estimating climate-change vulnerability, the Habitat Climate Change Vulnerability Index. (Reproduced from Comer et al. 2019)

3. Fire risk (as departures from natural fire return intervals) 4. Risks from forest pests or diseases (from national databases) Adaptive capacity of each community and location was indexed in terms of (1) climate-change vulnerability of any identified keystone species in the community, (2) documented diversity within groups of species known to play key functional roles in the community, and (3) topographic complexity as this might effect microclimate variability and the existence of microrefugia. The final index of habitat climate-change vulnerability was generated by estimating separate scores for community resilience (half sensitivity, half adaptive capacity) and exposure and combining these into a single index. This index was then binned into a few categorical levels of vulnerability (Fig. 10.4). The final map products were aggregated into 100 km2 hexagons for display (Fig. 10.5). This illustration is compelling because it addresses all components of vulnerability (exposure, hazard, sensitivity, and adaptive capacity) in a spatially explicit manner. Relative to Butt et al.’s (2016) caveats, this effort addresses recent changes as well as future climate; it looks at average climate expectations as well as changes in extremes; and it includes ratings to reflect indirect impacts that affect sensitivity or adaptive capacity. As an index of vulnerability, this effort does not make explicit recommendations for management beyond the implicit prioritization that the most vulnerable sites and communities might be more compelling as management priorities. Relative to the framing offered by Schmitz et al. (2015), this assessment addresses landscape intactness and permeability by including these in estimates of sensitivity and adaptive capacity; it does not offer recommendations in terms of directed connectivity beyond those implicit in the mapped product. NatureServe has since begun to adopt the R-T-T framing of Peterson St. Laurent et al. (2021, Fig. 10.2) to develop adaptation guidelines for their vulnerability assessments.

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N

Climate Change Vulnerability Low

High

Fig. 10.5 Habitat-level climate vulnerability for 1 of the 52 community types in the western USA, Intermountain Basin Big Sagebrush Shrubland, aggregated to 100 km2 hexagons from 30 m cells. Vulnerability incorporates climate exposure and community sensitivity and adaptive capacity. (From Comer et al. 2019)

10.4.2 Species Range Shifts Implied by Climate Change Species-level assessments are often estimated in terms of geographic range shifts implied by future-climate scenarios. These assessments are typically based on correlational species distribution models (SDMs) using climate variables as predictors. This is an enormous industry, reflecting ongoing development of the tools themselves along with an increasing number of climate-related applications. Thomas et al. (2011) noted that under climate change, some species will likely benefit by increasing their ranges, while others will contract their ranges and be at risk from climate change. Most species, perhaps, will contract one (the trailing) edge of their range while increasing the other (leading) edge. Thomas et al. (2011) presented a general framework for integrating the benefits and risks posed by range shifts, along with other exacerbating factors, to a single index of climate risk. The protocol also incorporates the level of confidence in the information, and the index is weighted to favor more certain information.

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Illustrations of Approaches

305

Brown and Yoder (2015) assessed climate-change implications for 57 species of lemurs in Madagascar, indexing impacts in terms of range expansions and contractions. They ensembled (averaged) the results from several SDMs to generate more robust predictions of range shifts. The model ensemble included several popular techniques: artificial neural networks, classification trees, generalized additive models, boosted regression trees, discriminant analysis, multivariate adaptive regression splines, random forests, surface range envelopes, and maximum entropy modeling (all this via BIOMOD, Thuiller et al. 2009). They modeled current ranges and future range shifts in terms of a large set of bioclimatic variables, including 26 via Bioclim (worldclim.org, Hijmans et al. 2005), and statistically downscaled versions of 16 additional variables from the CliMond project (climond.org, Kriticos et al. 2012). The future-climate scenario was based on a moderate emissions scenario (A1B, IPCC 2007), bracketing climate model projections by using a high- and low-sensitivity model. The projections were to the year 2080. They used the modeled ranges to identify current hotspots of lemur diversity, range shifts predicted under climate change, and areas of highest conservation concern (Fig. 10.6). They used the implied range shifts to identify regions that would likely be important to dispersal to the future-climate ranges.

Key Changes Contraction Both contraction and stability Stability Both Stability and expansion Expansion Human altered habitats Natural habitat

Spp.Richness and Microendemism High

Low

Core Range Shifts Centroid change Start: current End: future Human altered habitats Natural Habitat Protected Areas 2013

Line densities High Low

a

b

c

d

Fig. 10.6 Diversity patterns for Malagasy lemurs under climate change: (a) patterns of range contraction, stability, or expansion as aggregated over species; (b) patterns of species richness and micro-endemism, combined for current and future climate; (c) range shifts, as arrows from the centroids of current to future ranges; and (d) implied dispersal routes to future-climate ranges, based on density of change vectors in (c). (From Brown and Yoder 2015)

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This example is a useful illustration of this approach, as it applies many current best practices in species distribution modeling and uses a variety of increasingly standardized and widely available data products for climate assessments. Brown (2014) has also implemented many of the processing steps into a user-friendly package (SDMtoolbox.org). Note that this application does not attend possible interspecific interactions and so probably overestimates diversity (recall Chap. 7, Sect. 7.4.3, and joint species distribution models), but the spatial patterns and trends in diversity are probably robust. Relative to the elements of adaptation itemized above, this example focuses on current and future biodiversity in response to climate risk exposure, identification of potential refugia (i.e., stable ranges), and directed connectivity to future-climate habitats.

10.4.3

The Nature Conservancy’s Resilient Landscapes Initiative

The Nature Conservancy (TNC) and a large number of collaborators generated a mapping of resilient landscapes in eastern North America (Anderson et al. 2016). The initial approach was based on geophysical settings as the basis for estimating site quality in terms of capacity for biodiversity support and local connectivity (permeability) as a key aspect of resilience (Anderson et al. 2014; Anderson et al. 2016). This analysis was later extended to address larger-scale, directed connectivity (Anderson et al. 2016). A broader analysis of the entire conterminous USA has been completed recently (Anderson et al. 2023). A basis for the approach is the identification of geophysical settings, reflecting the argument that climate-smart conservation should “conserve the stage” rather than focusing on individual species as actors (Anderson and Ferree 2010; Lawler et al. 2015). The focus on geophysical settings echoes the finding that such variables are more strongly associated with biodiversity than climate variables. Part of the argument for using settings as focal units is that, under climate change, particular landforms or settings would likely support communities similar to what they now support, even if the actual member species would change. For example, acidic outcrops would select for kinds of certain species, while mesic toeslopes or coves would tend to support different species, and so on. TNC derived its settings first from bedrock and surficial geology within ecoregions. These were augmented with information on landforms defined by topographic position and elevation range (controlling this for the role of elevation in defining landforms), as well as occurrence of wetlands and local diversity of soils. These latter elements were added to prevent the analysis from favoring mountainous terrain over the flatter landscapes of the Coastal Plain. TNC overlaid the geophysical settings with the locations of ~200,000 occurrences of >4500 rare species as captured in Element Occurrence records (these

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307

records are stewarded by natural heritage programs in each state in the USA, often in collaboration with NatureServe). They used these to calculate the strength of association between each Element (species) and particular settings. Thus, the settings they used are expected to show a “distinct biotic expression” at present and into the future. They indexed the conservation value of sites in terms of the local variety of geophysical settings, tallying these within 100 Ac (~ 40 ha) zones around each 30 m cell used in the analysis. The aggregation was intended to capture the local availability of different microhabitats, contributing to buffering capacity under climate change. In the initial assessment, TNC focused on local connectivity (permeability), matching this concern to the accessibility of microhabitats or microrefugia. They assigned a relative resistance to dispersal to each land cover class (using the National Land Cover Database in the USA and its Canadian equivalent). They then used a kernel-based estimator (Compton et al. 2007) to capture the expected flow, outward from each cell, to a maximum distance of 3 km. Smoothed over all cells, this provides a visual estimate of local intactness and identifies potential barriers to local movement. The overall index of resilience is a combination of local variety of geophysical settings and local permeability. For interpretation, these scores were normalized regionally so that the “best” sites were scaled relative to local (as compared to subcontinental-scale) availability. Anderson et al. (2016) extended this analysis by adding directed connectivity. In this, they began with the same relative resistances to dispersal as with the earlier analysis. They used Circuitscape (McRae et al. 2008) to model connectivity but using a novel approach that did not require the definition of discrete patches to be connected (Pelletier et al. 2014). Instead, they tiled the study area with large aggregates of base-scale grid cells and modeled circuit flow across each tile (i.e., edge to edge). They then mosaicked these tiles together and smoothed the results into a continuous connectivity surface. This analysis was further augmented by weighting the resistance surface to favor upslope (in the mountains) and northward migration. In flatter ecoregions, they biased the analysis to use riparian forests as corridors because such forests are naturally cooler than uplands. Finally, TNC incorporated places recognized for their current biodiversity value based on two sources: (1) published ecoregional assessments performed by TNC and partners over a 16-year period (Groves 2003) and (2) state-based assessments performed by agency staff as part of their state Wildlife Action Plan or a similar comprehensive assessment. The net result of this multistaged analysis is a map that prioritizes biodiverse, resilient, and connected landscapes, at high spatial resolution and over broad spatial extent (Fig. 10.7). In terms of the elements of adaptive planning (from Schmitz et al. 2015), TNC’s approach is a bit unusual in that it does not explicitly include climate exposure at all, nor does it model the relative sensitivity of conservation targets. Rather, the focus is

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Resilient Sites Resilient Resilient and Prioritized for Diffuse Flow Resilient and Prioritized for Diversity Resilient and Prioritized for Diversity and Diffuse Flow

Linkages Within Resilient Lands Between Resilient Lands Outlines on linkages slightly inflated (300m) for visibility

Lands more vulnerable to climate change

N

0

70

140

280

Kilometers 0

65

130

260 Miles

Fig. 10.7 Resilient and connected landscapes of the eastern USA (Anderson et al. 2016). Sites are scored on geophysical diversity weighted by known current biodiversity, local permeability, and directed connectivity; scores are ranked regionally rather than globally (see text). (Image courtesy M.G. Anderson, The Nature Conservancy)

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309

on site-level resilience and adaptive capacity. In particular, the approach focuses heavily on the role of microsite variability in supporting biodiversity and resilience and on local and regional connectivity in facilitating species movement. An attractive feature of this approach is that it has generated an enormous richness of high-resolution geospatial data products (final maps and all intermediate products), and these data are freely available from TNC’s website. These can be downloaded at the state, regional, or national level. In this way, for example, local land trusts can use TNC’s analysis to inform climate resilience planning within their local service areas.

10.4.4

The Adaptation for Conservation Targets Framework

By contrast to the map-based assessments above, the fourth illustration is not spatially explicit but instead incorporates climate-change adaptation into an existing planning framework. The Adaptation for Conservation Targets framework (ACT, Cross et al. 2012) was designed to take advantage of local knowledge and participation by local stakeholders and does not require detailed information about climate change or its effects beyond a conceptual level. The approach is framed in terms of adaptive management and is implemented as a participatory, structured decisionmaking process. Key to the ACT framework is a conceptual model that articulates the basic understanding of how climate change might propagate through the study system. Cross et al. (2012) illustrated the approach for the Greater Yellowstone Ecosystem, in terms of climate-change impacts on the hydrology of the Upper Yellowstone River. In their model, these impacts are mediated through a web of interactions among domestic and agricultural water withdrawals, cattle grazing management, floods, wildfire, and vegetation management with climate and hydrology (Fig. 10.8). The model is complicated (!) and represents a consensus statement by experts and stakeholders. The management model is articulated in terms of the conceptual model, by posing a set of alternative management interventions and tracing their interaction pathways through mediating factors to their expected influences on the desired outcomes (Fig. 10.9). This path model (or means-ends diagram) is the basis for structured decision-making. Stakeholder participation is key to the decision-making process, as it is the relative preferences for management options (and hence outcomes) that informs the decision. Once made, the decisions return to the adaptive management cycle, with monitoring and evaluation of the outcomes. This example is interesting because it is quite flexible in terms of the specificity of the climate scenario. While the approach could use detailed and spatially explicit climate projections, it can also be implemented with qualitative scenarios; in this case, the scenarios were “warmer and wetter” and “warmer and drier” (Cross et al. 2012).

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Beaver

Groundwater

Snowpack Upper Yellowstone River Hydrograph, Water Quality Temperature

Climate: Temperature and Precipitation Evapotranspiration

Vegetation Management

Distribution and Density of Upland Trees Riparian Vegetation

Grazing Management

Cattle Grazing Bank Destabilization Number and Intensity of Floods

Sedimentation

Wildfire Management Agriculture Practices Urban/rural Development

Wildfire Frequency and Severity

Domestic and Agricultural Water Withdrawals

Fig. 10.8 Conceptual model for how climate-change impacts propagate through the Greater Yellowstone Ecosystem. (Redrawn from Cross et al. 2012)

More generally, the use of path models to guide management is well established in conservation (e.g., CMP 2007), and there is growing interest in using conceptual (Olander et al. 2018) and evidence-based path models (Tallis et al. 2017; Game et al. 2018; Qiu et al. 2018; Tallis et al. 2019) to inform environmental decision-making. These types of applications will be crucial to the actual implementation of climate action plans (Fig. 10.9).

10.4

Illustrations of Approaches

Intervention Points Agricultural and Domestic Withdrawals

Snowpack Management

Forest Management

311

Desired Responses

Potential Actions Secure Water Rights Reduce Withdrawals Water Conversation (Irrigation, Residential) Build Snow Fences Manage Tree Densities to Maximize Snow Rentention Manage Forests to Maximize Filtration

Hydrology

Install Check Dams at High Elevations

Beaver Populations

Increase Beaver Presence/Abundance

Riparian Vegetation

Restore Riparian Vegetation

Maximize Local Snowpack

Maximize Rain Retention

Increase Riparian Shading

Maximize Summer Baseflows

Maintain Peaked Hydrograph

Maintain Appropriate Water Temperature

Improve Riparian Condition

Fence Riparian Areas Grazing Practices

Reduce Livestock Density

Decrease Grazing Intensity

Fig. 10.9 Path model of how management interventions might affect ecological outcomes, based on the conceptual model in Fig. 10.6. (Redrawn from Cross et al. 2012)

10.4.5

Complementarity of Approaches

None of the examples illustrated here attend the full complexity of adapting conservation to climate change. In part, this reflects the challenges of integrating the enormous data—climate, landscape attributes, and information on species—which would be daunting indeed if done at scale. But adaptive planning is also an inherently two-scaled process. Climate exposure and directed connectivity are necessarily regional assessments, while land use management and conservation actions are typically local, implemented at the level of ownership parcels within a local planning unit or service area. From this perspective, larger-scale efforts such as those by NatureServe and TNC can provide context to inform more local activity such as the ACT plan for the Greater Yellowstone Ecosystem. Indeed, the now-continental map products generated by TNC are intended to support conservation planning efforts at the state or local level; reciprocally, local-scale data and expertise were integrated to produce those large-scale mapping efforts.

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Collateral Benefits and Leverage

While this discussion has focused on conservation applications, the adaptation approaches outlined here have broader implications. Here we address how climatechange adaptation relates to conservation practice, how adaptation planning contributes to climate-change mitigation, and how biodiversity conservation supports the provision of other ecosystem services. Collateral benefits, in terms of other ecosystem services, also have the potential to contribute directly to issues of environmental equity and justice.

10.5.1

Adaptation Planning and Conservation Practice

The overlap between biodiversity conservation and climate adaptation is well documented (e.g., CBD 2009). In the framework proposed by Schmitz et al. (2015), six activities were outlined as the key elements of adaptation. Of these, they emphasized that four of the elements are activities that are already central to conservation practice. These include the protection of areas that already support known biodiversity, especially large and intact areas of natural habitat. Further, conservation already focuses on improving local and regional connectivity. The focus on increasing local microhabitat variety as indexed by topographic position and geophysical factors has not been explicit in conservation practice except to the extent that such variety underlies biodiversity at the local to regional scale. The two activities that are part of adaptation but not “normal” conservation are the identification of climate refugia and sites that will be habitat of high conservation value in the future, and improving connectivity to these locations. But given that many climate refugia already support high levels of biodiversity and the most favorable sites in the future are likely to include sites that are also already good habitat (but farther poleward), it seems likely that these practices will fall naturally into the conservation toolkit. Indeed, as one popular mantra of conservation is “protect, connect, restore,” conservation positions itself as a leader in natural solutions to climate change. The six elements identified by Schmitz et al. (2015) cover the “protect” and “connect” pieces. The “restore” piece can address climate change directly by reforesting degraded sites to more fully stocked natural condition and by managing existing lands more effectively. Griscom et al. (2017) highlighted avoided conversion (a primary goal of conservation) and reforestation (restoration) as key elements of a green solution to climate change (and see below). There can be substantial overlap in the spatial distribution of sites identified as important for biodiversity support and the mitigation value of carbon storage. For example, Carroll and Ray (2020) mapped sites with high conservation value under climate change, based on several elements we have already considered (current

10.5

Collateral Benefits and Leverage

313

biodiversity, topographic or geo-diversity, climate refugia, and climate connectivity). They compared these sites to those with high mitigation value based on aboveground and soil carbon. They provided regional illustrations for the Pacific Northwest in the USA, as well as broad-scale patterns for the USA and Canada combined. They also positioned these applications within the policy context, nested across a range of scales from state or provincial programs (e.g., state Wildlife Action Plans), regional programs (e.g., the Northwest Forest Plan, caribou recovery planning), national processes via executive mandates as well as legislative action, and international treaties (e.g., the UN Framework Convention on Climate Change). That is, they went beyond what should be done, to focus on how it might be done.

10.5.2

Collateral Benefits

A focus on biodiversity as the goal of conservation belies the much broader impact of conservation actions with this focus. Biodiversity conservation supports a wide array of other ecosystem services. For example, protecting large tracts of habitat also provides for watershed benefits by protecting infiltration and groundwater recharge. If the protected sites are riparian, these contribute directly to water quality by reducing erosion and filtering nutrients and pollutants before they reach the stream. Natural vegetation improves local air quality and provides shading and evaporative cooling that can help mitigate local warming, especially warming due to urban heat islands (and recall Sect. 9.3.1, 9.4.2). Protected areas, especially those in or near highly populated areas, also provide opportunities to connect people to nature through active recreation (hiking, biking) or passive enjoyment (e.g., viewsheds) and thus can contribute to physical and mental health. Smith et al. (2019) evaluated a large number of land management practices or interventions in terms of their potential impacts on the four “land challenges” of climate mitigation, adaptation, land degradation (e.g., desertification), and food security. They found that of the 40 practices analyzed, about a fourth had medium to large benefits on all four challenges and that many more had positive influences on some challenges without adverse impacts on others. Only a very few practices would tend to increase competition for land, and in those cases improvements to our food systems (diet, production, and waste) could reduce that competition. Thus, most conservation activities have the potential to provide ancillary co-benefits at little or no extra cost.

10.5.2.1

Climate-Change Adaptation, Conservation, and Environmental Equity

The array of collateral benefits of conservation as a means of climate adaptation is especially compelling from the perspective of environmental equity and justice. It has been widely recognized that some of the worst impacts of climate change are

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likely to fall on communities with the least capacity to absorb or adapt to these impacts. This inequity is often illustrated by pointing to small island nations that contribute very little to climate change but are likely to be overwhelmed by its impacts (i.e., by sea level rise). But inequities exist not just globally but regionally and even down to the spatial resolution of urban neighborhoods. Nature-based solutions to climate change are especially well studied in cities (Chap. 9, Sect. 9.4.2; Hobbie and Grimm 2020), but the link between climate change and justice is much more general (e.g., Thomas and Twyman 2005). Certainly there are implementation details yet to be clarified (Kremen and Merenlender 2018; Seddon et al. 2020). For example, not all reforestation efforts aiming to increase carbon sequestration also contribute to biodiversity or equity. But the opportunity to make significant strides forward at the intersection of climate change, biodiversity support, and environmental equity is real, and the challenge is pressing.

10.5.3

Adaptation and Mitigation

Climate mitigation will ultimately require a transition to a low-carbon economy that will greatly reduce emissions of greenhouse gases. But in that transition, green solutions to climate change can contribute substantially to mitigation efforts. Griscom et al. (2017) analyzed 20 actions aimed at conservation, restoration, and improved land management across forests, agriculture, wetlands, and coastal systems globally. They constrained their estimates of these actions in terms of costeffectiveness, food security, and biodiversity protection. They found that natural climate solutions could provide more than a third of costeffective mitigation needed through 2030, toward a better than 66% chance of holding warming below 2° C. By far, the largest contributions to mitigation could come from reforestation and avoided conversion of existing forests (Bastin et al. 2019 echoed the potential for reforestation at a global scale). Griscom et al. (2017) further note that, if effectively implemented, these natural climate solutions would also offer co-benefits of water filtration, flood buffering, improved soil health, habitat for biodiversity, and enhanced resilience. Qin et al. (2021) underscored these potential benefits but emphasized that for the benefits to fully accrue, these actions must be undertaken now and at scale: delaying implementation would dramatically reduce the impacts (see Girardin et al. 2021 for a similar note of urgency).

10.6

Summary and Conclusions

Climate change comprises a syndrome of symptoms (warming, more extremes, and so on) that manifest differently for any given landscape. As exposure varies regionally, so does the relative vulnerability and adaptive capacity of local species and

References

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ecosystems. This local variability invites a risk-management approach by which the relative threat or impact of components of climate change is assessed to decide on strategies for adaptation. Adaptation strategies typically embrace a set of complementary tactics, including protecting current biodiversity and ecosystems of high conservation value; aiming to preserve and maintain large, intact landscapes; preserving fine-scale heterogeneity in edaphic or geophysical factors and microclimate; improving local permeability; and increasing regional connectivity, especially to climate refugia and high-value futureclimate habitats. Tools to support these tactics are increasingly available and used at scales ranging from local landscapes, to regions, to entire countries or continents and the globe. As many management actions are local to regional, the larger-scale analyses provide useful context and guidance for local action. Adaptive actions to increase landscape resilience will also contribute substantially to climate mitigation, especially by reducing deforestation, increasing reforestation, and better managing intensive land uses such as agriculture. These actions, in turn, will provide many collateral benefits for biodiversity conservation and watershed protection and, if implemented deliberately, support a more equitable and sustainable future. Managing landscapes for future resilience and sustainability will be a seismic shift in the way we manage. Rather than managing to retain or maintain a (perhaps unknown and idealized) historical state—a backward-looking perspective—we will be invited to adopt a forward-looking perspective, even though that future is uncertain today (Heller and Hobbs 2013). Adaptation to climate change will entail some very complicated natural science, but it also will require policies and financing at a level commensurate to the task. From that perspective, the ecology of climate-change adaptation is perhaps not the most difficult part of the solution. This is the huge challenge that we face, and we have the opportunity to make substantial contributions by managing landscapes to this purpose.

References Anderson, M.G., and C. Ferree. 2010. Conserving the stage: Climate change and the geophysical underpinnings of species diversity. PLoS One 5: e11554. Anderson, M.G., M. Clark, and A.O. Sheldon. 2014. Estimating climate resilience for conservation across geophysical settings. Conservation Biology 28: 959–970. Anderson, M.G., A. Barnett, M. Clark, J. Prince, A. Olivero Sheldon, and B. Vickery. 2016. Resilient and connected landscapes for terrestrial conservation. In The nature conservancy. Boston: Eastern Conservation Science/Eastern Regional Office. Anderson, M.G., M. Clark, A.P. Olivero, A.R. Barnett, K.R. Hall, M.W. Cornett, M. Ahlering, M. Schindel, B. Unnasch, C. Schoss, and D.R. Cameron. 2023. A resilient and connected network of sites to sustain biodiversity under a changing climate. PNAS 120 (7): e2204434119.

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Index

A Agents of pattern animals, 48, 49 biotic processes, 30 biotic processes x physical template, 34 dispersal, 45 disturbance, 63 illustrations of generality, 77 the physical template, 1, 3 Area effect, 90 See also Island biogeography Area versus configuration, 163 Autocorrelation, 100–103 and sampling design, 112 as scaling technique, 99

B Beta-diversity, 196 See also Metacommunity, approaches Biogeochemistry, 91, 92, 264, 265, 268 See also Ecosystem; Meta-ecosystem

C Catena, soil, 17, 227 Climate adaptation, 300 Climate analog, 291 Climate change, 287 adaptation, 288 Adaptation for Conservation Targets example, 309 adaptation strategies, 296

climate analog, 291 climate connectivity, 300 climate velocity, 291 collateral benefits of adaptation, 312 components, 290 and conservation practice, 312 environmental equity, 312, 313 geographic range shifts example, 304 Habitat Climate-Change Vulnerability Index, 302–304 illustrations of approaches, 302 mitigation, 288 model template, 301 the Nature Conservancy example, 306 NatureServe example, 302 risk management perspective, 290 species response, 291 species response options, 293 vulnerability, 293 Climate connectivity, 300 See also Climate change Climate mitigation, 288 Climate velocity, 291 Connectivity, 173 functional connectivity, 174 structural connectivity, 173 telemetry and dispersal, 175 Connectivity conservation, 173–178 Coupled natural and human systems (CNH), 256 See also Social-environmental system Curtis, John on forest fragmentation, 145

© Springer Nature Switzerland AG 2023 D. L. Urban, Agents and Implications of Landscape Pattern, https://doi.org/10.1007/978-3-031-40254-8

323

324 D Demographic processes couplings of processes, 33 dispersal, 43 life-history trade-offs, 35 Dispersal as agent of pattern, 43, 45 and gradient response, 45 mass effect, 46, 203 Disturbance as agent of pattern, 63 attributes, 57 definitions, 56 disturbance regimes, 58 heterogeneity, 63 human influences, 73–74 human perspectives, 76 interactions and indirect effects, 59 internal/external?, 58 legacies, 62, 64 lessons, 58 model template, 65 positive feedback, 61 Sierra Nevada, 66 spatiotemporal scaling, 71, 73 Diversity alpha diversity, 196 beta diversity, 196 gamma diversity, 196

E Ecosystem edge effects, 241 fast and slow dynamics, 233 legacy effects, 234, 237 positive feedback, 232, 233 (see also Metaecosystem) spatial heterogeneity, 226 Edge effects, 125, 142, 237 forest birds, 159, 194 forest carbon, 239 pervasiveness, 240 Environmental equity, 278, 313 Environmental filtering, 197 See also Metacommunity models Evapotranspiration scaling lessons, 92

G Geospatial data digital elevation model (DEM), 18 terrain, 18

Index Geospatial proxies hillslope processes, 18 hydrology, 18 Global change, 287 urban landscapes, 270 See also Climate change Gradient analysis, 2, 211 Gradient complex, 3 coastal and marine, 4 elevation, 4 river continuum, 4 Gradient response and competition, 36 Graph theory and metapopulations, 167 Grime, Phil plant strategies, 35

H Habitat fragmentation, 140 Hydrology geospatial proxies, 18

I Incidence function, 157, 194 Incidence matrix, 209 See also Metacommunity Island biogeography, 90 area effect, 193 incidence function, 194 isolation effect, 193 and landscape ecology, 192 and terrestrial habitat islands, 193 Isolation effect, 90, 193 See also Island biogeography

J Joint species distribution model, 40, 205

L Landscape genetics, 176 Landscape pattern alternative framings, 127 area versus configuration, 142 components of pattern, 122 composition, 123 configuration, 123 connectivity, 140 diversity, 123 edge metrics, 125

Index graph-based models, 128 illustrations, 138 inferences on pattern, 135 inferential approaches, 136 interpretation, 129 levels of analysis, 121 metrics, 121–129 correlation and redundancy, 126 patch attributes, 121 patch definition, 119 sampling designs, 137 Landscape pattern metrics, 121 Land-use legacies, 234 See also Ecosystem, legacy effects Lapse rate, 9, 227, 291 Levin, Simon on scale and pattern, 86

M MacArthur, Robert island biogeographic theory (with E.O. Wilson), 89 scaling lessons, 87 Mantel test, 207 Mass effect, 46, 203 See also Metacommunity models Metacommunity approaches, 203 community assembly rules, 201 complementary analyses, 209 conceptual framing, 197–198 constrained ordination, 207 contributing processes, 197 generative models, 202 inferences on contributing factors, 198–200 management, 215 models, 202, 204 model template, 216 overview of approaches, 200 partitioning beta diversity, 206 Sierran forests, 210 and species distribution models, 204 Meta-ecosystem, 250 definition, 242 edge effects, 237 implications, 249 landform effects, 230, 231 lateral fluxes, 228 model template, 248 spatial coupling, 244 Metapopulation area versus configuration, 163

325 definition, 153 empirical criteria, 164 empirical evidence, 164, 165 and landscape genetics, 176 macroscopic approaches, 165, 166 model template, 163, 179–180 network models, 167, 172 theory, 154, 163 Metapopulation models and connectivity effect, 161 incidence function, 156 Levins model, 154 simulation models, 154, 163 source-sink model, 155 spreading-of-risk model, 155 Model specification scaling issues, 94 Model template biotic processes and gradients, 40 climate adaptation, 301 disturbance, 65 metacommunity, 216 meta-ecosystem, 248 metapopulations, 163, 179 socio-environmental system, 255, 257 urban biodiversity, 268 urban disturbance, 264 urban stream syndrome, 272 water balance, 5, 8

N Neutral landscape models, 129 See also Percolation theory Neutral theory, 203 See also Metacommunity models

O Ordination, 2, 207, 213 constrained ordination, 207 (see also Partitioning beta-diversity; Variance partitioning) direct ordination, 2 Orographic lifting, 15

P Partitioning beta-diversity, 202 Patch dynamics, 209 See also Metacommunity models Patch-mosaic model, 118 Pattern and process paradigm, 30, 117

326 Percolation theory, 130 Pests/pathogens as agent of pattern, 49 Physical template and ecosystem processes, 227 precipitation, 15 radiation, 11 Sierra Nevada, 21 temperature, 9 Positive feedback, 91 disturbance regimes, 60 ecosystem processes, 232–233 Potential evaporation (PET), 5 Precipitation, 15 orographic lifting, 15

R Radiation, 11–15 See also Solar radiation Resilient and connected landscapes, 308 Resource subsidy, 244 River continuum, 4

S Scale characteristic scaling, 95 definition, 85 extent, 85 grain, 85 model specification, 94 as observational filter, 87 and sampling design, 110 scaling techniques, 99 Sierra Nevada, 107 tactical scaling, 110 Scaling lessons bird communities, 87 evapotranspiration, 92 sampling grain and extent, 95 semi-arid grasslands, 91 Scaling techniques, 103 autocorrelation, 101 correlogram, 102 for lattice or spatial point data, 106 (see also Scale) semivariance, 104, 105 semivariogram, 104 Semivariance as scaling technique, 103 Sierra Nevada fire regime, 66–70

Index forest community, 206, 210 gradient response, 40 physical template, 21–25 scaling of physical template, 107 water balance, 24 SLOSS (single large versus several small), 194 Social-environmental system, 255, 256 ecology in, of, and for cities, 256 model template, 257 Social-environmental-technological systems (SETS), 256 Soils, 1, 2 catena model, 18 geospatial data, 17 water balance, 16 Solar radiation, 11–15 biophysical models, 13 geometry, 11 geospatial proxies, 14 topographic effects, 12 Space-for-time substitution climate analogs, 291 succession, 33 Spatial data types, 98 Species-area effect, 193 Species distribution models (SDMs), 197, 199 and global change, 297 Succession, 30 shifting mosaic steady-state, 32 Watt's beechwoods, 32 Surficial processes, 1 geospatial proxies, 18 hillslope processes, 17 lapse rate, 9, 16 orographic lifting, 15

T Tansley, Sir Arthur on scale, 86 Temperature, 9 factors affecting, 9 geospatial proxies, 11 lapse rate, 10 Terrain analysis, 18 Trophic cascades, 50

U Urban ecology empirical approaches, 258 Urban heat island, 260

Index Urban landscapes, 255 agents of pattern, 259, 262 biodiversity, 266–268 biotic agents of pattern, 262 and climate change, 276 disturbance, 262 disturbance regimes, 262 ecosystem processes, 269 environmental equity, 278 hydrology, 271 implications of pattern, 265 physical template, 259 scale, 264 (see also Urban ecology, Socialenvironmental system) urban heat island, 260 urban stream syndrome, 271 Urban stream syndrome, 256, 271

327 V Variance partitioning, 208

W Water balance, 5, 227 estimation, 9 factors affecting, 7 Sierra Nevada, 22 supply and demand, 5 temperature, 9 Watershed as sampling units, 272 Watt, Alex beechwoods, 30 pattern and process paradigm, 30 the unit pattern, 30, 43