The Macroecological Perspective: Theories, Models and Methods 3031446100, 9783031446108

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José Alexandre Felizola Diniz-Filho

The Macroecological Perspective Theories, Models and Methods

The Macroecological Perspective

José Alexandre Felizola Diniz-Filho

The Macroecological Perspective Theories, Models and Methods

José Alexandre Felizola Diniz-Filho Departamento de Ecologia, Instituto de Ciências Biológicas Universidade Federal de Goiás Goiânia, Goiás, Brazil

ISBN 978-3-031-44610-8    ISBN 978-3-031-44611-5 (eBook) https://doi.org/10.1007/978-3-031-44611-5 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 This work is subject to copyright. All rights are solely and exclusively licensed 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.

To Mariana, Anas, and Joões

Preface

It has been a while since J. H. Brown and B. A. Maurer proposed the term “macroecology” in a Science paper published in 1989. Their proposition was the basis for reinterpreting relatively straightforward relationships between ecological variables, such as body size, geographic range size, and abundance for assemblages at broad spatial and taxonomic scales. This initial idea was then expanded by incorporating the investigation of patterns and processes previously discussed in community ecology, geographical ecology, and comparative physiology, coherent with the idea that we had “macroecology before macroecology” (Smith et al. 2014). Moreover, the development of macroecology coincided with the need for more comprehensive approaches to biodiversity conservation due to the recognition that the multiple human threats require global and regional strategies and not only local interventions. Macroecology provides an alternative way to answer many questions in ecology and evolutionary biology, improving our understanding of the origin and maintenance of biodiversity patterns at multiple scales, the discovery of fundamental principles underlying these patterns, and eventually helping to establish more effective strategies for their conservation. So, with this broad range of interest and applications, we can characterize macroecology as a particular way to look at the natural world, identifying ecological patterns and the underlying processes and mechanisms from a given “perspective,” a view from somewhere. From a philosophical point of view, this scientific perspective, as defined by Ronald Giere (2006), encompasses the way scientific activity happens within this field, including the theoretical approaches, the strategy of model building, how to obtain and analyze data, and how to communicate the results of these analyses. Exploring and reinforcing the interest in this perspective is the overarching theme of this book. My professional career is intrinsically related to macroecology, with a relatively short time lag of 10 years or so since the original proposition by James Brown and Brian Maurer. Up to the doctoral level, my research was mainly focused on population genetics and phylogenetic comparative analyses. However, in 1994, I was appointed to teach general ecology at the Federal University of Goiás, Central Brazil. I had never done any research on ecology and (I confess) had just attended a vii

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few introductory courses on the subject. I quickly started looking for a research program that matched the new job requirements. The late Harold G. Fowler then called my attention to a paper published by Taylor and Gotelli (1994) in The American Naturalist and argued that macroecology was an emerging and integrative research field that probably would develop fast in the following years. We got some data, did some analyses, and eventually published a paper together on ant macroecology a few years later (i.e., Diniz-Filho and Fowler 1998), consolidating my interest in the field. It was indeed a very different perspective compared with what has been done in Brazilian ecology up to the late 1990s. Nevertheless, it was very promising and attractive precisely because I could apply my skills in multivariate and spatial statistics and phylogenetic comparative analysis. In those days, many talks with Miguel Petrere Jr. and Thomas Lewinsohn, my first references in Brazilian ecology at that time, helped me to define my scientific interests and set macroecology as a priority research theme. Also, my basic knowledge of statistics and philosophy of science that allowed me to see macroecology as an opportune research avenue were shaped by the long talks (actually, throughout my entire life) with my father, José Alexandre Diniz, at that time a geographer at the Federal University of Sergipe. A next important step in developing our research group was the publication, a few years later, of a paper in Ecology Letters on spatial analysis of mid-domain effect predictors about diversity patterns in South American birds of prey. The key issue was that Brad Hawkins and Rob Colwell reviewed the paper, and both kindly signed their reviews! These generous reviews were the starting point of very productive scientific cooperations with both, as well as a nice friendship. In particular, Brad Hawkins opened several opportunities for consolidating our research group and showed us how our ideas and skills in spatial and comparative analyses would be helpful to the field. The initial contacts provided by Brad and Rob developed into an effective international research network that remains until now. In the meantime, I advanced into multiple themes in macroecology, forming the basis of my perception of the field, which is now someway materialized in the present book. Thus, this book is undoubtedly the outcome of an extended collaborative research enterprise among many people. In the long term, my profound thanks to Luis Mauricio Bini and Thiago Fernando Rangel for lifelong collaborations in basically all topics discussed throughout this book. It would be very hard to name all, but I thank all my collaborators and students for the last 30 years or so, both in writing and conducting research papers and for participating in many courses, workshops, and meetings worldwide. I also thank Rob Whittaker, David Currie, Carsten Rahbek, and Miguel Araújo for inviting me to be associate editor for different periods in the Journal of Biogeography, Global Ecology and Biogeography, and Ecography. Definitely, these were important opportunities to learn, discuss, and hopefully contribute to the development of macroecology and biogeography. More pragmatically, I thank Kelly Silva Souza, Lucas Jardim, Jesus Pinto-­ Ledzema, Leila Meyer, Paulo Inacio Prado, Levi Carina Terribile, Mario Almeida-­ Neto, Guilherme Oliveira, Fabricio Rodrigues, Laura Barreto de Paula e Souza, Matheus Lima, Rhewter Nunes, Guilherme Rogie, Livia Frateles, Elisa Barreto,

Preface

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Igor Bione, Gabriel Nakamura, and Jhonny Guedes for help with datasets, R-scripts, figures, discussions on statistical analyses, and preparation of the manuscript. I particularly thank Marco Tulio P.  Coelho for the help with Sect. 6.2.4 and Gabriel Nakamura with his new approach on tip rates and diversification. Throughout the book, several examples and datasets used in previously published papers were further explored, but I would like to thank Kelly Silva Souza and Lucas Jardim for organizing the global amphibian dataset, and Jesus Pinto-Ledezma for full access to the Neotropical Furnariidae dataset. I also thank Ana Clara Diniz and Levi Carina Terribile for help with the cover art. Brad Hawkins, Marco Tulio Coelho, Levi Carina Terribile, Matheus Lima-­ Ribeiro, José Alexandre F.  Diniz, Bruno Ribeiro, Ricardo Dobrovolski, Leandro Duarte, Sidney Gouveia, Jhonny Guedes, Fabricio Villalobos, Thiago Rangel, Kelly Silva Souza, José Maria Cardoso da Silva, Joaquin Hortal, Rafael Loyola, and an anonymous reviewer read preliminary versions of different chapters of the book or the original proposal, and I deeply acknowledge their criticisms, comments, and suggestions. I also thank the team of Springer Nature, in particular Zachary Romano, for the first invitation to write this book and for all his support during the editorial process. Of course, any remaining mistakes or misunderstandings are completely my fault. I acknowledge the Universidade Federal de Goiás for providing the working conditions throughout my entire career and my colleagues at the Department of Ecology and the graduate program in Ecology and Evolution for providing a nice and stimulating scientific environment. Our research program in macroecology, geographical ecology, and biodiversity conservation has been continuously supported by many grants from the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) and the Coordenação para Aperfeiçoamento de Pessoal de Ensino Superior (CAPES), and more recently for supporting the National Institute of Science and Technology (INCT) in Ecology, Evolution and Biodiversity Conservation, in a partnership with our State Research Foundation of Goiás State, the FAPEG. Goiânia, Brazil

José Alexandre Felizola Diniz-Filho

Contents

1

The Macroecological Perspective������������������������������������������������������������    1 1.1 What Is Macroecology?��������������������������������������������������������������������    1 1.2 Patterns and Processes in Macroecology������������������������������������������    4 1.2.1 Macroecological Patterns������������������������������������������������������    4 1.2.2 Ecological Processes, Mechanisms, and Macroevolutionary Dynamics����������������������������������������    6 1.3 Organization of the Book������������������������������������������������������������������   12

2

 Scientific Reasoning for Macroecology����������������������������������������������   15 A 2.1 Theories and Models������������������������������������������������������������������������   15 2.1.1 The Basic Framework ����������������������������������������������������������   15 2.1.2 Theory-Based and Model-Based Reasoning������������������������   21 2.2 Some Philosophical Background on Scientific Practice ������������������   29 2.2.1 Realism, Instrumentalism, and Perspectivism����������������������   29 2.2.2 Constructivism and the Scientific Debates in Macroecology ������������������������������������������������������������������   33 2.2.3 Paradigms, Research Programmes, and Research Traditions������������������������������������������������������������������������������   36 2.2.4 Naturalizing Macroecology��������������������������������������������������   40 2.3 Model Building in Ecology and Evolution ��������������������������������������   41 2.3.1 Strategies of Model Building������������������������������������������������   41 2.3.2 Null and Neutral Models������������������������������������������������������   44 2.3.3 Computer Simulation Models ����������������������������������������������   47 2.3.4 Statistical Models������������������������������������������������������������������   49 2.4 Empirical Evaluation of Models and Hypothesis Testing����������������   51 2.4.1 Hypotheses and Models of Data ������������������������������������������   51 2.4.2 Popperian Falsificationism and Classical Hypothesis Testing����������������������������������������������������������������������������������   53 2.4.3 Bayesian Inference����������������������������������������������������������������   60 2.4.4 Comparing Alternative Models��������������������������������������������   65

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2.4.5 Causality, Explanation, and Understanding��������������������������   72 2.4.6 Strong and Weak Tests in Macroecology������������������������������   76 3

Macroecological Data������������������������������������������������������������������������������   79 3.1 The Structure of Macroecological Data��������������������������������������������   79 3.1.1 Biodiversity Geographical Data��������������������������������������������   79 3.1.2 Gridding Systems and General Scale Issues������������������������   82 3.1.3 The Matrix M and Its Expansions����������������������������������������   86 3.1.4 Models of Data����������������������������������������������������������������������   91 3.2 Statistical Issues on Basic Macroecological Data����������������������������   94 3.2.1 Null Expectations of Community-Weighted Means ������������   94 3.2.2 Diversity Fields, Dispersal Fields, and Regional Pools��������   97 3.2.3 Spatial and Phylogenetic Autocorrelation����������������������������  101 3.3 Deconstructing Macroecological Patterns����������������������������������������  111 3.3.1 Dimensions for Deconstruction and Generality of Patterns ����������������������������������������������������������������������������  111 3.3.2 Some Methodological Issues on Deconstruction������������������  113 3.4 Biodiversity Shortfalls����������������������������������������������������������������������  116 3.4.1 The Seven Biodiversity Shortfalls����������������������������������������  116 3.4.2 Filling the Gaps��������������������������������������������������������������������  118

4

 Structure and Dynamics of Geographic Ranges ����������������������������������  125 4.1 Patterns in Abundance and Geographical Population Structure ������  125 4.1.1 Basic Population Models������������������������������������������������������  125 4.1.2 The BAM Diagram ��������������������������������������������������������������  128 4.1.3 Abundance, Population Genetics, and Central-Peripheral Dynamics������������������������������������������������������������������������������  130 4.2 Defining and Modeling Geographic Ranges������������������������������������  134 4.2.1 Spatial Modeling of Occurrences�����������������������������������������  134 4.2.2 Species Distribution and Ecological Niche Models��������������  136 4.2.3 Virtual Species and Simulated Species Ranges��������������������  141 4.2.4 Properties of Geographic Ranges�����������������������������������������  144 4.3 Comparative Analyses of Geographic Ranges����������������������������������  146 4.3.1 Range Size Frequency Distributions (RSFD) ����������������������  146 4.3.2 Geographic Range Size, Abundance, and Occupancy����������  150 4.3.3 Rapoport’s Rule��������������������������������������������������������������������  153 4.4 From Geographic Ranges to Local Assemblages and Metacommunities������������������������������������������������������������������������������  158 4.4.1 Macroecological Assemblages and Local Communities������  158 4.4.2 Species Abundance Distribution (SAD) ������������������������������  159 4.4.3 Species-Area Relationship (SAR)����������������������������������������  163

5

 The Macroecological Understanding of Ecological Niches������������������  167 5.1 Niche Concepts and Macroecology��������������������������������������������������  167 5.1.1 Grinnellian, Eltonian, and Hutchinsonian Niches����������������  167 5.1.2 Hutchinson’s Duality������������������������������������������������������������  170 5.1.3 Ecophysiology and Thermal Tolerance��������������������������������  173

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5.2 Measuring and Comparing Niches����������������������������������������������������  175 5.2.1 Ordination and Niche Dimensionality����������������������������������  175 5.2.2 Multivariate Distances and Niche Overlap ��������������������������  179 5.2.3 Ecological Networks and the Macroecology of Biotic Interactions����������������������������������������������������������������������������  181 5.3 Niche Evolution��������������������������������������������������������������������������������  184 5.3.1 Geographic Range-Mediated Niche Evolution��������������������  184 5.3.2 Niche Evolution and Ecological Speciation ������������������������  189 5.3.3 Phylogenetic Niche Conservatism����������������������������������������  193 6

Species Richness Gradients��������������������������������������������������������������������  203 6.1 Latitudinal and Elevational Gradients����������������������������������������������  203 6.1.1 The Generality of Latitudinal Gradients ������������������������������  203 6.1.2 Elevational Gradients������������������������������������������������������������  207 6.2 Geographical Patterns and the Richness-Environment Relationships������������������������������������������������������������������������������������  209 6.2.1 Geometric Constraints and the Mid-domain Effect��������������  209 6.2.2 Richness-Environment Relationships ����������������������������������  213 6.2.3 Climatic Stability, Biotic Interactions, and Ecological Specialization������������������������������������������������������������������������  219 6.2.4 The Geography of Climate: Back to Hutchinson’s Duality����������������������������������������������������������������������������������  222 6.2.5 A Note on Spatial Autocorrelation and Richness Gradients ������������������������������������������������������������������������������  224 6.3 Evolutionary Dynamics and Richness Gradients������������������������������  226 6.3.1 Diversification Rates and Time for Speciation ��������������������  226 6.3.2 Cradles, Graveyards, and Museums (and Casinos)��������������  229 6.3.3 Tropical Niche Conservatism������������������������������������������������  230 6.4 Phylogenetics and Estimates of Speciation and Extinction Rates����  233 6.4.1 Basic Concepts and Methods������������������������������������������������  233 6.4.2 Regional Estimates of Diversification Rates and Dispersal������������������������������������������������������������������������  236 6.4.3 Species-Specific Diversification Rates����������������������������������  239 6.5 Simulating Richness Patterns������������������������������������������������������������  243 6.5.1 Initial Developments Coupling MDE and Environmental Tolerance������������������������������������������������������������������������������  243 6.5.2 Creating Evolutionary Dynamics������������������������������������������  245 6.5.3 Theorizing from Computer Simulation Models��������������������  248

7

 Diversity Patterns in Macroecological Assemblages����������������������������  251 7.1 Phylogenetic Diversity����������������������������������������������������������������������  251 7.1.1 Concepts of Diversity and the Equivalence of Species��������  251 7.1.2 Measuring Phylogenetic Diversity����������������������������������������  253 7.1.3 Phylogenetic Endemism�������������������������������������������������������  260 7.1.4 Genetics, Genomes, and Population Diversity����������������������  261

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7.2 Trait Diversity and Functional Biogeography����������������������������������  265 7.2.1 Divergence in Phenotypic Traits and Functional Diversity��������������������������������������������������������������  265 7.2.2 Phylogenies as Backbones and Proxy for Understanding Functional Diversity��������������������������������������������������������������  269 7.2.3 Dimensionality����������������������������������������������������������������������  273 7.3 Beta Diversity ����������������������������������������������������������������������������������  275 7.3.1 Scale Issues and the Concept of Beta Diversity��������������������  275 7.3.2 Geographical Patterns in β-Diversity and Its Components ��  276 7.3.3 Phylobetadiversity����������������������������������������������������������������  282 7.3.4 Regionalization ��������������������������������������������������������������������  287 8

 Patterns in Body Size ������������������������������������������������������������������������������  293 8.1 The Ecological Implications of Body Size ��������������������������������������  293 8.1.1 Body Size as a Proxy of Ecological Processes and Evolutionary Dynamics��������������������������������������������������  293 8.1.2 Measuring Body Size������������������������������������������������������������  297 8.2 Body Size, Geographic Range Size, and Abundance�����������������������  299 8.2.1 Body Size Frequency Distribution����������������������������������������  299 8.2.2 Range Size: Body Size and Abundance – Body Size Patterns����������������������������������������������������������������������������������  305 8.3 Macroecological Trends and Phylogenetic Patterns ������������������������  310 8.3.1 Phylogenetic Patterns and Evolutionary Models������������������  310 8.3.2 Cope’s Rule��������������������������������������������������������������������������  316 8.4 Two Ecogeographical Rules��������������������������������������������������������������  321 8.4.1 Bergmann’s Rule������������������������������������������������������������������  321 8.4.2 Island’ Rule��������������������������������������������������������������������������  328

9

From Theoretical to Applied Macroecology������������������������������������������  339 9.1 Human Macroecology����������������������������������������������������������������������  339 9.1.1 Origins and the Geographic Expansion of Homo sapiens����  339 9.1.2 Genetic and Phenotypic Variation in Human Populations����  345 9.1.3 Human Cultural and Social Diversity ����������������������������������  349 9.1.4 Toward Global Civilization and Ecosystem Domination������  353 9.2 Macroecology and Biodiversity Conservation����������������������������������  359 9.2.1 The Macroecological Perspective on Conservation Science����������������������������������������������������������������������������������  359 9.2.2 Rarity and Extinction Risk����������������������������������������������������  362 9.2.3 Geographic Range Collapse, Climate Change, and Biological Invasions ������������������������������������������������������  368 9.2.4 Biodiversity Hotspots, Systematic Conservation Planning, and Gap Analysis��������������������������������������������������  373

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10 Concluding Remarks ������������������������������������������������������������������������������  387 10.1 On Theory, Models, and Methods��������������������������������������������������  387 10.2 Prospects from the Past: Patterns and Processes in Macroecology ����������������������������������������������������������������������������  390 10.3 The Future��������������������������������������������������������������������������������������  391 References ��������������������������������������������������������������������������������������������������������  395 Index������������������������������������������������������������������������������������������������������������������  447

Acronyms

ABC AET AIC ANOSIM ANPP ANSKEW AOGCM ARM AUTEUR BAM BAMM BEM BH BIC BiSSE BMR BSFD CA CBD CE CI ClaDS COUE CPD CTmax CTmin DD DPAC DR EB EBA

Approximate Bayesian Criterion Actual EvapoTranspiration Akaike Information Criterion Analysis of Variance based on Similarity Above Ground Net Primary Productivity Analysis of Skewness Atmospheric-Ocean Global Circulation Models Auto-Regressive model Accommodating Uncertainty in Trait Evolution Using R Biotic, Abiotic and Movement Bayesian Analysis of Macroevolutionary Mixtures Bioclimatic Envelope Model Biodiversity Hotspots Bayesian Information Criteria Binary State Speciation-Extinction (model) Basal Metabolic Rate Body Size Frequency Distribution Correspondence Analyses Convention on Biological Diversity Crisis Ecoregions Conservation International Bayesian Cladogenetic Diversification Rate Shift Centroid, Overlap, Unfilling and Expansion (of geographic ranges) Center of Plant Diversity Critical maximum limit for Temperature Critical minimum limit for Temperature Data Deficient (species) Discriminant Analysis of Principal Component Diversification Rates Early Burst (evolutionary model) Endemic Bird Areas xvii

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Acronyms

EBV Essential Biodiversity Variables ED Evolutionary Distinctiveness EER Energetic Equivalence Rule ENFA Environmental Factor Analysis ENM Ecological Niche Modeling E-Space Environmental Space (in the context of SDMs/ENMs) FD Functional Diversity FDist Functional Distance (among species) FF Frontiers Forests FMR Field Metabolic Rate G200 Global 200 ecoregions GAM Generalized Additive Model GARP Genetic Algorithm for Rule Set Production GBIF Biodiversity Information Facility GIS Geographic Information Systems GLM General Linear Model GME General Metabolic Equation GSAD Generalized Species-Abundance Distribution G-Space Geographic Space (in the context of SDMs/ENMs) GWR Geographically Weighted Regression HBWA High Biodiversity Wilderness Areas HSM Habitat Suitability Models (HSB) IBC Inference to the Best Cause IBD Isolation-by-Distance IBE Inference to the Best Explanation IBE Isolation-by-Ecology IBM Individual-Based-Model ISAR Island Species-Area Relationship ITT Into the Tropics IUCN International Union for Conservation of Nature IV Importance Value j-SDM Joint Modeling of Species Distributions LCBD Local Contribution for Beta-Diversity LGD Latitudinal Diversity Gradients LTT Lineages-Through-Time LW Last of the Wild MAXENT Maximum Entropy (in the context of SDM) MC Megadiverse Countries MCMC Markov Chain Monte Carlo MCP Minimum Convex Polygons MDE Mid-Domain Effect MEDUSA Modeling Evolutionary Diversification Using Stepwise AIC METE Maximum Entropy Theory MIH More Individual Hypothesis MPD Mean Pairwise Distance

Acronyms

MSER MTE MuSSE NDT NMDS NODF NOT NPP NRI NTE NTI OFRD OLS OMI OTT O-U PCA PCSP PD PDist PE PERMANOVA PET PGLS PIC PNC POM PSR PSV PVR QuaSSE RMA RSFD SAC SAD SAR SCBD SCP SDGD SDM SEE SEM SESAM SPR

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Maximum Sustainable Evolutionary Rate Metabolic Theory of Ecology Multi-State Speciation-Extinction (model) Niche Divergence Test Non-Metric multiDimensional Scaling (NMDS) Overlap and Decreasing Fill Niche Overlap Test Net Primary Productivity Net Relatedness Index Neutral Theory of Ecology Nearest Taxa Index Orbitally-Forces Range Dynamics Ordinary Least-Squares Outlying Mean Index Out of the Tropics Ornstein-Uhlenbeck process Principal Component Analyses Principal Coordinates of Phylogenetic Structure Phylogenetic Diversity Phylogenetic Distance (among species) Phylogenetic Endemism Permutational Multivariate Analysis of Variance Potential EvapoTranspiration Phylogenetic Generalized Least-Squares Phylogenetic Independent Contrasts Phylogenetic Niche Conservatism Pattern-Oriented Modeling Phylogenetic Signal–Representation (curve) Phylogenetic Species Variability Phylogenetic Eigenvector Regression quantitative trait Speciation-Extinction (model) Restricted Major Axis (regression) Range Size Frequency Distribution Species Accumulation Curve Species-Abundance Distributions Species-Area Relationship Species Contribution for Beta-Diversity Spatial Conservation Prioritization, or Systematic Conservation Planning Species Diversity – Genetic Diversity (relationship) Species Distribution Models State Speciation-Extinction (model) Structural Equation Modeling Spatially Explicit Species Assemblage Modeling Species-Productivity Relationships

xx

S-SDM STR TNC TPC TSA WWF ZNGI ZSM

Acronyms

Stacked Species Distribution Models Species-Temperature Relationship Tropical Niche Conservatism Thermal Performance Curves Trend Surface Analysis World Wide Fund for Nature Zero Net Growth Isocline Zero-Sum Multinomial

Chapter 1

The Macroecological Perspective

1.1 What Is Macroecology? After more than 30  years of the publication of J.  H. Brown and B.  A. Maurer’s (1989) paper in Science, macroecology can be considered an impressively successful way to investigate ecological patterns. Their idea was to focus on “big questions” and develop an empirical and operational research agenda based on a few synthetic variables available for many species in taxonomically defined biotas (e.g., mammals or birds in North America). More explicitly, in the abstract of their seminal paper, Brown and Maurer (1989, pg. 1145) wrote that: Analyses of statistical distributions of body mass, population density, and size and shape of geographic range offer insights into the empirical patterns and causal mechanisms that characterize the allocation of food and space among the diverse species in continental biotas. These analyses also provide evidence of the processes that couple ecological phenomena that occur on disparate spatial and temporal scales-from the activities of individual organisms within local populations to the dynamics of continent-wide speciation, colonization, and extinction events.

So, they proposed to turn back to broad-scale empirical analyses started in the 1950s and 1960s by G.  E. Hutchinson, Robert MacArthur, Richard Levins, and many others, which at that time received less attention than experimental approaches at more local scales (McIntosh 1985). A few years later, in the first textbook on the subject, Brown (1995) more explicitly defined macroecology as …a non-experimental, statistical investigation of the relationships between the dynamics and interaction of species populations that have typically been studied on small scale by ecologists and the process of speciation, extinction and expansion and contraction of ranges that have been investigated on much larger scales by biogeographers, paleontologists and macroevolutionists. It is an effort to introduce simultaneously a geographic and historical perspective in order to understand more completely the local abundance, distribution and diversity of species… (Brown 1995, pgs. 6–7)

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 J. A. F. Diniz-Filho, The Macroecological Perspective, https://doi.org/10.1007/978-3-031-44611-5_1

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Brown (1995) highlights that he did not see macroecology as a field but rather as a relatively new and integrative approach to some questions more commonly investigated using experimental tests at local scales. Indeed, the overture of his 1995 book defines precisely such a problem (i.e., extinctions of small mammals at mountain tops under climate change) that could be investigated from a “bottom-up” or “top-­down” approach. It is clear now that macroecology may effectively integrate several different research fields, such as ecology, evolutionary biology, physiology, behavioral sciences, climatology, and paleontology (Shade et al. 2018; Leitão et al. 2019). This integration is necessary to understand natural patterns and processes better and support general strategies for biodiversity conservation under rapid global changes at multiple spatial scales (Kerr et al. 2007; Keith et al. 2012). In a widely cited review and philosophical discussion on theory and laws in ecology, Lawton (1999) highlights the importance of the identification of macroecology as a new integrative discipline that can be viewed as “…a blend of ecology, biogeography, and evolution and seeks to get above the mind-boggling details of local community assembly to find a bigger picture, whereby a kind of statistical order emerges from the scrum….” He continues by stating that “…macroecology is the search for major, statistical patterns in the types, distributions, abundances, and richness of species, from local to global scales, and the development and testing of underlying theoretical explanations for these patterns.” Some important lessons can be extracted from these general definitions, shedding light on macroecology today. Since the beginning, the evaluation of broad-­ scale patterns has been considered more important (and someway evident by a simple semantic reason) than the search for fundamental laws associated with such patterns. One reason for this choice is that it was consistently recognized that the statistical patterns originated from alternative potential processes and mechanisms (Warren et al. 2022). Gaston and Blackburn (2000) indeed emphasized in a more pragmatic way that macroecology “…is concerned with understanding the abundance and distribution of species at large spatial and temporal scales.” Gaston and Blackburn (1999, 2000) also highlight macroecology as an integrative and non-­ reductionist approach by reinforcing that the emergent patterns observed are not evident from the unique local components we identified and that have been studied for a while in related research fields at more local scales. Under this definition, it is common to think about the ecological patterns arising from the “diffusion” of high-level biological “particles” (typically species), throughout broad scales of space and time, so integration between macroecology and macroevolution becomes evident (McGill et al. 2019). Indeed, all early books by Brown (1995), Maurer (1999), and Gaston and Blackburn (2000) reinforce this link, even though only more recently it became viable to apply statistical and computational tools from macroevolution to investigate the origin and maintenance of macroecological patterns. In particular, the pioneering paper by Brown and Maurer (1987) proposes some explanations for the relationship between body size, range size, and abundance at the species level as “constraint envelopes” (rather than functional relationships), explaining their limits by evolutionary processes at higher hierarchical levels (Diniz-Filho 2004a; Rabosky and McCune 2010; Nürk et al. 2020).

1.1  What Is Macroecology?

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From a historical point of view, it is also interesting to note that although Brown and Maurer (1989) proposed the term macroecology in 1989, basic ideas now aggregated under this term can be traced back to the early developments in ecology, comparative physiology, biogeography, and evolutionary biology (Smith et al. 2008, 2014). These early developments include several fields and research areas, including many ideas ranging from species abundance distribution (SAD) models and the relationship between local and regional species pools in community ecology (Ricklefs 1987; Magurran and McGill 2011). Macroecology also started dealing with many questions originally proposed in comparative physiology to understand the relationships between abundance, metabolic rate, and body mass across species, some of which relate to ecogeographical rules (Ashton 2001; Gaston et al. 2008). We can also recall several classical papers on “ecological biogeography” dealing with species-area relationships, geographical range edges (with another straightforward interface with population and evolutionary genetics), island patterns, and elevational and latitudinal diversity gradients. The explicit incorporation of these geographical patterns into macroecology (e.g., Ruggiero and Hawkins 2006) is of particular interest as they are one of the earliest ecological and biogeographical patterns discovered by naturalists, such as Robert Forster and Alexander von Humboldt in the early nineteenth century (Hawkins 2001; see also Ladle et al. 2015). In particular, the latitudinal diversity gradients (LDGs) were jointly explored by ecologists and biogeographers using new tools and data in the 1960s and 1970s (e.g., Pianka 1966). Still, a subtle increased interest allowed a complete renovation of models and methods after the start of macroecology, with particular emphasis on trying to disentangle testable hypotheses from the myriad of explanations developed for so long to explain the pattern (Whittaker et al. 2001; Colwell 2011; Worm and Tittensor 2018; Dawson et al. 2023). For instance, Witman and Roy’s (2009) book on “marine macroecology” is focused on diversity and geographic range patterns at broad scales in the marine realm. More emphasis on the broad-scale geographical components of diversity and variation in some morphological variation, such as body size, promotes an approximation of macroecology to some research questions traditionally associated with community ecology and ecological biogeography. Simultaneously, considering species or populations as diffusing particles in time and space leads to reevaluating problems more frequently associated with macroevolution and comparative physiology. It is interesting to highlight that these two ways of thinking in macroecology subsume the responses by Blackburn and Gaston (2002) and by Marquet (2002) to a comment by Fisher (2002) on the overlap between macroecology and biogeography. Whereas the former reinforced the integration between distinct disciplines and the discussion of mechanisms explaining broad-scale geographical patterns, the later response highlighted the primary goal of macroecology as identifying general principles or natural laws underlying the structure and function of complex systems. Indeed, recognizing this apparent duality of goals is the central synthesis achieved in McGill’s (2019) excellent review and discussion of what macroecology is. He suggested that macroecology can be viewed both as ecological analyses at broad

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scales in time, space, and taxonomy and as an investigation of complex systems based on first principles and looking for general and unifying laws. Thus, based on all definitions shown above and moving to more conceptual issues in philosophy of science (further discussed in Chap. 2), we can now view macroecology as a “scientific perspective,” a particular way to look at the natural systems “from a distance” (Giere 2006). The focus relies on the overall and emergent patterns instead of idiosyncrasies and local variation, seeking to understand the ecological and evolutionary processes, usually at lower hierarchical levels underlying them (Keith et al. 2012; Shade et al. 2018). Nevertheless, there are more optimistic and pessimistic views on whether this “macroecological perspective” can be coupled with more traditional and experimental analyses of ecological patterns at local scales (Paine 2010). Historically, we can also add that the macroecological perspective evolved in at least two partially overlapping research traditions, more or less in line with the two goals recognized by McGill (2019), each following different scientific reasoning on building and evaluating theories and models using various methods (Laudan 1977). We can think, for instance, of a study that identifies and validate a broad-scale pattern in nature. A first research tradition evaluates which explanatory variables would be surrogates for potential ecological or evolutionary processes underlying these patterns and attempt alternative “explanations” for them. On the other hand, one can start from some first principles of population dynamics or ecophysiology and develop theories and models that can lead to emergent broad-scale patterns. These two approaches, roughly related to inductive and deductive scientific reasoning (e.g., Maurer 2004), encompass several important epistemological questions, including how to develop theories and test them by confronting models with empirical data and how such findings would lead to a better understanding of ecological and evolutionary processes driving the patterns (see Chap. 2 for details).

1.2 Patterns and Processes in Macroecology 1.2.1 Macroecological Patterns The main goal of the macroecological perspective is to look for general and emergent patterns in nature and try to understand the underlying ecological and evolutionary processes, even though this has been done based on different scientific reasoning and methodological approaches. As Pearse et al. (2018; see also Shade et  al. 2018) pointed out, linking patterns and processes has long been the “Holy Grail” of macroecology, but first, there are many discussions about how to do this and what patterns and processes mean. We can start with a brief overview of the most frequently analyzed macroecological patterns discussed throughout this book. For instance, it is opportune to recall, on a historical note, that Lawton (1999) and Gaston and Blackburn (2000) provide overlapping lists of several emergent macroecological generalizations

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(patterns) that deserve investigation, with some minor additions highlighted below. We provide below a more synthetic and operational way to understand these macroecological patterns based on how data can be organized and analyzed (Sect. 3.1.3), combining in different ways the species-level variation in body mass, geographic range size, and abundance (see Blackburn and Gaston 2001). In short, investigating the SAD has been a standard research topic in community ecology at local and regional spatial scales. An analogous macroecological pattern appears for range-size frequency distributions (RSFD). Moreover, if the information on abundance in local communities throughout the geographic range of species is available, it is possible to obtain SAD curves for the overall species abundance (i.e., at a global scale). The shape of these distributions is usually right-skewed but varies with spatial scales. There is a vast literature on how to fit alternative models to these data and interpret them by considering the assumptions and ecological mechanisms underlying each one, now rediscussed from a macroecological perspective (McGill 2010, 2011). The statistical distribution of body size (BSFD) follows similar right-skewed patterns, with large-bodied species much rarer than small-bodied ones. Some models describe BSFD as emerging from the relationship between body size speciation and extinction rates, mediated by geographic range size and abundance, thus revealing a direct integration between macroecology and macroevolution. Evaluating patterns in body size in deep time sometimes allows an understanding of how climatic changes are associated with faunal shifts and succession. Thus, an obvious follow­up in searching for patterns is to explore the relationships between the three variables. In some cases, the relationships among these macroecological variables are linear, or at least functional, and one of the first research motivations came from the positive relationship between body size and metabolic rate, previously known in ecophysiology. Damuth (1981, 1987) proposed that, as the two slopes are equal but with inverse signs, all the species in a community would use the same amount of energy, known as the energetic equivalence rule (EER) (Stephens et al. 2019; Sect. 8.2.2). On the other hand, some relationships are better described by “constraint envelopes,” in which species occupy distinct regions of the 2-D or 3-D space defined by these variables (Brown and Maurer 1987, 1989). Hence, the idea is to interpret the limits of the polygons instead of the functional relationships among variables, despite some methodological difficulties. An example is the relationship between geographic range size and body size (Sect. 8.2.2), in which the lack of large-bodied species with small geographic ranges suggests an important role for extinction dynamics in shaping this relationship. Overlaying species’ geographic ranges opens a wide research avenue on what we could call “geographical macroecology” (Ruggiero and Hawkins 2006; see also Kent 2008 and Blackburn and Gaston 2006 for a reply). Indeed, since the early formal developments in geographical ecology by Robert MacArthur (1972), geographic ranges have been considered the “basic unit” generating patterns of biological diversity in space at multiple scales. Hereafter, we use the term “assemblages” to refer mainly to these sets of species in a region resulting from overlaying their

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geographic ranges, except when notice otherwise and to contrast with the local assemblages (i.e., based on local direct samples) or communities (see Sect. 3.1.3). We can obtain several patterns from these “macroecological assemblages” based on species’ geographic ranges. For instance, it is possible to analyze geographical patterns in richness and find correlates with environmental characteristics, especially temperature, and productivity, helping to disentangle processes associated with several diversity gradients at global scales. More recently, coupling these data with phylogenetic information and trait variation allows the evaluation of phylogenetic and functional diversity in geographic space, with consequences for understanding broad-scale patterns at distinct scales. The same framework allows evaluating geographical patterns in species body size and other species-level traits, such as geographic range size, so we have a general framework to deal with ecogeographical rules widely discussed in biogeography and ecophysiology for a while, including Bergmann’s and Rapoport’s rules (e.g., Gaston et al. 2008). Despite some difficulties in obtaining primary data in  local communities for broad geographic extents, it would also be possible to compare patterns arising from macroecological and local assemblages. This comparison would give insights into assembly rules based on the relationship between local and regional diversity and broad-scale patterns in β-diversity (Ricklefs 1987). It is also possible to investigate SAD by compiling abundance data from several local communities and thus evaluate the relationship between abundance and position of populations within a geographic range, allowing some inferences about the population structure within them. Under similar reasoning, the species-area relationships (SAR) have also been a common research theme in community ecology and biogeography, evaluating, for instance, the local assemblage patterns in islands (Matthews et al. 2021). From a macroecological perspective, the overlap of geographic ranges allows more analytical possibilities, including investigating how slopes of SAR change along spatial hierarchies from local to continental scales.

1.2.2 Ecological Processes, Mechanisms, and Macroevolutionary Dynamics A common approach in macroecology is to infer the ecological and evolutionary processes or mechanisms explaining the patterns described in the previous section (Brown 1999; Keith et al. 2012). Shade et al. (2018) start a recent review explicitly stating that “…Macroecology is the study of the mechanisms underlying general patterns of ecology across scales.” The previously mentioned definition by Gaston and Blackburn (2000) also reinforces the importance of seeking processes underlying macroecological patterns. However, there are two general and fundamental conceptual and philosophical issues that we must deal with here before moving on to this step. First, what do we mean by “explain” and “understand,” and second, what do we mean by “processes” and “mechanisms” in distinct research traditions within

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macroecology? Moreover, it is important to wonder how these processes and mechanisms can be integrated across different perspectives, i.e., coupling local perspectives and experimental approaches with macroecology (Paine 2010). These questions are far from trivial, and each possible answer has profound philosophical and conceptual implications, discussed in more detail in Sect. 2.1. Still, we focus here on processes and mechanisms as a primary issue to make sense of a macroecological perspective to investigate nature. For instance, we can say, for a start, that we “understand” the latitudinal gradient of species richness if we find significant correlations with environmental variables, such as temperature or productivity. This result may be enough and “count as an explanation” for many researchers following a more empiricist philosophical tradition. However, McGill and Nekola (2010) argued that this attitude has led to some criticisms because researchers would not be really “understanding” the pattern (mechanistically), just describing one pattern by another. Indeed, there are different ways for these empirical relationships between richness and temperature or productivity to emerge, with different causal pathways linking processes to patterns. One of the ideas is that identifying at least some of these plausible potential causal pathways would allow finding other empirical surrogate variables that may help disentangle the underlying mechanisms with further analyses. From a different philosophical point of view, an alternative approach is to evaluate patterns predicted from theoretical explanations derived from first principles and based on fundamental mechanistic processes at the population or individual levels. If these theoretical deductions correctly predict empirical patterns, it is usually considered that these theories are confirmed, corroborated, or at least supported (see McGill 2003a). It is possible to move on and try several pathways, for instance, in a Popperian cycle of conjectures and refutations, improving theories and models by incorporating new components and ideas. These two alternative ways of scientific reasoning are at the root of the two research traditions within the macroecological perspective abovementioned and are discussed in more detail throughout Chap. 2. For now, the crucial issue is that researchers usually wonder, in different ways, about the potential ecological or evolutionary processes or mechanisms “underlying” such patterns to understand them better (Shade et al. 2018). It is opportune to illustrate how processes underlying macroecological patterns can be investigated following these two alternative scientific reasonings. For instance, Gaston and Blackburn (2000, pg. 109) suggested the following explanations for the RSFD: (1) random sampling, (2) range position, (3) vagrancy, (4) metapopulation dynamics, (5) niche breath, (6) niche position, and (7) speciation, extinction, and temporal dynamics. When proposing these alternative explanations for a pattern, Gaston and Blackburn (2000; see also Gaston 2003) always pointed out that they should not be “mutually exclusive.” They discuss how we could try to choose among them, disentangling the pathways based on additional information or correlations between ranges and other surrogate variables. As discussed in more detail in Chap. 2, it is not straightforward to define this approach as “exploratory” or sometimes as “inductive reasoning” (see Maurer 2004), as there are distinct theorizing processes necessary to derive all these alternative pathways.

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The assessment of the available empirical evidence at that time suggested, for RSFD, that random sampling, metapopulation dynamics, and niche position were the most plausible explanations for the pattern (Gaston and Blackburn 2000). However, in what sense are they not “mutually exclusive”? Are we saying that patterns in different groups or organisms, so that ectotherms against endotherms, for instance, may be explained by different processes? Are we talking about different explanations for geographic regions with distinct evolutionary histories and species pools? Or are we saying there may be a unique explanation for RSFDs, but we do not know yet? Or do we hope to find additional data that allows (inductively) to disentangle the potential explanations independently of scale? Do we expect to be successful in this enterprise? All these questions are explored in more detail throughout Chap. 2. In this example, Gaston and Blackburn (2000) pointed out that explanations 1–3 are most likely to explain RSFD at smaller spatial scales, thinking in partial geographic ranges within a region (e.g., birds’ geographic range in England). As these species could be found throughout Europe or even be cosmopolitans, their ranges would be partial and thus create short-scale explanations for RSFDs). Bimodal distributions are more common in such cases, and some explanations for RSFDs at the species level would fail. As will be extensively discussed in Chap. 4, both metapopulation models and niche characteristics of the species explain geographic range size and their edges, and an alternative would be to develop mechanistic models in advance and evaluate how distinct parameter combinations for species varying in ecological or demographic trait would lead to different RSFDs (e.g., Maurer and Taper 2002). An important lesson from this initial example is that as we start to disentangle such alternative explanations and try to interpret them as illuminating alternative causal pathways, we are usually more confident in talking about “understanding” the patterns mechanistically or in a process-based way. However, the second important issue is how we can better understand these “explanations” regarding the mechanisms acting in the geographic range within and among species. How do we define at which level we are talking about processes and mechanisms or just describing correlative patterns at lower and lower hierarchical levels? Although some of the above explanations for RSFD involve population dynamics within geographic ranges and could be theoretically derived from the first principles of population growth and evolutionary ecology (i.e., the mean fitness of populations related to species’ niche), some are just correlations with other macroecological patterns (such as species’ niche breadth). So, we are back to just a pattern explained by another pattern. On the other hand, another set of explanations reflects distinct balances between speciation and extinction rates that also require, in turn, explanations at lower hierarchical levels. From an operational point of view, the best we can do is to make efforts to think that we have nice empirical surrogates for such processes. Looking for explanations by deciding among alternative causal pathways may be much more complicated because most, if not all, processes or mechanisms are not actually “observable,” which leads to important philosophical implications (see Sect. 2.2.1).

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Thus, it is also opportune to highlight now the differences between the terms “processes” and “mechanisms,” particularly in a modeling context. Connolly et al. (2017) proposed that “processes” refers to explaining a pattern based on the dynamics of other correlated variables that drive variation in the response variable. So, for instance, we could think that species richness in a region is a consequence of speciation-­extinction dynamics, explained by models in which parameters depend on temperature changes in geologic time. However, rather than modeling richness by a process involving the two rates, the individual responses of the species to temperature changes would be mechanistically modeled, with speciation occurring by splitting populations within geographic ranges based on local extinctions and adaptations at the local (or even individual) level. So, a mechanistic approach involves a better definition of how the causal links between different components of the system, usually at a lower hierarchical level, lead to the emergence of patterns. It is common to think of process-based and mechanistic-based explanations as providing degrees of a more profound knowledge or understanding of a pattern (and both “superior” to purely correlative approaches). However, things are not that simple for several conceptual and methodological reasons further discussed in Chap. 2, so it is better to think about them as two different ways to understand the patterns, depending on the research tradition. Some researchers adopt a more conservative view and suggest that mechanistic explanations would necessarily involve individual-level or population-level models that lead to emerging macroecological patterns at higher levels (see Hagen 2023). However, this leads to other critical discussions on avoiding reductionist macroecology explanations. We are then forced to ask if it is possible to understand macroecological patterns by building theories based on population or individual level (McGill 2019). Although these attempts to explain macroecological patterns may be interesting as a starting point for theorizing, this approach frequently requires dealing with many exceptions and developing more complex and sometimes “ad hoc” theories and models. Lomolino (2000a) even mentions the idea of “protean macroecological patterns,” in which different theories and models are successively built up and adjusted to fit patterns in different groups of organisms or geographic scales. McGill and Nekola (2010) proposed a broader definition of mechanisms that do necessarily involve population dynamics or individual variation. They argue that intrinsic statistical constraints and geometric properties, such as central limit theory, fractal geometry, dispersal constraints, and regional replacement under neutrality, random sampling, and maximum entropy, also lead to emergent macroecological patterns, especially SAR and SAD, so they should count as explanatory mechanisms. Interestingly, some of these mechanisms, such as random sampling and neutrality, involve the origin of patterns without effects from environmental or evolutionary mechanisms, leading us to a discussion about null models and neutral dynamics (Sect. 2.3.2). For instance, in a more traditional perspective based on population dynamics, these would hardly count as a “mechanism.” Indeed, it is not uncommon to say, when patterns arise by stochastic processes or geometric constraints, that they are an “artifact” and “do not exist” or “do not matter” (rather than saying that random processes create a pattern).

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There is another point to consider based on this broader definition of mechanisms by McGill and Nekola (2010). Even if we assume a more reductionist view and consider geographic ranges as emerging from individual reproductive dynamics and dispersal, how can these population-level processes within geographic ranges allow an understanding of the RSFD or a latitudinal gradient in species richness? The main problem is that we do not know why a particular group of species have those demographic characteristics that drive variation in abundance, how these characteristics will lead to global extinction at the level of the entire species, or how they will be inherited if speciation occurs. So, the answer is that we cannot, so mechanistic (in a traditional sense) explanations at these lower hierarchical levels tend to fail. Following the above reasoning, we can, at best, understand RSFD only if we think more in “how” explanations than in “why” ones (see Warren et al. 2022). The first question (“how”) arises by combining different empirical patterns to explain how such a pattern emerges, providing thus a proximal explanation as in the several ideas discussed by McGill and Nekola (2010). On the other hand, a mechanist explanation for RSFD would require adding speciation-dynamics to have a “why” answer, providing thus a “distal” or “ultimate” evolutionary explanation (Mayr 1961; but see Laland et al. 2012 for some important criticisms of using these terms in genetics and evolutionary biology). These two ways of thinking in causality and explanation are someway complementary. Dealing with these two questions simultaneously requires moving away from a more traditional empiricist view, which is usually more focused on “how” (i.e., explaining refers to finding the fundamental laws associated with some natural phenomena; see May 1986), toward a more realistic explanation based on unobservable causal pathways throughout evolution more related to “why” (Shade et al. 2018). Thus, following the above reasoning, we acknowledge that when thinking only about population-level processes, we are missing an important component of those patterns: the origin of species. Adding this origination component requires expanding our reasoning and incorporating into our framework the dynamics of speciation, extinction, and origin of species’ pools at much broader time scales, which is, for instance, the last explanation in the list by Gaston and Blackburn (2000) for explaining RSFD. In a more traditional view, macroevolution deals with patterns in deep time and phylogenetic scale that evolve by standard population-level processes. However, adding a way to create differentiation between species’ parameters is necessary. An initial and straightforward idea is to create barriers to gene flow in an allopatric speciation process, such as a large river or mountain chain that divides the geographic range into two pieces. After some time, this division allows the evolution of reproductive isolation and the differentiation of the original species into two new species, both by adaptation to distinct environments on each side of the barrier by a neutral stochastic divergence. Each of these two derived species can adapt to changing conditions and expand or retract their ranges in time (and even go extinct). If this process continues for a long time, a group of species linked by ancestral-­ descendent relationships (a phylogeny) emerges. Depending on how the speciation processes lead to differentiation in the niche due to local adaptations of each species

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after the allopatric event, the group of evolving species in a clade can occupy distinct environmental regions in a given broad geographical domain (e.g., Rangel et al. 2007). However, how would these sequential events of speciation and extinction throughout time generate a skewed RSFD? To evaluate this issue, we must consider how macroevolutionary dynamics, in terms of speciation and extinction processes through time, affects range size in the first moment and how the species ranges and their demographic and ecological parameters change after each species become independent. For instance, it seems obvious how population-level processes discussed above may lead to extinction, but how range size interferes with speciation (if it interferes) is more challenging. So, important questions are why speciation happens and how these events relate to range size and niche breadth at each time. In the previous example, we thought about a barrier in an allopatric process, but there are other possibilities. Species endemic to oceanic islands can often arise from peripatric speciation and evolution at range borders in small and isolated populations. We can also think in more general processes dividing species ranges into complex and unpredictable ways if the change in environment isolates some of the populations of a species that can evolve into new species adapted to different environments (see Rangel et al. 2007). Nevertheless, when thinking about multiple adaptive traits of a species, is it possible to assume a continuity between demographic and adaptive processes at local scales and those processes leading to a new species? What if, for example, some traits within a species, such as large niche breadths or variations in dispersal ability, drive the speciation-extinction dynamics? In this case, it would be even more difficult to understand patterns among species by their population-level range dynamics, which leads to all the discussions about emergent processes at a macroevolutionary scale (see Rabosky and McCune 2010; Jablonski 2017a, b). Again, this clearly shows the difficulties in adopting reductionist approaches to macroecology. So, from the macroecological perspective, it is helpful to expand how we think about processes and mechanisms, as pointed out by McGill and Nekola (2010). It may be opportune to distinguish, for instance, ecological processes, which include mechanisms of dispersal, reproduction, drift, and adaptation by natural selection driving abundance at local levels within species, from macroevolutionary dynamics resulting from variable speciation-extinction balances generating new species throughout deep time. These deep time dynamics drive interspecific phenotypic variation because traits follow distinct evolutionary models, reflecting adaptations to changing environmental conditions, neutral evolution, and restricted dispersal (Nürk et al. 2020; Davies 2021). This distinction between ecological process and macroevolutionary dynamics is interesting, because population ecologists usually do not consider natural selection or genetic drift ecological processes (as these are usually defined as “evolutionary” or “microevolutionary” processes). Moreover, we are explicitly assuming that, at least in part, macroevolution is decoupled from microevolution. From a macroecological perspective, this is helpful because it allows for explaining emergent patterns avoiding reductionism towards population-­ level explanations only.

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1.3 Organization of the Book This book resumes all the above issues in more detail. First, in Chap. 2, we discuss the philosophical basis for more integrative reasoning in macroecology, mainly based on Ronald Giere’s (2006) scientific perspectivism. We discuss his basic framework and the distinction between theory-based and model-based approaches, which is the basis of macroecology research traditions. The following section focuses on the strategy of model building and the different types of models, followed by a more methodological section on hypothesis testing. Then, we move on to the many operational issues related to datasets in macroecology (Chap. 3), starting with recording the presence-absences or other continuous metrics, such as abundance, environmental suitabilities, or probabilities of occurrence), for each species, building a matrix of species by spatial units defined at multiple spatial scales. Interacting rows and columns and other more complex numerical manipulations of this matrix allows evaluation of the macroecological patterns described in Sect. 1.2.1. We evaluate the main properties of emerging variables, including spatial and phylogenetic structure, richness and diversity field patterns, and the definition of regional species pools. We also discuss how to partition (deconstruct) the data under this framework and how missing data (i.e., biodiversity shortfalls) can be accounted for, avoiding jeopardizing our understanding of the macroecological patterns. This operational framework will guide the discussion in the rest of the book. After these initial theoretical and methodological issues, it is opportune to start describing empirical patterns and discuss underlying processes and mechanisms. Following the logic of our framework delineated in Chap. 3, we start by discussing geographical ranges and abundance patterns in Chap. 4, starting from basic population and metapopulation patterns and moving up to larger scales and comparative analysis of geographic ranges and abundance or occupancy patterns, including RSFD and Rapoport’s rule. As a first glimpse into issues related to geographic range overlap in (macroecological) assemblages, we end this chapter discussing SAD and SAR. It is challenging to discuss geographic range size without considering niche concepts, so there is some overlap between Chaps. 4 and 5. More technically, this is due to what has been called “Hutchinson’s duality,” which is the conceptual basis allowing niche investigation in a macroecological context and related to patterns in geographic space (G-space) and environmental space (E-space). Chapter 5 discusses models and methods to evaluate this E-space, mostly related to the Grinnellian niche, including ecophysiological patterns and thermal tolerance, also highlighting some new advances in biotic interactions from a macroecological perspective. Chapter 5 ends with the patterns and processes related to niche evolution, from adaptive dynamics within species range to discussions on phylogenetic niche conservatism. Chapter 6 reinforces how geographical and elevational patterns in species richness can be derived from the macroecological assemblages. Following the above reasoning, we show the overall patterns in species richness and then discuss their

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ecological and evolutionary drivers. We start with the basic richness-environment relationships traditionally discussed as due to “ecological” processes. Still, it is much easier to understand them based on macroevolutionary dynamics, considering geographic and environmental gradients in speciation, extinction rates, and phylogenetic niche conservatism. We end that chapter by discussing a different approach to investigate these patterns in species richness based on computer simulations, which in turn provides an excellent way to illustrate the discussions about theory-­ based and model-based from a macroecological perspective previously discussed in Chap. 2. Most of the discussions of diversity patterns continue in Chap. 7, expanding the concept of diversity by incorporating phylogenetic and functional dimensions and many issues related to β-diversity. In Chap. 8, we discuss patterns in body size, which is traditionally a surrogate for several ecological and evolutionary processes and one of the most common ways to express functional variation among species. We start with operational issues on measurement and discuss how interspecific and intraspecific variations in body size explain BSFD and the relationships of body size with geographic range size and abundance. We move on to macroevolutionary trends in body size, including recent methodological developments on using phylogenies to fit alternative evolutionary models and discussing deep-time trends under Cope’s rule. The chapter ends by examining different ways to investigate two “ecogeographical rules,” the latitudinal gradients in body size (Bergmann’s rule) and the evolution of gigantism-dwarfing gradients in islands (Island’s rule). Finally, after discussing all these ecological and evolutionary patterns and processes from a macroecological perspective, it is opportune to think about how the macroecological perspective can be helpful in biodiversity conservation, or conservation science in a broader way (i.e., Santini et al. 2021). We start with an overview of the recent research topic on human macroecology, both to give a different perspective to understand the ecology and evolution of Homo sapiens and how these emerging patterns trigger most, if not all, biodiversity conservation problems in the early twentieth century. We then go back to the main macroecological patterns explored throughout the book and highlight how they may help evaluate extinction risks, responses to anthropogenic climate change, and biological invasions. We end by discussing the emerging field of conservation biogeography and how it was integrated into a macroecological perspective to establish better strategies for systematic conservation planning at global and regional scales. In the concluding remarks, we revisit three main themes permeating the book. First, how can we make sense of theory, models, and methods as components of the scientific activity in macroecology? Second, we go back to prospects to the future, written in the late 1990s, to see how we advanced in understanding macroecological patterns and underlying processes. Finally, what about the future of macroecology?

Chapter 2

A Scientific Reasoning for Macroecology

2.1 Theories and Models 2.1.1 The Basic Framework Macroecology, as a new perspective for ecological research, has distinctive characteristics that require profound philosophical changes in how evidence is used to support and assist in building theories and models. One reason for these differences is the impracticability of controlled or manipulative experimental studies at broad spatial and temporal scales. However, other underlying issues that deserve attention arise from the historical moment when macroecology was formally defined as a research field in the late 1980s. In this chapter, we pursue these many issues with two primary goals: (1) to give some uniformity to expressions like theories, models, and hypotheses throughout the book and how they can be better understood in the context of macroecology and (2) to give researchers interested in macroecology a basic knowledge of these conceptual and epistemological issues so they can consciously adopt (or not) some views and define their scientific practices within a broader philosophical context. We start by providing an overview of scientific reasoning mainly based on Ronald Giere’s (1999, 2006) ideas, which may provide an exciting and unifying road map to some essential conceptual, methodological, and philosophical issues in macroecology. Early research in macroecology in the 1990s was mainly based on descriptive and “exploratory” analyses (but see below), aiming to determine the generality of some broad-scale patterns, such as SAD; SAR; the relationships among body size, geographic range size, and abundance; ecogeographical rules; or richness gradients (Sect. 1.2.1). General explanations proposed for such patterns are usually referred to as non-mutually exclusive “hypotheses” (e.g., Gaston and Blackburn 2000; Gaston 2003). However, calls for a more theoretically oriented approach based on the search for fundamental principles that could provide a © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 J. A. F. Diniz-Filho, The Macroecological Perspective, https://doi.org/10.1007/978-3-031-44611-5_2

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Fig. 2.1  A framework for scientific reasoning that can be useful to describe the main characteristics of scientific reasoning in macroecology. (Adapted from Giere 2006)

unified and integrative explanation for these macroecological patterns soon appeared (e.g., Brown et al. 1993; Brown 1999; Gaston and Blackburn 1999). The first important component of Giere’s (2006) framework (Fig. 2.1) is to define a scientific theory in terms of general principles and conditions, which are templates that help build more specific models. As these principles and conditions are usually very general and abstract, it is crucial to design models that can make explicit predictions about the data verifiable in the real world. So, we have a model-based understanding of scientific theories, with the primary goal of representing some aspects of the real world. We now use the more general term “representational models” to describe these models, following from the idea better explored below that concepts and principles can be organized in multiple ways through a theorizing process. Even so, we highlight that models are still abstract or idealized tools for scientific research, especially if they are “interpretive” models directly derived from a formal theorizing process in a hierarchical scheme (see below). Models are used for many different purposes, even when their primary goal is representing the empirical systems or observed phenomena (see Sect. 2.3). Traditionally, principles, concepts, conditions, and representational models, and even the rules by which data are collected for hypotheses testing and

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generalizations, can be viewed as part of a “theory.” As discussed in more detail in the following Sect. 2.1.2, this definition of theory is still somewhat vague, and there are additional complicating issues in the relationship between theory and models. So, in one hand, it may be more interesting to think in the general term “theorizing” to describe the mental and cognitive processes of thinking in abstract principles and conditions to help build models, instead of necessarily defining theory as a formal axiomatic and hierarchical static structure. On the other hand, the entire scheme shown in Fig. 2.1 is better viewed as a higher-level part of the epistemological hierarchy, forming a framework (Sect. 2.2.2). It is also important to define how obtaining data from the “real world” can be used to test hypotheses and, in a second step, to generalize applications of the models, allowing the evaluation of predictions and providing feedback to the theorizing component. As discussed in more detail in Sect. 2.4.1, it is critical to realize that most, if not all, data in macroecology are not really “empirical,” in the ordinary sense of the word, and definitely not “observed” (in this context see Haack 2007 for an extensive discussion on what is empirical “evidence” and how it can be used to evaluate theories and models). Instead, the data provide an excellent illustration of what Giere (2006; see also Van Fraassen 2008) calls “models of data.” For instance, when analyzing patterns of species richness at global scales (Fig. 2.2), we are hardly dealing with “observed” richness expressing the famous LDGs (i.e., the tropics have more species than temperate regions). Indeed, we have a representation of richness in a grid with a given resolution based on overlaying geographic ranges of species that are, in turn, defined by different ways to make spatial generalizations from species occurrences (see Sect. 3.1). The observed empirical data in the “real world” would be, in principle, these occurrence records of an individual organism that we attribute to a given species in a place on Earth. But even so this assignment of individuals to a species also starts by assuming a conceptual model of categorizing continuous variation in phenotypes and genotypes and defining species as discrete units for operational purposes. Thus, in short, there is a lot of modeling and practical

Fig. 2.2  Richness patterns of amphibians at the global scale, defined by overlaying the geographic ranges (extents of occurrence) of 7193 species counted on cells with 1° of latitude/longitude. We usually refer to this pattern as “empirical,” but it is not an “observed” pattern and is better viewed as a “model of data.” Hypothesis testing in macroecology usually involves comparing representational models with “models of data.” (See Fig. 2.1 and text for details)

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decision-making up to arriving at a variable that we usually call “species richness” (Sect. 3.1.4). The term hypothesis is used ambiguously in the literature and commonly confounded with theory (e.g., Pianka 1966). Hypothesis, for instance, is usually thought of as a “non-confirmed” or attempted theory that still requires more testing (Hilborne and Mangel 1997; Ford 2000; see also Betts et  al. 2021), but this seems to be a legacy of the tradition of logical positivists and empiricists from early twentieth century, based on a strong emphasis on inductive confirmation of empirical scientific theories. Hereafter we use the term hypothesis “…for claims that there is a good fit between a fully specific model and a concrete object or system”, following Giere (2006). So, this usage explicitly refers to the comparison between representational models and models of data, matching quite well the more general use of the term from a statistical point of view (Sect. 2.4). Finally, we can think about generalizations and predictions, which are critical to evaluating the theorizing component (although the importance of successful predictions will vary in different ways to validate theories and models). Houlahan et al. (2017) highlight that prediction is commonly understood as synonymous with forecasting. However, it is more appropriate to think of prediction as a statement about different systems based on a model. Despite the importance of the representation goal, other criteria have been widely discussed to evaluate theories, especially their generality and internal coherence, as well as their ability to explain different phenomena or fit multiple datasets (see Marquet et al. 2014; Houlahan et al. 2015). The success (or not) of the generalization and prediction allows for evaluating back the theorizing process, with consequences for the acceptance or rejection of theories and models and, in a more abstract sense, for the idea of “understanding” the patterns and processes under study (Sect. 1.2.2). In general, understanding may also involve a critical evaluation of these decision processes involving rejection or acceptance that provide feedback for improving theories and models. Thus, it is necessary to highlight that all methodological rules used to obtain models of data and to evaluate how they match representational models and test hypotheses can also be guided, explicitly or implicitly, by the theorizing process. This possibility justifies why it is common to refer to this entire framework as “theory” in a fuzzier way (as in the original proposition by Giere 2006; but see Giere 2008 for an update and Sect. 2.1.2 below). However, it is more appropriate to use a broader definition of epistemological frameworks, and even though many exciting alternatives exist, Thomas Kuhn’s (1962) paradigms are the better-known frameworks (Sect. 2.2.3). Keeping with Giere (2006), we can now see that all the concepts defined above and associated methodological issues form a “perspective,” characterizing a particular way to conduct science and evaluate the empirical world. Thus, what counts as an “explanation” depends on the framework, as discussed about defining patterns and processes in macroecology (Sect. 1.2.2). It is also important to realize that, in principle, the reasoning from the scheme shown in Fig. 2.1 follows a deductive mode, in which a model is derived after the theorizing process and then used to evaluate patterns coming from the real world (see Maurer 2004). Notice that defining a rigid boundary between induction and

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deduction is challenging under this framework. Even under a “correlative approach” to explain the macroecological patterns and build statistical models, in the absence of a formal theory, we always start with the theorizing process, following then a more Popperian reasoning against induction for the development of theories (see Betts et al. 2021 for a discussion). On the other hand, as discussed in the following sections, the relationship between theory and model is more subtle, with awkward implications when deciding the validity of the theorizing process (by confirmation). This issue leads to some interesting questions, such as what does it mean to generalize, and how can this step validate the model, confirm or refute a theory, or improve the theorizing process? It may be helpful to clarify this issue with an example of the geographical patterns in species richness shown in Fig. 2.2, which is further explored in the following sections of this chapter. When one first realizes the existence of such a pattern for a group of organisms, say amphibians, the goal is to “explain it” via ecological or evolutionary processes. It is not difficult to inductively infer a potential correlation between richness and productivity or temperature by a simple visual inspection of a pattern in which more species accumulates in the tropics (hotter and wetter regions are more productive than cold and dry regions). In this case, we could be talking about an inductive mode in principle, as the data suggests the explanation (i.e., the theory). Nevertheless, is this the “theory”? Recalling a topic mentioned in Sect. 1.2.2, saying that richness is “explained” by productivity is usually not considered satisfactory because this correlation can arise from several mechanisms involving multiple physiological, behavioral, and ecological responses to changing environments through time (McGill and Nekola 2010). It would be possible to improve the explanation by finding surrogates that may help disentangle theoretical pathways. For instance, the effects of temperature would happen through diversification rates that could be estimated from phylogenies, and even so, there would be drivers more related to speciation or extinction at the population level. However, these different causal pathways involving multiple mechanisms at distinct scales form the theory’s abstract and usually unobservable component and would hardly appear by pure induction (Maurer 2004). It comes from the mental and cognitive process of theorizing based on fundamental principles, even when this is not formally established or mathematically structured. If a researcher trusts or not that science can successfully discover these underlying unobservable mechanisms, this is an issue to discuss later (on scientific realism; see Diniz-Filho et al. 2023a). After establishing the initial theoretical explanatory component (i.e., the causal pathways), the first and more intuitive idea is that if the correlation between richness and productivity appears for other groups of organisms, the theoretical rationale is “confirmed” and could be generalized. This approach would indeed characterize an inductive mode for scientific confirmation of theories. Still, the main question is whether successively finding this correlation for other groups of organisms supports the theorized mechanisms behind the correlation between richness and productivity, not the correlation pattern per se. From a strict empiricist point of view, these mechanisms do not matter, and the support appears for what can be effectively experienced and measured (i.e., the correlation between richness and productivity or other

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empirical correlations that may lend support to some of the causal links in the theorizing process). However, as pointed out in the introductory chapter, even when the analysis starts with empirical correlations, we frequently look for more subtle interpretations of these patterns in different degrees, both thinking in mechanisms or more statistical explanations (McGill and Nekola 2010; Connolly et al. 2017). If, after a long series of good statistical tests across several groups of organisms, the relationship between richness and productivity does not appear for a single new group of organisms analyzed, how do we deal with the previous generalization and the theoretical component previously defined? It is important to stress that, in this case, we can keep using some arbitrary statistical criteria to say that the correlation is, in general, “confirmed” (i.e., for instance, the idea that a “rule” appears if more than 50% of cases agree with it). We must consider that this decision on generalization refers only to the empirical patterns in richness and their correlation with productivity. But we are now forced to change, or at least revise and someway improve, the theoretical, unobserved components of the explanation. Perhaps, for that group of organisms, it is necessary to think of other processes that can help explain the absence of the pattern observed in all other groups. On the other hand, perhaps the previous theorizing component is entirely wrong, and a more comprehensive explanation is required to deal with both old and new correlation patterns. Sometimes the revision of these explanations leads to confusion when someone says, for instance, that scientific theories or models are always “tentative.” Even when widely confirmed, some of them will be put aside in the future if further evidence fails to support them. So, the question is how a theory or model well established in the past now appears to be wrong. The point is that new interpretations and explanations commonly refer to the unobservable components (i.e., the underlying mechanisms) and not to the empirical patterns they proposed to explain. The revision of theoretical explanations involves other deeper philosophical issues, including many about the more realistic versus instrumentalist views of theories and models (Sect. 2.2.3), the difficulty or impossibility of testing empirical theories (the Duhem-Quine thesis; see Sect. 2.2.1), and more operational aspects of hypotheses testing related to the Karl Popper’s famous view that it is impossible to confirm theories, only to falsify them (Godfrey-Smith 2016; Sect. 2.4.2). From a more deductive point of view, one can always argue that the model derived from the theorizing process refers to the underlying mechanisms that lead to the empirical correlation between richness and productivity. So, it is always possible that generalization fails at some point (and thus, a new theory or model must be developed, accounting for both patterns previously described from an empirical point of view, in a broad Popperian view of science). This possibility also provides an intriguing potential link between empiricism and realism, as suggested by Godfrey-Smith (2021) (see Sect. 2.2.1). Finally, we are now in a better position to understand that, from a philosophical point of view, macroecology can be characterized as a “scientific perspective,” i.e., a way to study ecology, focusing on inferring ecological and evolutionary processes

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underlying general principles and emerging patterns (see Sect. 2.2.1). Historically, this perspective evolved into at least two partially overlapping “research traditions”, which are “…a set of general assumptions about the entities and processes in a domain of study, and about the appropriate methods to be used for investigating the problems and constructing theories in that domain” (Laudan 1977). These traditions are similar to the better-known Kuhnian paradigms (see Sect. 2.2.3 for more details). Nevertheless, researchers have no strong commitment to a core of central and well-­ defined theoretical principles in the research traditions, so traditions are more vaguely defined and structured than a paradigm. As discussed below, the two research traditions in macroecology can also be roughly identified with model-­ based and theory-based scientific reasoning (McGill 2019). We believe these two research traditions can be coherently accommodated within a single macroecological perspective using Giere’s (2006) framework mainly by considering a broader definition of the theorizing process, but there are more details to discuss.

2.1.2 Theory-Based and Model-Based Reasoning There has been much discussion on the relationship between theory and models. Hopefully, considering current controversies around this issue may help us understand the different research practices and traditions in macroecology. In principle, the different relationship between theory and model could be viewed as a minor question of emphasis and formalization, with a subtle inversion in the direction of paths from theory, model, and data, as shown in Fig.  2.1. However, this minor change may lead to entirely different scientific approaches and is the basis of what we can call “model-based” and “theory-based” reasoning in science that clearly appears in macroecology (Del Rio 2008; Godfrey-Smith 2016). Although we can keep the basic framework provided by Giere (2006) in both cases, it is interesting to refine some issues in the theorizing component to understand variations in the scientific practice among research traditions. We can start by questioning the nature of scientific theories, traditionally considered the core of scientific knowledge. In short, we think of theories as explanations for natural or empirical phenomena (e.g., richness gradients, species-area relationships, species abundance distributions). More formally, Pickett et al. (2007) point out that a theory “…is a system of conceptual constructs that organizes and explains the observable phenomena in a stated domain of interest”. Note that this definition does not make any statements about the structural components of the theory and its internal relationships. Notwithstanding, there are many disagreements and interpretations regarding the term “theory” and its meaning. As Giere (2006, 2008) points out, words like theory and hypothesis have been applied ambiguously in the scientific literature, to say the least. As pointed out in the previous section, the term hypothesis is used here specifically for empirically testable statements derived from theories or models. In many situations, hypotheses refer to “provisory” theories, whereas laws usually

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refer to widely confirmed and accepted empirical generalizations. However, given the “protean” aspect of such generalizations in ecology and evolution (e.g., Lomolino 2000a), it is more appropriate to use the term pattern to replace law. Scheiner and Willig (2011) provide a more comprehensive and operational definition of theory and point out that theories are “hierarchical frameworks that connect broad general principles to highly specific models” and later that “…models are where the theoretical rubber meets the empirical road.” They allocated models in the lowest level of their hierarchical framework, defining theories as composed of a general theory, constitutive theories within the general theory, and models within constitutive theories. Indeed, scientific theories have been more explicitly related to models since the early 1970s at least. However, as these models are derived from the axioms of theories, their empirical adequacy gives an idea of how valid they are and validate the entire process of theory-building. Cartwright (1983, 1999) originally called these “interpretive” models. Theories can be viewed thus as a cluster of these models that “interpret” different components of theories and incorporate concepts and properties that allow translations that match empirical data (Scheiner and Willig 2008, 2011; Connolly et al. 2017). This view of the theory-­building process is called the semantic view of theories (Travassos-Britto et al. 2021). A good example of the semantic view of theories, following the framework discussed by Scheiner and Willig (2011), is perhaps the gradual development of the metabolic theory of ecology (MTE), formulated by J. H. Brown and collaborators (see Brown 2004). MTE aims to derive mechanistic models that can explain many ecological patterns, ranging from individuals to ecosystems, building up from fundamental principles and based on allometric scaling to combine the effects of body size and temperature on metabolic rates. Formally, this general metabolic equation (GME) is given by

P  f  M ,T ,R 



where P is the rate of some metabolic process, given as a function of the body mass M, temperature T, and concentration of material R. GME is defined as the statistical model

P  B0 M 3 / 4 exp   E / kT  f  R 



where B0 is an empirical constant, E is the empirically derived average activation energy of the respiratory complex (i.e., the activation energy of metabolism), and k is Boltzmann’s constant (and note that the effects of temperature and body mass on metabolism are multiplicative) (Brown 2004; Marquet et al. 2004a). Multiple models can be derived from these fundamental equations by adding more concepts and assumptions, explaining patterns in biomass production, ontogenetic growth, population growth rates and densities, interspecific interactions, species diversity, and several ecosystem processes (Brown 2004; see Arroyo et al. 2022 for recent developments). Thus, following the hierarchical framework proposed by Scheiner and

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Willig (2011), GME can be viewed as a broad and abstract generalization from fundamental thermodynamic and biological principles and is the basis of MTE as a general theory. Several additional concepts, assumptions, and auxiliary principles have been used to axiomatically build constitutive theories to deal with a range of problems (i.e., explaining multiple ecological patterns) within well-defined domains. In the end, interpretive models are derived from these constitutive theories to confront their predictions against empirical patterns (see Sect. 2.4). Each hierarchical level has its overall assumptions, concepts, and laws. For example, Allen et al. (2002) derived from GME a model to explain the latitudinal diversity gradient (a constitutive theory) that predicts a linear relationship between the logarithm of species richness S against the inverse of environmental temperature T (scaled by E and Boltzmann’s constant k), with a specific slope equal to approximately −9 (later rescaled by Brown 2004), so that

Ln  S     E / 1000 k 1000 / T   C



This model encompasses several assumptions, including temperature-invariant body sizes and abundances along the gradient and the energetic equivalence rule EER (Damuth 1981, 1987; see Sect. 8.2.2). The EER, in this case, is used in the model as a “natural law,” in the sense of being a pattern, i.e., an empirical generalization that is part of the theorizing process and required to develop the interpretive model (see Lawton 1999; Lomolino 2000a). As discussed in more detail in Sect. 2.4, this equation allows an explicit way to confront the abstract and idealized components of the theory with the (model of) data. A slightly different example of theorizing comes from the unified macroecological theory developed by McGill and Collins (2003) to explain several macroecological patterns. They start with three general premises: (1) each species’ geographic range is located in space relatively independently of the others, (2) different species vary in global abundance according to a hollow curve, and (3) abundance across a range is structured according to a “peak-and-tail pattern.” Each of these premises is expressed mathematically as models that are combined and lead to predictions about positive correlations between geographic range size and abundance, SAR, SAD, and the distance-decay similarity of ecological communities or assemblages (see Sect. 4.4.1 for more details). McGill and Collins (2003) present their theory structuring it from general principles and premises to models at a lower hierarchical level as an integrated cluster of three models (thus following a semantic view). Still, it seems more empirical and less structured than MTE. Each of the models was independently developed from former studies in particular contexts, and perhaps we could say that they emerge from different theorizing in a more abstract sense. For example, independent and random (Poisson) distribution of species peaks may apply mainly to small spatial scales, as broad-scale latitudinal or altitudinal gradients imply some autocorrelation of species peaks, especially under niche conservatism and geographically structured diversification rates (e.g., Chaps. 5, 6, and 7). Spatial abundance patterns within

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species ranges have been widely discussed as part of niche theory and the balance between local adaptation and dispersal under central-peripheral population dynamics within species ranges (see Kirkpatrick and Barton 1997; Maurer 1994; see Chap. 4). The point here is that this unified theory can be viewed more pragmatically as a combination of previously existing models with different goals derived from distinct principles. Another important theory widely discussed in macroecology was proposed by Hubbell (2001) under the general title of “Neutral Theory of Biodiversity and Biogeography,” or simply Neutral Theory of Ecology (NTE), to explain and unify several ecological and evolutionary patterns (see also Bell 2001). Hubbell (2001) discussed how neutral dynamics, in which processes are equivalent at the individual level, emerged from McArthur and Wilson’s (1967) equilibrium theory in biogeography. There would be a general contrast between neutral dynamics, defined as a dispersal-based structure of ecological communities, with a niche-based approach to understanding this structure. Hubbell’s (2001) NTE was built from first principles that create ecological drift (demographic stochasticity) in saturated communities, and it is possible to derive more specific models explaining several ecological patterns. NTE is also related to Harte’s Maximum Entropy Theory (METE; Harte et al. 2008; Harte 2011; see Xiao et  al. 2016), which uses principles from maximum entropy to find the least informative probability distribution for several parameters under constraints given by their correlation (and from this approach realistic patterns in SAR and SAD appears). An interesting discussion can be derived from examples of NTE and METE, as McGill (2010) later proposed a “unification or unified theories.” He showed that six theories developed more or less independently (including his own 2003 proposal, as well as NTE and METE) explain some macroecological patterns based on three general principles: (i) individuals are spatially clumped within a species; (ii) maximum or total abundance between species varies and follow hollow curves; (iii) individuals among species can be treated as independent and are spatially distributed independently with respect to other species. These principles generate abundance patterns within and among species similar to Fig. 2.3 because of an effect called “stochastic geometry.” This common effect occurs because individuals of each species are randomly distributed in a constrained spatial domain according to slightly different rules or mechanistic processes in all these theories. Thus, this tentative unified theory attempts to build a general theory by unifying independent models and may provide an interesting basis for some empirical tests (e.g., Jones et  al. 2011). Although McGill (2010) shows that they share principles and some properties (i.e., stochastic geometry), they can hardly be viewed as a strongly structured framework expected under axiomatic views of scientific theories. Nevertheless, recall that stochastic geometry follows a broad definition of processes and mechanisms empirically explaining the pattern, as proposed by McGill and Nekola (2010) (Sect. 1.2.2). It is also opportune to differentiate between integrating and unifying theories or models. Unification refers to finding a unique theory that leads to different representational models and makes multiple predictions. However, merging different

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Fig. 2.3  A single realization of the unified theory proposed by McGill and Collins (2003), generating 50 species abundance patterns along an arbitrary environmental gradient

theories to generate a unique and more general prediction is an integration approach that may help to understand a given pattern (Odenbauch 2011). Thinking in a hierarchical structure from general theories to models, as suggested by Scheiner and Willig (2011), there may be a conceptual continuum between unification and integration. Unification is likely invoked at higher and more abstract levels, like fundamental principles and concepts. In contrast, integration allows a more comprehensive description of complex patterns by a combination of models (and this idea of continuity between unification and integration will be more evident when discussing a more explicit model-based reasoning). Despite their different principles and underlying mechanisms, all these original theories that are being unified generate similar empirical patterns, leading to some interesting discussions. For instance, because all the distinct unified theories McGill (2010) discussed generate figures like Fig.  2.3 for spatial patterns in abundance, they roughly predict the same patterns for SAR and SAD. Of course, one can think that this is precisely why they should be unified, as proposed by McGill (2010), but what about their fundamental principles and mechanisms? How should one choose among them to “understand” a macroecological pattern from a more mechanistic basis? Recall that we can go back to the previous discussion about explanation and think about understanding richness gradients based on the empirical correlation with productivity or trying to account for the underlying unobserved processes and mechanisms (Sect. 1.2.2). For instance, the concept of stochastic geometry may

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provide a unified empirical explanation. Still, perhaps the different ways in which SAR or SAD was mechanistically explained in the original theories give an example of what has been called in philosophy of science the “underdetermination” of theory by the data, which occurs when the available evidence is insufficient to identify which explanation accounts for that evidence. This problem of underdetermination, also called the Duhem-Quine thesis, is essential to work out how to interpret model fit and the goal of our theoretical reasoning and define the relationship between theory and reality (see Godfrey-Smith 2021; Diniz-Filho et al. 2023a). There are different forms of underdetermination, including issues on holism about testing (see Sect. 2.2.3), which states that no theory or hypothesis can be tested in isolation (holistic underdetermination), undermining much of the naive views of confirmation and falsification of abstract theoretical ideas by empirical data (see Laudan 1977; Dilworth 2007; Godfrey-Smith 2021). We can also wonder about our confidence in how hypothesis testing based on empirical data is tied with theory support, as different theories can generate similar predictions (contrastive underdetermination). From a practical point of view, contrastive underdetermination is the basis of the common idea that “correlation does not imply cause” that, as discussed below, is only partially true (see Shipley 2016). It is also well-known that different mechanistic causal pathways may lead to similar ecological patterns (Warren et al. 2022). We can adopt stronger or weaker commitments with the different versions of the underdetermination thesis, reflecting a pessimism-optimism gradient in our ability to support theoretical claims from the empirical data (Diniz-Filho et al. 2023a). Despite the widely accepted role of theory in scientific research, some philosophers have questioned the general and more traditional view discussed above. They claim that due to the complexity of nature and due to the lack of “true” natural laws, models should be the appropriate level to do science in practice (Cartwright 1999; Morgan and Morrison 1999; Keller 2002). In these more pragmatic approaches (see Travassos-Brito et al. 2021), the models are built directly from general principles and concepts, sometimes derived from distinct and independent “theories,” incorporating policy views and multiple operational backgrounds (mathematical, statistical, and computational). Following Cartwright (1999), what we have now are “representative” (rather than the previously defined interpretive) models, which are built to be directly compared to data and used to gain knowledge about the empirical phenomena (patterns) under investigation. Notice that Giere (2008) keeps the more general term “representation models” to refer someway to both interpretive and representative models, a helpful proposal to integrate research traditions in macroecology within the same perspectival framework shown in Fig. 2.1. The type of model, following the terminology by Cartwright (1999), depends only on how the theorizing component is defined, more loosely or more formally and hierarchically structured. Simulations approaches and the strategy of “pattern-oriented modeling,” discussed in Sect. 2.3.3, and Bayesian inference, addressed in Sect. 2.4.4, provide excellent examples of the continuous conceptual range between interpretive-representative models, both considering model-building strategies and their importance to the theorizing process. These models gradually incorporate more and more effects to achieve a more accurate description of patterns and thus improve their

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representation ability, sometimes using principles from multiple theories and specific conditions. The critical issues are that, in this more pragmatic view of science, a theory is considered an amorphous entity, usually built “a posteriori” and consisting of general concepts and principles. In this view, the hierarchical subordination of models to theories disappears. Giere (2008) points out that “… I myself would not now identify a theory with a set of models. Indeed, I think the term ‘theory’ is used so ambiguously in general scientific and philosophical discourse that a sound understanding of science is better achieved by not trying to adopt ‘theory’ as a technical notion.” In practice, these alternative ways of thinking in scientific theories can be better understood as a continuum along a multidimensional understanding of the meaning and usefulness of theories. Actually, the main issue here is a discussion between those that believe that science needs a more formal and general theoretical axiomatic structure and those focused on practical aspects of scientific activity and reasoning by modeling. Despite this continuum, this difference between axiomatic versus pragmatic views of theories, centered on the relationship between theories and models, can lead to distinct approaches to scientific reasoning, forming what could be called “model-based science,” contrasting with “theory-based” science (see Keller 2007; Enquist and Stark 2007; Del Rio 2008). As pointed out in detail by Godfrey-Smith (2006), “An understanding of models within recent philosophy of science has been distorted by the formalist priorities of the ‘semantic view.’ This has resulted in attempts to force all scientific theorizing into a procrustean bed with a shape determined by the notions of “model” that have proven useful in logic and set theory, and sometimes in physics. Model-theoretic ideas can, of course, be used as the basis for a general theory of meaning, but such an approach has well-known problems in its pure forms, and in any case has no particular connection to representations in science as opposed to elsewhere. Once this project is abandoned, it becomes possible to recognize and analyze model-based science as a distinctive style of theoretical work, which yields particular kinds of representations, explanations, and patterns of change”. This emphasis on representational models seems consistent with many previous theoretical approaches in ecology since the early 1960s (Levins 1966; Peters 1991, discussed in Sect. 2.3.1). These approaches, however, have been strongly criticized by authors defending more formalism and structure of scientific theories in ecology (i.e., Ford 2000; Pickett et al. 2007; Scheiner and Willig 2011; Marquet et al. 2014). Kolasa (2011), for example, points out that “…books devoted to theoretical ecology … make no mention of this or similar conceptual debates. These texts present theory as collections of mathematical models. Although such models are powerful and illuminating theoretical constructs, their very dominance of the theoretical landscape of ecology may have unintended consequences because it may detract from or undervalue the significance of efforts to reorganize framework of ecology.” For instance, going back to the interpretive model from MTE developed by Allen et al. (2002), the question is what to do when the model does not provide a good representation of the empirical patterns. If this is an interpretive model, lack of

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model fit suggests problems with the theory at some hierarchical level “above” the model, following Scheiner and Willig’s (2011) framework. In principle, it is necessary to figure out what is wrong and restart. Still, on the other hand, it is possible to have a more comprehensive theorizing component to guide the search for other variables that would assist in “explaining” the pattern as a more pragmatic approach. There are many epistemological consequences of this change, but the important issue now is that the model gains much relative importance in comparison with the theory (the abstract component), and it would be much easier to integrate different models to represent macroecological patterns better. It is essential to make clear at this point that using model-based empirical reasoning is entirely different from a purely “exploratory” approach of adding more and more variables to “explain” the pattern from a statistical point of view (something now discussed in the context of artificial intelligence and data mining; see Betts et al. 2021). Under the framework in Fig. 2.1, even when the theorizing process does not lead to a formal, axiomatic, and structured theory, the “a priori” theorizing process is essential for selecting empirical variables that are added to a statistical model to improve its fit to empirical data. Another illustrative example of how to move from theory-based to model-based reasoning is provided by Hubbell’s (2001) NTE, previously discussed. On the one hand, we can test the equations derived from NTE by contrasting them with empirical data (see Chap. 4 for a discussion involving modeling SAD) and “reject” or “accept” the theory. However, it may be more interesting to use predictions of NTE in the form of surrogate variables that could express underlying processes or mechanisms as part of more general statistical or simulation models coupled with predictions from niche-based theories, focusing on better representing the empirical patterns. As discussed in Sect. 2.4, we can perform variance partitioning, and rather than “rejecting” or “accepting” NTE, we can evaluate the relative importance of the neutral dynamics (assuming ceteris paribus the abstract components of NTE, i.e., that it works under particular circumstances) with respect to other niche-based processes driving community structure or macroecological patterns. We can use these results to go back and obtain feedback for the improvement of NTE, for instance, which may be a more appropriate geographic extent, timescales, or life history and ecological characteristics of the group of organisms NTE better applies. However, this feedback does not involve going back to first principles and rebuilding and necessarily reviewing the original theorizing component of NTE. The idea is only to use them as one of the tools to build a better representational model. Thus, we must recognize that it may be exciting and reasonable to try to integrate or unify, or at least organize, the knowledge obtained from models that describe or explain a given macroecological pattern in a general theory, as suggested by Kolasa (2011; see also Halpern et al. 2020). However, at the same time, it is also important to recognize that doing this could also be viewed as a pragmatic strategy in which a theory is created a posteriori from model evaluation and not formally derived hierarchically from first principles. This process of theorizing in the more pragmatic view occurs by continuous positive feedback between the outcome of model fitting and new data in more “local” applications. Hilborne and Mangel (1997) point out

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that models are tools for testing hypotheses (following a semantic view, in principle), but we can also think the other way around because the outcome of an independent or integrated model can support or not a given general theory. In the pragmatic view, theories are only tools to help build better models, as discussed above. Indeed, as Dutra (2008) pointed out, “…models as abstract structures used by working scientists not only to interpret their theories but, most importantly, to construct them as well.” Kolasa (2011) also highlights that it is usually difficult to evaluate the importance of theory in current ecological research because of the fuzzy limits of the theory, lack of coherence in definitions due to the “…low cohesion of concepts, generalizations, and models in relation to one another.” He points out that this difficulty in recognizing an ecological theory is usually considered a diagnosis of the “immaturity” of ecology as a science. However, perhaps the recent progress in ecology and evolution comes precisely from the absence of strongly defined and formal theoretical structures that give researchers the liberty to deal with complex and contingent systems more pragmatically, in a non-reductionist approach. Perhaps, as Hacking (1983) pointed out, “…the ideal end of science is not unity but absolute plethora.” Finally, rather than trying to classify work in these categories of alternative views of theories, it may be more productive and more coherent, within a pluralistic view of scientific activity (and explicitly assuming a positive auto-reflexive criticism), to suspend “a priori” judgments about what has been done when developing theoretical ideas and empirical tests in macroecology. Although our focus throughout the book is closer to more model-oriented reasoning akin to the pragmatic view, including empirical and statistical modeling, it is not necessary to understate or ignore some formal attempts to build macroecological theories in a more axiomatic way, as well as reasonable attempts to a posteriori organize such models into unified theories (e.g., McGill 2010). These views are complementary and form a continuum in terms of formalism, and we can continually reinterpret a semantically developed theory in a model-based framework. As previously pointed out, although these alternative views can be associated with different research traditions, it would not be difficult to accommodate their differences within a broader macroecological perspective.

2.2 Some Philosophical Background on Scientific Practice 2.2.1 Realism, Instrumentalism, and Perspectivism Once we understand the alternative views of scientific theories and models, it is interesting to put them into a broader philosophical and sociological context. We think first about the confirmation or support of a theory or model from a philosophical point of view, relating “theory and reality” (Godfrey-Smith 2021). When we say

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there is strong empirical support for a theory or a model, does this indicate that we have found some fundamental explanation for the empirical word, especially considering the unobservable entities used to build them? Perhaps the first and more general issue to start this section on the main philosophical background for macroecology is that our scientific view of natural sciences, including ecology and evolution, has a strong legacy of the logical positivism and empiricism of the early twentieth century. As previously discussed, this intellectual movement had a strongly axiomatic (synthetic) view of theories (see Travassos-Britto et al. 2021) and firmly assumed that accumulating evidence under inductive reasoning confirms them. Empiricism refers to the idea that the only source of evidence is experience expressed by what can be measured, experimented with, or observed in the real world without invoking unobservable hidden entities, including some more abstract causal thinking. The advance of science was due to a clear and universal scientific method, thus providing a normative (rather than descriptive) role for the philosophy of science. Despite its initial importance, this movement’s main proposals were displaced by other ideas from different schools of thought, discussed throughout this section (Rosenberg 2011; Godfrey-Smith 2021). The first important issue to highlight is how to rethink the empiricist approach in a more comprehensive and modern way. As pointed out earlier, research in macroecology was initially strongly empiricist because the goal was mainly to describe and explore patterns in data, including statistical distributions of some variables, such as population density, body size, and abundance, and their relationships. Latitudinal gradients in richness, ecogeographical “rules” and species-area relationships are important broad-scale patterns to be investigated within the new macroecological perspective as it develops (Gaston and Blackburn 2000). From an empiricist perspective, the goal thus was to describe and synthesize these patterns, with theories viewed in a “hypothetical” sense and as provisory explanations to guide future empirical research and an initial attempt to explain and understand the patterns. However, at the same time, we can identify a departure from a more classical empiricist tradition as there was a search for ecological and evolutionary mechanisms underlying the macroecological patterns. This theorizing component even invoked looking for surrogate variables that empirically represent the unobserved phenomena and causal mechanistic pathways to improve the models. Mainly during the second half of the twentieth century, there were many discussions of the meaning of scientific theories, starting from the central question of how to make sense of the unobservable entities that were predicted or used to build theories when these theories are confirmed, or supported (or not falsified). This discussion about scientific realism starts with two main issues: (1) if a scientific theory is confirmed or accepted, can we say that we found something that is “true” in terms of the fundamental explanations of the empirical patterns; (2) and what about the unobservable entities postulated by the theories, including events or processes leading to causal relationships among observable empirical variables? If the theory is confirmed and supported, is this an indication that these non-observable components exist in the real world? These two points would equally apply to models because although these are not “true” or “false” from the outset (see Sect. 2.3.1),

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they can capture some components of the world that can, in turn, lead to a realistic interpretation (Psillos 2008; see also Godfrey-Smith 2016). This is a metaphysical discussion, and some philosophers of science thought this was vague and, in practice, useless. Others, however, pointed out that there are consequences of adopting alternative metaphysical views, so thinking about these issues is quite important. The answer to the questions above is “yes” for a strongly realistic view, so confirming theories indicate that a fundamental property, component, or part, of reality, was discovered. The Nobel-prize winner Steve Weinberg, assuming a profound realist view (that Giere 2006 calls “objectivist realism”), pointed out that the “…truth is out there” and when theories “…are discovered (they) will form a permanent part of human knowledge.” Nevertheless, this is perhaps too strong (too optimistic), and a more moderate view of realism states that science aims to describe reality, including some unobservable hidden entities. We may never be sure that we have achieved this goal with a given theory at any time. Van Fraassen (1980), one of the most important antirealistic philosophers, pointed out that “correct statement of scientific realism…is that science aims to give us, in its theories, a literally true story of what the world is like…and acceptance of a scientific theory involves the belief that it is true.” We could say that, in principle, most natural scientists tend to have a realist perception of scientific theories and models, and macroecology may provide an interesting example of a mixture of philosophical ideas, as reflected in the discussions in the previous section. Although macroecology is usually considered empiricist in terms of describing patterns and trying to understand them based on empirically derived relationships, there has always been an attempt to interpret the results in terms of underlying causal links due to ecological or evolutionary mechanisms. It is common to say that we interpret the results of statistical analyses by discussing alternative explanations for the patterns detected, under Duhem-Quine thesis. In practice, these mechanisms are hard to evaluate, and some are practically impossible to observe (as past speciation or extinction dynamics; see Turner 2007), even though we believe that they have left some “signal” that could be detected in current patterns. Suppose the hypotheses derived from a theorizing process developed to evaluate possible events that occurred in the past are confirmed. This common practice represents a realistic interpretation incompatible with empiricism, at least in a more traditional definition (but see Godfrey-Smith 2021). Of course, the realist view is more explicit in more formally theory-based reasoning applied to macroecology, such as discussed for MTE, as fundamental laws are assumed to exist and provide the starting point for building theories out from which interpretive models are derived. If these models have a good fit to empirical data, the basic conclusion is that MTE principles are validated. On the other hand, in model-based reasoning, a realist view should make less sense, even because the main goal is understanding by prediction and representation. Hacking (1983) adopted a realist view but pointed out an interesting distinction between realist interpretation that may help understand the origin of anti-realist views and that it is helpful to extend the discussion of realism to models. When supporting a theory or finding a strong fit of a model, one can think that some fundamental laws are discovered, but this does not necessarily indicate that the

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unobservable entities used to build it exist. These entities could be mere fictions that help design the theories. This anti-realism of entities is sometimes called nominalism. On the other hand, one can think that there are no fundamental laws or theories. But suppose this theory predicts or requires some unobservable entities. In that case, these entities may exist in the real world and will be eventually confirmed by further search and verified by auxiliary theories or detected by developing new equipment (this is the view of Nancy Cartwright concerning models, as pointed out by Psillos 2008). Finally, it is possible to be an antirealist of both theories and entities, in a more extreme view in which theories are only predictive instruments for empirical research. This view is sometimes called instrumentalism and thus adopts a firmly agnostic view of any reality in scientific theories. In this last case, the theory only works for helping to describe, synthesize, or organize empirical data and make predictions, with nothing to say about the underlying unobservable components, causes, and explanations for natural phenomena or the real world. Perhaps an interesting example of these distinct anti-realist views in macroecology can be based on Turner’s (2007) criticism of realism from a historical point of view, remembering that identification of processes in macroecological is always retrospective, happening in an evolutionary context. Suppose we have a computer simulation model or phylogenetic analysis that explains richness patterns based on a geographic variation in the balance of speciation and extinction rates, perhaps mediated by shifts in an environmental variable such as temperature (see Chap. 6). We usually interpret high model fit as a suggestion that such causal structure is somehow “real,” given differences in speciation and extinction through time, sometimes mediated by climate changes, most likely drove richness patterns. This common practice makes sense in terms of understanding and usually unifies several phenomena regarding biodiversity patterns. However, although no one would claim that a particular speciation or extinction process in the simulations represents any actual events in the past, it supports the effect of these past events in a stochastic sense, matching thus Cartwright’s (1999) idea that models can be interpreted realistically (in their unobservable entities). There has been plenty of discussions of the meaning of theories and models, with arguments pro-realism and pro-instrumentalism alternating in the philosophical literature, with much back-and-forth in time. Some research groups adopt one or the other, which seems to be the case with the alternative research traditions in macroecology. It is beyond the scope of this book to review all of these ideas, and the interested reader can start with the excellent discussions in Dilworth (2007), Rosenberg (2011), and Godfrey-Smith (2021). In short, the debate between extreme objective realism and instrumentalism lies in a gradient of optimism and pessimism in terms of the achievements of science. Also, this attitude concerning the meaning of scientific theories strongly depends on the goals of different research traditions and on an intrinsic belief in how current success and past failures of science can be interpreted. Giere (2006) provided an intermediate and interesting view between realism and instrumentalism, called scientific perspectivism, or perspectival realism. As no empirical observations can be detached from the methods used for observation, there can always be different perspectival perceptions of the same object or

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empirical pattern. From a perspectival realist point of view, the best we can state is that according to a strongly confirmed or supported theory (or model), the world seems roughly in such a way. There is no strong commitment to “truth,” but this is not as pessimistic as instrumentalism because we admit that, given the confirmation of theory or good model fit, at least some part of the reality (from a given perspective) is most likely being captured in a realistic sense, even though we cannot ever be sure that we have a complete picture of the reality (although other perspectivists may be not so optimistic as Giere 2006; see Saatsi 2020). Finally, Giere (2006) points out that “…the grand principles objectivists cite as universal laws of nature are better understood as defining highly generalized models that characterize a theoretical perspective. Thus, Newton’s laws characterize the classical mechanics perspective. Maxwell’s laws characterize classical electromagnetic perspective; the Schrodinger equation characterizes a quantum mechanics perspective; the principle of natural selection characterizes an evolutionary perspective, and so on. On this account, general principles by themselves make no claims about the world, but more specific models constructed in accordance with the principles can be used to make claims about specific aspects of the world.” This long citation characterizes perspective realism but, more importantly, conforms quite well with the pragmatic view of theories, matching Cartwright’s (1983, 1999) model-based scientific reasoning discussed in the previous section. To summarize, objectivist realism, based on a deep philosophical commitment to the truth and reality of scientific theories, adopts what is sometimes called a “God’s eye” view of the world. This extreme realist view usually also reinforces science’s neutrality with respect to other external factors besides hard evidence. These two ideas combined lead to the alleged scientific objectivity and provide “a view from nowhere.” As discussed in the next section, this is not that simple, and in this case, the perspective realism may be a helpful alternative and provide a humbler “view from somewhere.”

2.2.2 Constructivism and the Scientific Debates in Macroecology There is a widespread view that science is “objective” and that, once defined, scientific evidence is entirely rational and independent of any other source of knowledge or cultural background. However, from the early 1960s on, another discussion overlapping the one on realism began, involving deeper issues coming from the sociology of science. The idea of social constructivism, which arose against empiricism and realism mainly in social sciences and humanities, is that there may be a poor relationship between accepted scientific knowledge and “reality.” According to this view, at best, scientists can achieve a consensus about what they say they found in the real world according to the theories that are accepted at a given time. The idea is that, for example, as the natural selection theory was proposed in 1858, in a

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relativistic view, it does not make sense to apply this concept to anything before 1858. Although this may sound absurd on a first reading, this was precisely what was proposed by some authors, and this is one of the reasons that triggered what has been called “science wars” in the 1980s (Giere 2006; Oreskes 2019; Godfrey-­ Smith 2021). Again, there are both stronger and more moderate versions of these constructive views. The example using natural selection is undoubtedly extreme, but some mild versions deserve some consideration. One such idea is that the process of doing science is so complex and based on so many judgments and decisions that, at some point, scientists agree that their theories or models represent reality. Thus, other factors beyond “evidence and rationality” may drive scientific practice, and even when we have widely successful theories that replace old views, the rationality of the process is sometimes only apparent and part of a retrospective rationalization (Laudan et al. 1988; Hull 1988; Giere 2006). This view is also related to more complex epistemological frameworks on which scientific activity occurs. This more moderate constructivist view does not oppose realism (except in very extreme forms of objectivism), as the idea, in this case, is that science aims to describe reality with theories or models but not necessarily that this goal is ever achieved (Hacking 1983; Dilworth 2007). Thus, this conception is not undermined if the process of doing science is also driven by other social factors, by in some way advocating a separation between science as an abstract and idealized institution and its day-to-day practice by scientists (and this may be particularly important when thinking, for instance, in a macroecological perspective to biodiversity conservation; see Sect. 9.2.1). For instance, the perspectival realism by Giere (2006), without reinforcing constructivist or relativistic views, admits the possibility that sociological components in the scientific community may mediate some consensus. However, these components must be discovered by further investigation and considered when understanding scientific progress. All these decisions may be driven by many factors and are not necessarily “the best” in theoretical terms. This consensus is not even questioned by researchers most of the time because there is not a continuous discussion about specific approaches or methods, especially if they come from other areas (such as statistics applied to ecology, for instance). So, most of the time, there is simply an acceptance that these approaches are adequate. For example, most researchers in ecology and evolution now use AIC to select the “best” models without being aware of the more detailed discussions around its validity and other potentially more informative related approaches (see Sect. 2.4.4). Getting into these discussions leads us to very “earthly” or “mundane” points, including hierarchical structures of personal power in science, their role in getting funding and getting published in the top and prestigious journals, the role of supervisors in directing student’s projects into some directions, recommending them for postdocs and jobs, discrimination against women and minorities, and so on. These issues certainly exist and have been extensively discussed in the more recent literature on scientific practice. Still, especially in natural sciences, there is only minor consideration of how they affect scientific results “per se.” Everyone recognizes that they may affect the research agenda and drive research fields toward some

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directions, although it is still rare to question if such factors affect judgments about theories or models and the establishment of consensus on how to collect data and analyze them and, consequently, on how these theories and models are supported and defended. Even more interesting, sometimes the effect of different groups reaching a consensus based on different standards may be hidden at the basis of some scientific debates, including some in macroecology. In retrospect, an illustrative example seems to be precisely the discussion of latitudinal diversity gradients and metabolic theory as proposed by Allen et al. (2002) and mentioned above, which is discussed in more detail from a methodological point of view in the Sect. 2.4 (e.g., Hawkins et al. 2007a, b; Gillooly and Allen 2007). By considering all of the issues discussed above, it is now clear that the arguments were not about diversity gradients and the underlying processes alone but instead were due to much deeper alternative views about the theorizing process and the reasons underlying the acceptance or rejection of a scientific theory (see also Del Rio 2008; Marquet et al. 2014; Houlahan et al. 2015). It reflects a major distinction in the way science is viewed and practiced, and this cannot be solved by a simple “vote counting” approach based on how many datasets support MTE model or even by more formal meta-analytical methods. The point is that the standards to define what is acceptable and what is not dependent on these deeper conceptual issues within frameworks as paradigms or research traditions. Most likely, misinterpreting the depths of the debate leads to unfruitful and endless discussion. Thus, it may also be interesting to briefly review some theoretical issues about scientific debates in the philosophy of science (e.g., De Cruz and De Smedt 2012). In practice, scientific debates involve distinct attitudes among the scientists involved, and we can think of at least four possibilities for dealing with these controversies, hierarchically structured. In the first level, one idea is to decide whether or not the debate should be continued. If researchers recognize that there is no additional basis to go on with the debate, this must be due to a recognition that there is no evidence to disentangle the causes of the divergence. For instance, there would be no further empirical data necessary to test between the auxiliary hypothesis that may be decisive in choosing among alternatives. In this case, judgment is suspended until further evidence appears (and there even would be rules about what to do when such evidence is found). On the other hand, the debate can be suspended because there is no possible agreement between alternatives, and this may be well the case when divergence is more profound, involving epistemological issues on how to think about the theory and the standards for their evaluation. But in this case, the discussion is not resolved, and each research group can go on with their views. If, on the other hand, the debate continues, in the sense that there is interest in identifying the best alternatives, there are two possible outcomes. First, one of the groups can be more successful through reasoned argument in convincing other researchers that its view is better or more useful if there are common standards for evaluating theories or models. Still, this may be related to sociological ideas related to research programmes or traditions discussed in the next section. However, considering the complexity of macroecological patterns, perhaps a more common

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outcome is some form of conciliation. For instance, the discussion around middomain models for diversity gradient may be an example in macroecology and biogeography by considering its later importance in developing more complex simulation models developed later based on the same approach (see Chap. 6). Finally, a widespread possibility in ecology and macroecology is to find a balance between the factors initially proposed as alternative explanations, as may be the case for niche-based and neutral dynamics of ecological communities. This balance generates some potential consensus that both parts explain the structure, although the debate on the relative magnitudes of these factors continues. Irrespective, the critical issue regarding the scientific debates over underlying explanations of macroecological patterns is that we can see different outcomes of the debates for more specific models and theories. It is also important to consider how sociological factors are involved in each case and how strategies to deal with them. In a nutshell, if moderate forms of constructivism are plausible, as admitted within a realistic or perspectival point of view, all discussion and debate about specific subjects, such as evaluating MTE exemplified above, should consider all these issues. In practice, we must pay attention to the social factors and cultural or historical backgrounds underlying some points of view defended. Under reasonable rules of engagement (in scientific journals, for instance), it is necessary to explicitly ask participants in the debate to be clear about fundamental standards and motivations behind alternative points of view. Although, in the end, the groups can keep their original points of view, further judgments would be made a posteriori by independent research groups, following a more “naturalistic” approach to the philosophy of science discussed in Sect. 2.2.4 (see also Laudan et al. 1988; Godfrey-Smith 2021). It is today viable to conduct more systematic reviews of the literature and scientometric and historiographic research to analyze the debates in light of these ideas. Nevertheless, it is always important to keep an eye on these serious issues to avoid naïve and unproductive endless discussions on particular matters.

2.2.3 Paradigms, Research Programmes, and Research Traditions As discussed above, the overall idea of objectivity in science and realism was also criticized on sociological grounds, although there may be limits to the influence of social context and cultural background on epistemic issues, especially in the natural sciences. The main issue involved in this discussion is that the scientific community rarely includes individuals working in complete isolation. The main questions here are how the scientific community is structured, how this structure affects the dynamics of science in achieving consensus on the research agenda, defining standards for evaluating theories and models, and so on. The purpose idea here is to show the frameworks that encompass scientific practice. This discussion, again, occurs at the interface among epistemology, history, and the sociology of science.

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In the views of logical empiricists and other renowned philosophers, such as Karl Popper, up to the middle twentieth century, scientific theories were evaluated in different ways (i.e., scientific advances by confirmation or refutation), but there was no discussion of a more general framework in which all these approaches were included (Popper 1959, 1962; see O’Hear 1995 for a comprehensive review). Although Popper, for instance, recognized that in his cycle of “conjectures and refutations” different groups of researchers may be involved in the process of scientific advance, the emphasis was on the bold individual attitude of rejecting risky theories that prove to be false. This view is strongly influential, especially in some areas of ecology and evolutionary biology (Hull 1988). Another issue that appears when evaluating theories and models and that provided a strong criticism in the early empiricist views was the problems related to holism about the testing, one of the components of the Duhem-Quine thesis (see Diniz-Filho et al. 2023a). As previously mentioned, this thesis states that the test of a hypothesis is never independent of the auxiliary hypotheses, background assumptions, and data statements. Thus, we do not know exactly what has gone wrong when a test fails. On the other hand, if the hypothesis is accepted, the problem remains as we are not certain of why this occurred. These problems were first pointed out by Pierre Duhem in the early twentieth century and reformulated by W. V. O. Quine’s (1951) paper, “The two dogmas of empiricism,” leading to the issue of underdetermination of theory by the data. We can separate the discussion into two slightly different parts, one involving Quine’s “web of beliefs” (i.e., the role of hierarchical structure connecting theory and specific models with all concepts, assumptions, and laws) and the other involving how the hypotheses can be tested with respect to the underdetermination issue. Under the Duhem-Quine thesis, it is also difficult to support strong realistic views of theories or models, and Duhem was one of the early antirealists (Achinstein 2004). In the end, this discussion of holism about test and underdetermination reinforces that a simple and objective test or evaluation of a theory does not exist but is instead a more complex scheme involving epistemological, historical, and even sociological components. In 1962, Thomas Kuhn published one of the most influential books in the philosophy of science, the Structure of Scientific Revolutions, challenging several positivist and empiricist claims. He proposed that science works at two levels, “normal science” and “scientific revolutions.” Then he divided the history of any field into cycles of pre-paradigmatic, paradigmatic, crisis, and revolution phases. In short, the center of Kuhn’s philosophy is the idea of paradigm in a broad sense, that is, a set of rules and worldviews that all scientists in that field share. The paradigm is a research framework within which there is agreement about the most important questions to be tested and the standard for evaluating theories and models. Within the paradigm (“normal science”), the researchers’ day-to-day work is like puzzle solving, without much questioning of the standards, major theories, concepts, and even methods used. However, in time, “anomalies” begin to accumulate, and researchers gradually start to see problems that may lead to questioning major issues until someone triggers a scientific revolution by developing a new set of ideas and standards, so we have a “paradigm shift.” The new paradigm may be so different from

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the previous one that Kuhn said they are “incommensurable” (i.e., there is a difficulty in communication between paradigms due to a lack of common terms, standards, different meanings of fundamental concepts, and even issues related to the importance of research topics). The main point related to the idea of paradigms is that there is only one paradigm at a time, defining the field, a paradigm shift does not necessarily involve rational elements and new evidence and, consequently, “progress” in the ordinary sense is doubtful, as paradigms are incommensurable. These are the most controversial aspects of Kuhn’s idea and triggered much discussion. Regarding progress and rationality, Kuhn was not defending nonrational views, and he understood that progress during shifts could be measured by the puzzle-solving abilities within each paradigm. However, the idea of incommensurability and lack of progress was quickly absorbed by scientific relativism, as discussed in the previous section. The main problem of thinking in a unique paradigm at a time is that this implies that scientists do not adopt a critical attitude toward fundamental ideas. In practice, they only solve minor issues, compiling more data to confirm known and established theories. This attitude clearly contrasts with Popper’s view of the bold and almost “romantic” attitude of scientists criticizing theories. There is also ambiguity in using the term paradigm, with at least two sets of different meanings. Kuhn later recognized this himself by referring to the “disciplinary matrix” (the broad-sense definition of a paradigm) and the “exemplars” (a model of scientific reasoning that guides further research, a narrow sense meaning of paradigm) (see Giere 2006; Godfrey-Smith 2021). Moreover, most scientists and philosophers of science disagreed with Kuhn’s more radical and extreme view of a framework, although it is widely recognized that he triggered a meaningful discussion that led to more widely accepted and perhaps more exciting frameworks. Moreover, in a sense, he also initiated a more naturalistic view of the philosophy of science. Imre Lakatos (1978), advancing from some of Popper’s ideas, proposed an interesting framework that he called research programmes (used as in the original with British spelling to differentiate from a research program in a more general sense). Such research programmes are similar to paradigms in defining a hierarchical framework but have a more precise theoretical basis when compared to Kuhn’s paradigm. For Lakatos, the research programmes are centered around a hard-core, a broad-scale theory that is not directly tested. What is tested, confirmed, or rejected are small-scale theories and hypotheses surrounding the core theory, forming a belt that protects it (and perhaps this idea is related to Scheiner and Willig’s 2008 view of general and constitutive theories tested by models in ecology). Lakatos was trying to avoid what was sometimes called “naive falsificationism” in the Popperian view and thus recognized that broad theoretical conjectures are hard to test and even harder to falsify using empirical data. So, even when rejecting hypotheses, there are always other ideas to test and assumptions to check, before the core is seriously impacted. So, the entire research programme is also trying to account for Duhem-­ Quine thesis of holism about testing.

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More interestingly, Lakatos did not add a constraint that only a single programme exists in a field at a given time. On the contrary, he insisted that different programmes compete with each other, with some of them improving if the central theory is supported by tests of the belt and others collapsing as the belt is gradually eroded, exposing this core. Here enters the sociological component of the framework, as the size and support of the programme would be related to the adherence by different researchers to each. This also involves the decisions of individual researchers to move from one program to another. The evaluation of the progress of a programme is determined by these temporal dynamics of healthy and degenerating research programmes. The framework of Lakatos can be understood, thus, on a much smaller “scale” than Kuhn’s paradigms and is more clearly related to operational issues in comparing multiple models. Larry Laudan (1977) proposed another framework based on what he called “research traditions” (Sect. 2.1.1). These traditions are, in principle, similar to Lakatos’s research programmes in progress and dynamics, but there is a significant difference related to cores and belts. In research traditions, there are no such cores, and the focus is on the ontological and methodological components of the framework. The success of a research tradition is measured in terms of the capacity for problem-solving and answering questions. To achieve this, it is possible to reorganize the main theories and even promote the fusion between theories from different traditions. This view is consistent with Laudan’s antirealist and more pragmatic view of theories, as discussed in Sect. 2.1.2 (see also Laudan et al. 1988). Moreover, researchers can move or alternate between traditions. This idea describes well the historical development of macroecology as there may be no sharp distinctions among these traditions, and they may overlap from time to time in terms of adopting alternative theorizing processes, strategies, or model building and statistical methods for data analysis. So, there can be a gradient of the commitment of researchers within a broad view of science, a framework, reducing Kuhn’s paradigms to research programmes and research traditions. Moreover, we can also view Giere’s perspectives as providing another alternative way to define a framework (a point of view defining a disciplinary matrix, for instance). The ideas about frameworks discussed above have been widely debated, and there seems to be agreement that, although some structure exists in science, the level of commitment of scientific activities to them remains open to discussion. Cuddington and Beisner (2005) tried to verify the paradigmatic status of ecology and concluded that, with few exceptions, ecology is not paradigmatic. There is hardly a single dominant idea and strong commitment of the researchers to this idea at a time. Although the terms “paradigm” and “paradigm shift” are common in ecology and evolution, they are not used consistently to refer to Kuhn’s original framework. In general, they mean just new, important, or emblematic theoretical ideas or methodological approaches, but these lack the main characteristics of the original definitions of paradigm. Even so, it is important that Cuddington and Beisner (2005) called attention to the importance of studying the history of the theoretical concepts in ecology to understand our current knowledge better (see also Layman and Rypel 2023).

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Connolly et al. (2017) mention a Lakatosian view in a more specific context of macroecology and mechanistic and process-based models for diversity gradients. However, it is not entirely clear if there are such persistent core theories defended by a research group in macroecology. In principle, it is possible to think in some of the well-known theories, such as Brown’s MTE and Hubbell’s NTE, as cores surrounded by protective belts, and research on these programmes continues testing hypotheses for constitutive theories. However, it is not clear if researchers have a general and permanent commitment to these views. Indeed, some recent attempts to deal with LDGs from a theory-based view propose a fusion of MTE and NTE principles (e.g., Storch et al. 2018). In practice, it seems that researchers are looking for the best explanation for specific patterns and trying alternative theories that can be useful, especially recently proposed ideas. For instance, researchers dealing with LDGs or SADs usually attempt to evaluate new theories and models from different origins and ideally shift toward them if they fit the empirical problems known by these researchers. In the extreme, this would be better viewed almost as an anarchical approach following Paul Feyerabend’s (1975) “Against Method” within a pragmatic view of scientific activity.

2.2.4 Naturalizing Macroecology Many of the philosophical ideas discussed in the previous sections, including Giere’s (2006) more recent perspectivism, are anchored in a general idea of naturalized epistemology. The origins of naturalized philosophy of science are usually also related to John Dewey and W. V. O. Quine, in the context of discussing a normative versus a more descriptive view of scientific practice and progress (Giere 1985; Godfrey-Smith 2021). For instance, logical empiricists and positivists, as well as Karl Popper, were strongly normative because they thought their philosophy was the best way to do science, as it provided more consistent progress and advanced theoretical understanding. Kuhn (1962), on the other hand, initiated a more descriptive and narrative view of science and its progress within a historical context (although he did not entirely abandon the normative view; Godfrey-Smith 2021). Another significant issue related to naturalism and normative views is the opposition to foundationalism, in which there would be intrinsically a fundamental way to do science, to be discovered by philosophy of science. In practice, the term naturalizing here means that it is possible to use scientific tools, such as data analysis and modeling, to investigate how theories and models are developed and evaluated by researchers and the extent to which there is progress, if any, in a given field, or approach, such as macroecology (see Donovan et al. 2008). So, the overall reasoning behind naturalizing macroecology in terms of theories, models, and methods is that we do not have to accept a priori any given approach or reasoning, both in terms of general strategies for scientific investigation or dealing with more specific research questions involving macroecological patterns. It may be good to examine what macroecologists are doing and which

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approaches are performing better, avoiding a priori judgments. So, contrary to what is usually thought, naturalism does not entirely avoid normative approaches to the philosophy of science. It only warns that this definition must not be based on an a priori foundational approach but instead on empirical research practice investigations. Of course, as previously discussed, it is impossible to be entirely objective as the framework may also guide the evaluation standards. For instance, in theory-based reasoning, the predictive power of a representation model derived from a theory may be relatively less important than in model-based reasoning. Also, it is important to consider the conceptual issues underlying the scientific debates and the more mundane sociological and historical components briefly discussed above. Even so, it is possible to derive at least some overall conclusions based on scientometric approaches and meta-analyses, many of which appear throughout this book.

2.3 Model Building in Ecology and Evolution 2.3.1 Strategies of Model Building As expected by the increasing adoption of semantic and pragmatic views of theories and all discussions of model-based reasoning in the last 50 years, there is now a vast philosophical literature on models and their importance to scientific practice (e.g., Morgan and Morrison 1999; Van Fraassen 1980, 2008; Cartwright 1999; Godfrey-­ Smith 2006, 2009; Morrison 2015). As previously pointed out, we can view models as attempts to describe and represent ecological systems. In ecology, this frequently involves quantitative models derived from analytical expressions developed from more formal theories, statistical relationships among empirical variables, or expectations derived from computer simulations. However, there are other models, such as graphical, physical, or even “verbal” models. What aspects of ecological systems the models represent vary a lot and depend on the research goals. Moreover, in some cases, we have models that purposely do not attempt to represent the empirical world but rather express idealized situations in which the influence of specific effects is ruled out (e.g., null and neutral models discussed in the following sections). Also, as previously discussed, in a semantic view, we can think of models as expressing (or, more appropriately, interpreting) different aspects of the theory directly derived from its axioms. These models do not represent the empirical data well, except in very particular conditions (“ceteris paribus”). It is possible to build models using different approaches even if they derive from the same theory (so justifying that they are “interpretations” of theories). A common possibility is to have analytical and stochastic simulation models to represent the same dynamics. For instance, Scheiner and Willig (2005) discuss how different models for natural selection can be built for allele frequencies or quantitative traits (i.e., the breeding equation). Moreover, following this example, it is common

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to incorporate population ecology parameters in natural selection models to generate more realistic and complex evolutionary dynamics (e.g., Diniz-Filho et  al. 2019a, 2021a). It is important to keep this possibility in mind when thinking about scientific realism when discussing models and theories, as pointed out in Sect. 2.2.1. In a more pragmatic context, the abovementioned issues are related to Morgan and Morrison’s (1999; see also Morrison 2015) view of models as “mediators” between the theorizing process and data. There are different ways to establish this mediation. First, Morgan and Morrison (1999) point out the autonomy of models with respect to both theory and empirical data, which is related to how models are built. Second, it is essential to ask how these models work. For instance, it is important to ask how they are helpful in theory exploration under different circumstances, including counterfactual approaches, as well as in helping empirical measurements and validation (i.e., estimating parameters). Third, as previously pointed out, models may provide a representation of both theory and the empirical world and thus establish a link between them. Finally, it is crucial to understand how to learn about the empirical world using models. Although we design models to represent reality, they can be the focus of the research, and knowledge can be gained about the model and only later transferred to the empirical or physical systems (if these systems are too complicated or hard to access, for instance). Each of these four ideas, which are not independent, has interesting examples in ecology and macroecology and are recurrent topics throughout the book. There is a long tradition of model building in ecology and evolution. It may sound almost cliché to start discussing models starting from Richard Levin’s (1966) “The Strategy of Model Building in Population Biology.” This seminal study proposed a well-known framework in which building models are subjected to certain constraints. Thus, researchers with different goals decide among several possible strategies for model building by balancing realism (in a slightly different sense from what was discussed in Sect. 2.2.1), generality, and precision (Fig.  2.4). Despite

Fig. 2.4  A representation of the constraints between realism, generality, and precision in Levin’s (1966) strategy of model building, which must take into account the relationship effectiveness of models and respect to their complexity, defining what Grimm et al. (2005) called “Medawar zone”

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criticisms and many controversies, especially around the formal definition of each of these three properties of models (see Orzack 2005; Odenbaugh 2006), there are still exciting ideas in this pioneering paper that led to the pragmatic view of theories and model-based reasoning (see Peters 1991). In short, Levins (1966) pointed out that, due to the complexity of ecological and evolutionary systems, it is impossible to fully describe any system in terms of realism, generality, and precision. Depending on their goal, researchers must sacrifice at least one of these three properties when building a model, forming three strategies for model building: (i) sacrifice generality to gain precision and realism, (ii) sacrifice realism to gain generality and precision, and (iii) sacrifice precision to gain generality and realism. So, we can see a movement toward well-known properties of idealization and abstraction and how this last property relates to models’ generality (Morrison 2015). The model-building strategies proposed by Levins (1966) also lead to another interesting discussion about model complexity. Building analytical models that fully describe the complexity of ecological systems at broad spatial and temporal scales, with multiple processes occurring at the individual level giving rise to emerging properties over long-time temporal dynamics, is a challenging task. The overall reasoning of modeling is to provide abstraction and idealization, so this would not be the goal even within a representational view, as discussed in the previous sections. On the other hand, the enormous growth of computational power in the last two decades allows the building of very detailed simulation models with hundreds or thousands of parameters that could, in principle, represent very well the empirical system. However, the question here is how informative or representative such models are. If we are thinking about representational models, it is great to be able to generate very complex models. Still, the truth is that it is easy to become lost in parameters and their (unknown) intrinsic potential relationships throughout the dynamics. So, adding complexity for the sake of realism has its operational limits. There are several problems in increasing model complexity, both operational and theoretical. From an operational perspective, complex models are challenging to run and produce testable predictions. In terms of high model fit, it is common to gain representation for a particular system and quickly lose predictivity and generalization power. In a more theoretical or conceptual sense, it is difficult to interpret the outcomes and evaluate which properties of the real world these models represent and, consequently, how helpful they are to understanding reality. Moreover, recall that models may have multiple goals, so they should represent “parts” of reality in a perspectival approach (see Giere 1999, 2006). The best strategy lies then somewhere in an intermediate position along a complexity gradient, in what has been called the “Medawar zone” (see Grimm et al. 2005) (Fig. 2.4). Under the idea that models mediate theory and data, models are instruments of investigation, allowing our learning of both theory and data with positive feedback with the representation goal. This learning happens during model building when defining the necessary components that are important for the application of each model. For particular aims of model use, it is essential to build models with variables (or parameters) that present a justifiable biological meaning directly contributing to interpreting the modeled phenomena. By applying these models, researchers

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can better understand if specific variables are important or irrelevant for interpreting natural phenomena as part of the idealization and abstraction. Learning from models is a common activity in ecology, especially considering Levins’ Type III strategy of sacrificing precision for generality and realism. In this case, the idea is to start with a simple model, confront it with empirical patterns, and learn from its failure to gradually improve the model, which is more appropriately discussed in the context of hypothesis testing in Sect. 2.4. The model could be enhanced by following Levin’s (1966) framework moving from strategy III to strategy I or II, depending on the goal. In this case, models capture simple, general ideas and principles so that these can be studied by contrast with data with different properties. Notice that the simple initial model would express an axiomatic conception of the theory and thus represent, for instance, natural laws or intrinsic properties of an ecological system, so that deviation in observed or modeled data would be due to idiosyncratic issues. This is a common interpretation, but the path to using models as a scientific tool follows different ways if one adopts theory-based or model-based reasoning. As discussed with an empirical example in Sect. 2.4, if such a model fails to represent the system under study, what is the next step, to learn from the model and improve it or go back to the principles and natural laws to build another one? In synthesis, the current use of models in ecology and evolutionary biology is a complex interaction among construction, representation, and learning, akin to a more pragmatic view and model-based reasoning proposed by Morgan and Morrison (1999).

2.3.2 Null and Neutral Models Some classes of models are now widespread in ecology and evolutionary biology to represent some idealized or hypothetical situation that would not necessarily appear in the empirical world. Null and neutral models are good examples of these idealized (and in some cases even “utopic”) models and their goal, in principle, is to represent counterfactuals with respect to some process that could be driving the patterns. First, it is important to distinguish between these two types of models, and Gotelli and Graves (1996) define a null model as: …a pattern-generating model that is based on randomization of ecological data or random sampling from a known or specified distribution. The null model is designed with respect to some ecological or evolutionary process of interest. Certain elements of the data are held constant, and others are allowed to vary stochastically to create new assemblage patterns. The randomization is designed to produce a pattern that would be expected in the absence of a particular ecological mechanism.

This definition highlights the idealized aspect of null models and the idea that these models are built to evaluate expected patterns in the absence of a particular ecological mechanism. Nevertheless, the expression at the start of the definition, “pattern-­ generating model,” is interesting when considering the pragmatic view of models. In other words, it is interesting to deepen the discussions about how to build such models, their function as an investigation tool, and how we learn from them by

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analyzing the emergent patterns (and this is also related to the simulation models discussed in the next section). Gotelli and Graves (1996) reinforce the idea of randomization or resampling of empirical patterns to generate null expectations, so the goal is usually to identify if there are deterministic ecological processes driving patterns or if the patterns under investigation could emerge by chance alone. The aim of using null models is to check whether the investigation patterns are “real” or not, concerning biological explanations purposely excluded from them. Because ecological systems are complex, the idea is to rule out processes and evaluate how the randomized patterns resemble observed ones, which is done by fixing specific properties of the system and allowing others to vary stochastically. For instance, keeping species richness constant but allowing their identity to vary allows evaluating whether patterns in species’ attributes are related to coexistence. One can then compare the observed frequency of co-occurrences of a pair of species with thousands of frequencies obtained by randomly allocating all species to the sites (i.e., an empirically derived null distribution). If the frequency is the same, there is no reason to suspect that any biotic interaction process underlies observed co-occurrence patterns. Notice that the null model is required in this case because the null expectation is not easily obtained or analytically derived and thus can be viewed as a complex null hypothesis when thinking on standard null hypothesis statistical tests (see Sect. 2.4.2). Neutral models, on the other hand, are also models that remove factors to understand if empirical patterns could emerge even in the absence of these factors (Gotelli and McGill 2006). However, in neutral models, the idea is that the stochastic dynamics of the system can generate patterns that could be confounded with deterministic processes. But the resemblance is only superficial (in terms of stochasticity), as the neutral models are process-based models (see Connolly et al. 2017; next section on this) and not simple null expectations based on complex and user-based randomizations of data. The idea underlying “neutrality” is that the entities (individuals or species) drift in space or time with realistic biological parameters but are subjected to certain constraints limiting their response to deterministic processes that could generate patterns. Two well-known examples of neutral models in ecology and evolution have been widely discussed in the last two decades. In Hubbell’s (2001) neutral theory, the individuals of different species are ecologically equivalent in birth, death, dispersal, and speciation, so their dynamics in neutral models are driven only by demographic stochasticity and not by differences in the ecological niches of the species. Another well-known example of neutral dynamics, in a more evolutionary context, is provided by Brownian motion in comparative analyses. Throughout the evolution of a clade, a given species trait (i.e., body size) varies randomly, but if species share a recent common ancestor, they tend to be similar for a trait because they have less time for independent random evolution. Thus, a strong relationship between trait divergence and phylogenetic distance appears under neutral evolution. This idea of neutral evolutionary dynamics was the leading intellectual movement underlying all the discussions that later originated Hubbell’s (2001) NTE.  Kimura’s (1983) neutral theory of molecular evolution provides the first insights that led to

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challenging the strong adaptationist view of evolutionary dynamics (part of what Gould and Lewontin (1979) called the “Panglossian paradigm”). We usually think that, for a given trait, we can model its neutral evolution using a Brownian motion process (see Sects. 3.2.3 and 5.2.3), which is also interesting in the context of models as analogies (Morgan and Morrison 1999). For instance, we can test if the phylogenetic distances can at least partially explain differences in body size (see Chap. 8). However, in a more general sense, phylogeny emerges as the simultaneous evolution of hundreds or thousands of traits (i.e., bases in a DNA sequence), whose variation is driven by a succession of speciation and extinction events in deep time. Neutrality, in this case, is explicitly defined by the absence of adaptive value of genetic variation, whose variation among populations and species arises as a function of random fixation (by genetic drift) of neutral or quasi-neutral mutations. There is, however, an important conceptual issue underlying Brownian motion and phylogenetic neutrality with respect to Kimura’s neutral theory of molecular evolution and process-based models. Even if the divergence of a trait, such as body size, is well captured by Brownian motion, it does not necessarily indicate that this trait is evolving under Kimura’s mutation-drift equilibrium. A strong fit to Brownian motion models is also expected if random adaptive pressures are driving the divergence of the trait in each species in each step along evolution (again, this can be viewed as an underdetermination problem, previously discussed). Over time, there can also be a general trend toward larger or smaller values affecting all species that could only be detected by explicitly searching for empirical data of ancestral states for the trait in the fossil record. Several chapters of this book discuss many specific examples and applications of null and neutral models. Still, there are interesting general aspects to discuss in terms of model-based reasoning, which are the focus of this chapter. Unlike null models, neutral models are process-based models regulated by multiple factors at distinct temporal and spatial scales. Reinforcing the learning component of the modeling process as mediators between theory and data, the neutral expectations can be viewed as an expected pattern if there is, for instance, no niche or adaptive process driving the patterns. For empirical evaluation, a simple approach is to evaluate how well the neutral expectations represent the empirical patterns. Even so, it is always possible to assess deviations from neutral expectations to learn about potential adaptive processes driving variation in some situations. For instance, a species that strongly departs from a closely related sister species in the niche or a morphological trait could be explained by an ecological factor, such as adaptation to a very different climate or acquisition of an entirely new behavior. Moreover, as previously pointed out and discussed in more methodological detail in the next section, it is possible to incorporate the adaptive process in the same simulation model, explicitly evaluating the balance between adaptive and neutral dynamics explaining a given pattern. In this case, the autonomous view of a model by Morgan and Morrison (1999) is quite interesting, as different theories, traditionally considered mutually exclusive views of the world, are merged into the same model.

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A more detailed discussion of null and neutral models for geographic ranges and LGDs also appears in Sects. 4.2.3 and 6.2.1, in the context of debates surrounding the mid-domain effect (MDE; Colwell and Lees 2000). The idea was to develop a null model to evaluate diversity gradients by removing the effects of the environment, which triggered an important debate on the null expectation of geographic range size under geometric constraints. It is also interesting to point out that subsequent studies showed that MDE could also be viewed as an emergent property of the neutral model (Rangel and Diniz-Filho 2005a). MDE discussions are linked to which ecological factors determine range edges and how they can change over time. Several models derived from population ecology and population genetics theory have been developed for a long time to deal with this issue. MDE and derived models incorporate all these previous ideas and principles. Under alternative models, keeping the environment constant would create a distinct null (or neutral) expectation, completely changing the expected patterns of range overlap and species richness. This insight leads us to the next section and to the discussion of more complex simulation models intended to describe complex ecological systems, such as species geographic ranges in space and their overlap, creating species richness patterns at macroecological scales.

2.3.3 Computer Simulation Models Simulation models perhaps provide the best example of Morgan and Morrison’s (1999) idea of models as mediators between theory and data in model-based scientific reasoning. With the increased computational power and availability, it was expected that building computer simulation models to understand complex systems would be a frequent scientific activity, especially in those fields that do not provide a universal opportunity for experimental research, such as macroecology and macroevolution. Some philosophers consider computer simulations as form of “in silico” experiment, or something intermediate between experiments and models (e.g., Morrison 2015). Computer simulations fit quite well Cartwright’s (1983, 1999) view of models as “nomological machines” (Bailer-Jones 2008; Morrison 2015) generating regularities given certain capacities to replicate the world, clearly exposing the idea of the autonomy of models from both theory and the empirical world. Indeed, simulations can create situations and scenarios that reflect a combination of different theories and generate patterns that are not actually found or expected (counterfactual) in the real world, forming what would be called “potential worlds.” Simulation results can also be used to look for parameters that best fit the empirical patterns. However, if the empirical systems are too complex or dominated by contingency (from an evolutionary point of view, for instance), it would be interesting to only evaluate these representation abilities in a loose sense and from an abstract point of view, quickly moving on to explore the model as an indirect way to assess the empirical patterns.

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Computer simulations have been applied in several contexts in macroecology, especially to reconstruct broad-scale diversity patterns, such as latitudinal or altitudinal gradients (Gotelli et al. 2009; see Cabral et al. 2017; Hagen 2023; Pilowsky et al. 2022 for general reviews and Sect. 6.5 for more details and empirical examples). Most simulation models developed to evaluate diversity patterns evolved from MDE models. The original idea of MDE was to define how richness emerges from the overlap of geographic ranges that vary in size but whose edges are limited only by the geometric properties of the domain (e.g., the continental borders or the biome limits). As previously pointed out, MDE patterns emerged under spatially constrained neutral dynamics (Rangel and Diniz-Filho 2005a). However, we can invert the reasoning and evaluate richness patterns obtained by overlapping randomly generated geographic ranges whose edges are related to some environmental variable, such as temperature, creating constraints to its spatial distribution (Rangel and Diniz-Filho 2005b; Rahbek et al. 2006; Gotelli et al. 2009) (see Sect. 4.2.3). Later, deep-time speciation and extinction dynamics of these geographic ranges were incorporated, using models in which the species’ niche is inherited among ancestral-descendent species pairs (Rangel et al. 2007, 2018; Sect. 5.3.2). This last case is interesting in the theoretical sense of showing the autonomy of models from theory and data, given that the model is built based on several theories (or general principles) from ecology and evolution at different scales and hierarchical levels. Another interesting issue of such simulation models that goes exceptionally well in the pragmatic view of theories and model-based science is to use pattern-oriented modeling (POM) approach (Grimm et al. 2005; see also Rangel et al. 2007; Diniz-­ Filho and Raia 2017 for macroecological applications), which was initially developed to work with individual-based models (IBMs). The idea is to allow each model parameter to vary within a given interval and look for which parameter set provides the best when confronting model predictions with empirical data. These parameter values, then, are inspected and interpreted to evaluate if they are in a plausible range or similar to empirical estimates in particular cases. Thus, parameters are not defined a priori by the researcher. Instead, model parameters are fitted to empirical data using one or multiple fitness criteria (e.g., approximate Bayesian criterion, ABC). Indeed, a more sophisticated version of these simulation approaches could be implemented, improving search strategies (by mathematical or computational optimization), adding more parameters, and consequently increasing model complexity. However, one issue that is not commonly investigated is how different and even contradictory combinations of parameters generate high and similar fits, revealing a potential underdetermination problem according to the Duhem-Quine thesis previously discussed. In addition, complexity is a problem in any model-building framework, as previously pointed out. Macroecological models, with hundreds of species diverging in deep time, would quickly produce too many parameters (even at the species level), making interpretations more challenging due to potential underdetermination and, in a more practical sense, becoming demanding of computational resources. Diniz-Filho et al. (2019a, 2021a) provide another example of simulating a macroecological pattern using an individual-based model to evaluate patterns of body

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size evolution in island-continent system (see Sect. 8.4.2). The simulation models were built using several principles from ecology and evolution, combining quantitative genetics theory of continuous polygenic traits and demographic parameters from population ecology in distinct scenarios of island colonization. The simulations incorporated more parameters than usually applied in more conventional (analytical) quantitative genetic models and allowed an estimate of the time necessary to promote the observed phenotypic divergence between body size of ancestral species in the continent and descendent species in islands. Inverting the reasoning, another application of the same model (with a few minor additional parameters) tried to evaluate if the substantial body size reduction in extinct forms of Cervus elaphus (the red deer) in Jersey, one of the Channel Islands, was plausible given the available time of divergence that would be “available” for evolution and given the current knowledge on the scenarios of island formation from geological and geomorphological data (Diniz-Filho et  al. 2021a). In these cases, the simulation model was used to investigate the body size evolution process and to determine if fast evolution would be possible under realistic genetic and demographic parameters (in the sense of being within empirically estimated ranges for different species and environments).

2.3.4 Statistical Models In a more general pragmatic sense of scientific activity and thinking in other forms of models, one can say, for example, that under niche conservatism theory, we expect that both old and new species or lineages are found in the tropics. In contrast, new species or lineages are found in temperate regions more frequently (assuming that at the origin of the clade, the world was mostly tropical) (see Chaps. 5 and 6). This expectation is a general and qualitative statement, too broad and abstract to be used in practice for fitting data, not leading to an explicitly quantitative (interpretive) mathematical model. However, it expresses a theorizing process and a basis for statistical testing by selecting surrogate empirical variables to represent niche conservatism that can be correlated with richness. For example, one could compare the mean root distance or related metrics obtained from a phylogeny for the two regions and test this type of hypothesis mentioned above (e.g., Hawkins et al. 2005a, 2007c). Most researchers would consider this exercise a simple curve-fitting, correlative nontheoretical, and empirical approach (usually confounded with “exploratory data analysis”). Still, a deep theorizing process allows the interpretation of correlation patterns and underlying variable selection. These correlations come from very abstract models in the mind of researchers. They are part of a more general sense of theorizing, even without more formal axiomatic theories. These statistical approaches are discussed in more detail when dealing with the empirical evaluation of the models (Sect. 2.4). Still, to illustrate how statistical models fit the overall theorizing under model-based reasoning, it is interesting to think about how local models can be scaled up to broader geographical scales. Eileen

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O’Brien used one interesting approach in the late 1990s with her interim general models (IGM) (see O’Brien 1998; Field et al. 2005; Vetaas 2006). The idea was to fit a regional model based on the “theory of biological relativity to water-energy dynamics” using climatic data and plant richness obtained from several Kenya localities. This theory is a broad set of ideas and principles based on plant physiology but does not generate an equation describing richness, as in Allen’s et al. (2002) interpretation of MTE. However, it is possible to fit an equation to local data using standard multiple linear regression in which explanatory variables are surrogates describing the theoretical processes, called “first-order climatic potential for richness.” This empirical equation provides an estimate of plant richness for the entire globe that was compared with observed richness, showing a good fit and providing a general baseline for describing overall patterns. Note that statistical modeling used in this sense also matches Morgan and Morrison’s (1999) idea of using models for learning and the more general pragmatic view of theories. In this approach, we usually use optimization processes to obtain the maximum fit with empirical data (or model of data; see next section). When some variables are excluded or added to the statistical model, we learn something about our “a priori” theoretical explanations for that pattern, especially when rejecting the hypothesis about the influence of certain factors. Although this would be viewed as an ad hoc explanation in some contexts, it is what happens in a more pragmatic sense. Moreover, suppose this is an ad hoc explanation based on a purely empirical perception of local patterns that may be idiosyncratic. In that case, the model will fail in the next round of generalization when trying to evaluate or predict patterns based on other datasets (see Laudan 1977 for deep discussions about “ad hoc” reasoning). At this point, it is interesting to show some relationships between the more standard statistical modeling approach with computer simulation strategy and conceptual connections between theories and models previously discussed. For example, one can directly evaluate the influence of temperature on species richness and assess the statistical fit between both variables. However, a different idea is to simulate how the species ranges of several species are affected by temperature and then obtain an expected richness that is compared with empirical data (Fig.  2.5). Generating this expected simulated richness involves a model on how temperature drives the limits of species’ geographic ranges, which is a representation of theoretical principles of geographic range dynamics (Sect. 4.1). Thus, rather than empirically or statistically evaluating the effects of temperature on species richness, we can use computer simulation models as mediators, expanding the logic of MDE to define more complex ways geographic ranges are affected by the environment. Usually, mechanistic models in macroecology are used to build the verbal mechanistic explanations that emerged when trying to explain the strong association between environmental variables and species diversity. In this case, the mechanistic simulations based on geographic range dynamics are built based on the reasoning that emerged after using a standard statistical model to evaluate richness patterns or

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Fig. 2.5  A comparison of two strategies of explaining empirical richness, by correlating or regressing it against an explanatory variable (narrow arrows), and the idea of using this explanatory variable in a simulation process that generates the predictive richness that, in turn, can be compared with the empirical patterns. (See Rahbek et al. 2006)

start from first ecophysiological principles derived from ecophysiology and metabolic theory, as discussed above. Thus, although traditional statistical and mechanistic modeling are usually thought to be examples of different model-building strategies, their application can be complementary in this case.

2.4 Empirical Evaluation of Models and Hypothesis Testing 2.4.1 Hypotheses and Models of Data After understanding the main types of models and their roles, it is time to discuss how to compare them with empirical patterns. In general, the main goal is representation, but other roles, especially dealing with counterfactual (in the context of null and neutral models) and learning processes, will emerge more clearly considering the iterative process between model (re)building and improving empirical fit. Thus, in this section, we advance with more standard and operational statistical analyses that are relatively well-known. However, it does not provide a detailed description of the plethora of possible methods. Other methods are discussed throughout the book, and readers should consult excellent textbooks on statistical analyses in ecology and evolution, including Bolker (2008), Gotelli and Ellison (2013), and Legendre and Legendre (2012).

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We start by discussing the evaluation of the interpretive model derived from the MTE proposed by Allen et al. (2002) to explain latitudinal diversity gradients. The goal is not to discuss in detail the processes underlying LGDs (see Chap. 6 for more details) or to restart the discussions about the validity or generality of MTE. However, this example is interesting to show the debate on model-building strategies, how different models can be compared with empirical data, and what we can learn about both theories and the real world. Formally, recall that Allen’s et al. (2002) final model derived from MTE. Compared with previous attempts to evaluate the ecological and evolutionary processes underlying the LGD by purely correlative models, the novelty in this model is that it predicts a slope for the relationship between richness and temperature. Thus, this interpretive model allows an explicit (sometimes treated as “objective” or “strong”) test of the theory in a Popperian sense. However, we must first consider which data we could use to evaluate the theory with this model (as it is an interpretive model). As we are working on LGDs and thinking in the overall domain of the general and constitutive theory, as proposed by Scheiner and Willig (2011), we use a dataset at the global scale for a relatively large group of ectotherms, the amphibians. We provide details of this type of macroecological datasets and many issues associated with hidden assumptions underlying data in macroecological research in Chap. 3. Still, it is enough, for now, to know that here we have amphibian richness at a 1o resolution, obtained by overlaying the geographic ranges of 7193 species obtained from IUCN, shown in Fig. 2.2. We refer to this richness map as showing “empirical” patterns and recall that these patterns are not “observed,” better viewed as a model of data (Sect. 2.1.1). For each assemblage (i.e., grid cell), the mean annual temperature from WorldClim (see www.worldclim.org) is also a model of data (i.e., a statistical interpolation of time series of climate variables in different regions of the world). Notice, as previously pointed out, that it does not make sense to affirm that a model (a representation model or a model of data) is true or false, and it is inescapable to quote the British statistician George E. P. Box., “All models are wrong, but some are useful.” However, hypotheses are semantically defined propositions derived from theories or models so that, in the end, they are accepted (i.e., as “true”) or rejected (i.e., as “false”). Again, recalling Giere’s (2006) definition from Sect. 2.1.1, hypotheses are “…statements that may be true or false depending on whether the indicated good fit is realized or not.” When we achieve a consensus on what allows us to accept or reject the hypothesis, despite difficulties with data statements, we can verify the possibility of generalizing the application of the theory or model in terms of representing, predicting, or understanding. The issue is then how to decide if a model represents the data (or model of data), and there are several ways to think about this. As discussed in more detail below, the main underlying reasoning is always to decide, using different approaches, if the model of data is similar to the representation model.

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2.4.2 Popperian Falsificationism and Classical Hypothesis Testing Moving now to the more operational idea of model evaluation and hypothesis testing, we can go back to our empirical data and test the hypothesis that amphibian richness spatial patterns are explained by temperature according to Allen’s et  al. (2002) model derived from MTE. In principle, the expectation is that species richness responds to temperature at a given rate (i.e., an increase in temperature leads to a given increase in richness) and that deviations in each region may vary stochastically around this general trend. So, a first attempt to evaluate if MTE explains the patterns would be regressing amphibian richness (at log-scale) shown in Fig. 2.2 against the inverse of temperature and checking the linearity of the relationship and if the slope matches the expected one. Indeed, we have a negative relationship between the two variables (Fig. 2.6a), and the slope on an ordinary least-squares (OLS) regression of the logarithm of species richness against scaled inverse temperature was equal to −0.459 ± 0.046. Following a more standard protocol for statistical analyses, researchers usually evaluate at first if this slope is different from the null expectation in which the slope equals zero, so we can say there is a pattern here. As the error of the slope is relatively small, we can say that we are confident that a slope of −0.459 ± 0.046 is unlike to appear if the “true,” parametric slope, equals zero. We can calculate the Type I error rate of this slope, saying that we have much less than a 5% chance of observing this slope of −0.459 if the true slope is zero, so we reject the null hypothesis assuming a t-distribution of regression slopes. In this case, the t-value associated with the slope was >100, so we conclude that richness does not vary at random regarding temperature gradient. However, in this case, we can do better than that, and it is important to stress that our goal here is not only rejecting the null hypothesis (i.e., the absence of a geographical pattern in richness patterns). Allen’s et al. (2002) model provides a more specific expected relationship between the two variables, making the simple pattern description from the previous paragraph a much stronger test (see McGill 2003a and Sect. 2.4.6 below). Our goal is to evaluate if Allen’s et  al. (2002) model fits the empirical pattern, and for practical purposes, we usually think of some similarities between these two patterns. Rather than thinking of the null expectation, we can explicitly test if the slope for amphibians matches the one expected under MTE. In Fig. 2.6a, the best-fit line from the standard regression is represented in the solid line. In contrast, the predicted richness decay with inverse temperature according to the model is shown in the dashed line. This prediction is obtained simply by getting the richness values that would appear for each temperature according to Allen’s et al. (2002) equation. A more straightforward way to show model fit matching the conceptual expectation of MTE is to use the equation above and generate expected richness values that are compared with empirical amphibian richness shown in Fig. 2.6b. When regressing empirically derived amphibian richness against expected richness under MTE, the idea is that an intercept equal to zero and a slope equal to

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Fig. 2.6  Relationship between amphibian richness and temperature according to Allen’s et  al. (2002) model using a standard regression (a), in which the solid line is the best-fitted model according to an OLS regression and the dashed line represents the expected slope of −0.65. Also, we can more explicitly evaluate the fit of Allen’s et al. (2002) model by plotting empirical and observed richness (b) and testing the intercept for zero and the slope for 1 (dashed line). Both t-tests are statistically significant at 1%, indicating deviations from null expectation (t > 100) and also deviation from expected slope under MTE (t = 12.3)

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1 are expected if the model fit the data well. Both tests failed for this particular case, so Allen’s et al. (2002) model seems to be not working as expected with this dataset. However, despite the problems in fitting the empirical data to Allen’s et al. (2002) model, there are several important issues to consider regarding what this particular result means and how we can think about MTE based on it. In short, when comparing a model (especially one derived from the theory, in the semantic and axiomatic view) and a model of data, how can we interpret their relationship in terms of the overall goal of assessing the validity of the more general theory? This idea leads us back to the problem of the Duhem-Quine thesis previously discussed, and a first issue to consider is, for example, how we know that we do not have a problem with the data, as this is also a model (of data). How are we sure that the way data are obtained matches the theoretical expectation? Thinking about these questions is critical in these cases based on models of data, also reinforcing the idea that the theory also may guide the way empirical data are obtained for testing and evaluation, as previously discussed. We can start by discussing “data statements” derived from the theory. We can wonder, first, if the standard statistical tests are valid or informative, given that the relationship between richness and temperature is not even linear. In principle, the model predicts a linear relationship between the two variables, with randomly distributed errors around the expectations. However, there are systematic deviations from this expected pattern, as shown in Fig. 2.6, so something is missing as a general (not idiosyncratic) explanation. Thus, rigorously speaking, the data are not well described by the model, so using a regression approach to test the slope, in this case, is not even necessary (or statistically sound). Thus, even if we continue testing and assume slope estimation robustness, there are many other operational issues to consider. For instance, as we have strongly structured spatial data, neighboring cells are similar in richness not necessarily because of similar temperature but rather by simple “contagious” processes (i.e., scale issues related to range definition, e.g., short-­ distance dispersal independent of the environment) (e.g., Diniz-Filho et al. 2003). So, degrees of freedom tend to be overestimated and create a form of pseudoreplication, upward biasing Type I errors of standard hypothesis testing. Several strategies exist to deal with this problem (see Sects. 3.1.2 and 3.2.3). Suppose we assume that errors are widely underestimated. In that case, the correct confidence intervals should be larger and more likely to encompass the parameter, allowing accepting a “good” match from a statistical comparison of slopes). However, even if we consider these biases and think that the confidence interval encompasses the theoretical expectation, much nonrandom variation around the expectation deserves attention. Another issue to consider is that perhaps Allen’s et al. (2002) model better fit more local data, as they assumed the energetic equivalence rule at the community level. In this case, perhaps the macroecological overlap of ranges tends to inflate the number of species in local communities (and indeed, the estimated richness is much higher than predicted by MTE; see Fig. 2.6b). Also, we have some potential problems in the way temperature is defined. Is mean annual temperature adequate, or should we use more specific measures related to exposure and accounting for other

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physiological or behavioral strategies to deal with heat that may bias this? So, we may have a scale issue that would affect the comparison of models and undermine its test. It is usually hard to objectively evaluate some of the issues related to models of data and data statements. This issue opens the possibility of many discussions regarding how independent data from theories is at multiple hierarchical levels (see Hacking 1983). The failure in hypothesis testing could be attributed to problems moving from a general abstract theory to more empirically oriented models. In an optimistic view, it would be possible to look along the hierarchy and determine if a revision of the principles, axioms, or laws, or perhaps of the domain of the theory, is required (Hawkins et al. 2007b). As hard as it may be, if we agree that problems with data statements are not severe enough to invalidate the comparison between the representational model and model of data, we must assume that hypothesis testing is valid. Hence, we must accept the test’s failure and consider what this means (otherwise, we would be stuck). In a theory-based view, the failure of the model to fit the data suggests that there may be problems with the theory, even though we do not know where the problem is, as the model is an interpretation of the principles and concepts helping to investigate the empirical world. It is, of course, possible to reorganize the theory by reviewing the principles, axioms, or laws and incorporating other factors (see Allen et al. 2007; Storch et al. 2018 for improvements in understanding the role of MTE as applied to richness gradients, for instance). But what to say about our example with global amphibians? What does this failure mean for the theory? And for the model? These are the main questions, but there are other issues to consider, so in practice, the case is more complicated than it seems. Beyond the data statements issues, the first and more prominent issue is if a simple test with a single dataset (i.e., global amphibians) would be enough to take a serious decision of rejecting MTE or even Allen’s et al. (2002) interpretive model. In a more general sense, the question is how we can interpret the failure of a test with respect to a theory. As pointed out above, most researchers, especially in the natural sciences, are aware of the influence of Popper’s idea that theories and hypotheses are never confirmed but can be refuted if they fail in a test, and that is how scientific knowledge advances (in the process of “conjectures and refutations”). Thus, a first interesting possibility is that we can more clearly say that we can reject the interpretive model derived from the theory, so we need to build a better model, and this would be a proper Popperian attitude. However, in practice, most researchers would avoid a “naive falsificationism,” even for a model. There is an even more interesting issue if we think that biological diversity provides a strong argument against these quick and naïve decisions regarding explanatory models, adding a potential new component to the Duhem-Quine thesis. It would be hard to decide if we reject or accept a theory or model based on a particular group or organism. For some reason, amphibians may have some unknown particularities, so MTE does not fit, but still, the theory would be valid for other types of organisms. This can be definitely viewed in the context of the induction problem. However, how to deal with this problem considering the multiple possibilities to define species richness for groups of organisms to calculate richness at distinct

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levels of biological hierarchy? Thus, can we consider biological diversity as a source of underdetermination? On the other hand, would deconstruction approaches (see Sect. 3.3) be a way to overcome underdetermination, in a more optimistic view (see Diniz-Filho et al. 2023a for a discussion)? Following this reasoning, Hawkins et al. (2007a) found that, for many empirical macroecological datasets, Allen’s et al. (2002) model does not fit the data well, and the distribution of slopes calculated for each of these datasets IS widely distributed around zero and not even closely aggregated around the expected slope of −0.65. In their reply to Hawkins et al. (2007a), Gillooly and Allen (2007) pointed out some problems with the datasets used and how, in some of them, assumptions of the model are most likely violated (so they are someway using the Duhem-Quine thesis in their favor). Also, they pointed out that what Hawkins et al. (2007a) considered a failure are, in their view, “promising” results, which leads us back to several interesting discussions again on the semantic versus the pragmatic view of models and theories in ecology. Under a more semantic view and considering this new proposed component of Duhem-Quine thesis, the problem is now how many datasets are needed to decide upon the validity of MTE in terms of explaining or representing the LDGs. This question exemplifies the generalization issue following hypothesis testing in Fig. 2.1, so we are now moving to a different way of thinking on an inductive confirmation of theories (and thus not the Popperian approach for rejecting the model). Indeed, this is widespread reasoning from early logical empiricism and positivism, i.e., if a hypothesis is confirmed for most groups and can be generalized, the theory is then “confirmed.” In practice, however, under this confirmation and inductive approach, we keep some “majority consensus rule,” and for MTE in our example, we could say that this is valid if we confirm the hypothesis for, say, 50% of the cases. This decision is obviously nonsense, in the same way that it would be naïve to say that a single failure would be enough to reject the model or the theory. There is no final answer to this problem in deciding how many datasets would be necessary to support or reject a model. The solution would depend on the goal of developing a theory such as MTE and evaluating the models derived from it. As previously pointed out, this confirmation and generalization problem is especially problematic as we open the “Pandora’s box” of biological diversity, analyzing multiple empirical patterns obtained for distinct groups of organisms in different regions and with distinct evolutionary histories. One possible generalization solution would be combining all available information and estimating the general effect size using meta-analytical procedures (see Becker and Wu 2007; Gurevitch et al. 2018) (see also Sect. 2.4.3 on Bayesian inference). For instance, following Latimer (2007) and conservatively using only slopes from the more linear (or at least monotonic) regressions from Hawkins et al. (2007a), it is possible to obtain a mean effect size equal to −0.183, with 95% confidence limits ranging from −0.3595 to −0.003 (Fig.  2.7). The Q-statistics that measures the heterogeneity of these slopes was highly significant This heterogeneity reinforces that there is not a single “parametric” slope in this dataset, and even if there were, the slope would be much shallower than the expected slope of −0.65. So, based on this simple meta-analysis, we can

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Fig. 2.7  Forest plot of slopes (full circles) from 23 studies in which a linear relationship between log(richness) and inverse temperature is obtained, with confidence intervals based on errors conservatively adjusted for spatial structure in data (see Hawkins et al. 2007a, b; Latimer 2007 for details). The mean effect size is shown as a diamond at the bottom of the figure, whereas the expected slope according to Allen’s et al. (2002) model is shown as a solid line

reject Allen’s et  al. (2002) model as a general explanation for the correlations between richness and temperature. However, one could still argue that these datasets do not provide consistent or independent evidence for deciding about the theory or model, accounting for data quality problems. There is indeed a comprehensive discussion about the need to standardize protocols better to evaluate data quality and confidence in the studies used for meta-analysis or systematic literature reviews (e.g., O’Dea et  al. 2021). Indeed, Cassemiro et al. (2007) and Cassemiro and Diniz-Filho (2010) showed that Allen’s et al. (2002) model seems to have a better fit for datasets or conditions in which assumptions of MTE are not violated. For instance, slopes are closer to the one predicted by MTE when there is less influence from other factors (such as water availability) and when the assumptions of the model are fulfilled, including the absence of geographical gradients in abundance and body size and when group tends to follow EER (see also Gillooly and Allen 2007) (see also Sect. 2.4.4 on multi-model inference for support of this reasoning). It is widespread in

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macroecology to try to identify correlates of model fit or acceptance of a given hypothesis, trying to find a situation in which, for example, temperature variation explains richness patterns better than productivity (e.g., Weiser et  al. 2017; Bohadalková et al. 2021). More operationally, this is also related to the “deconstruction” of data, which is discussed in more detail in Sect. 3.3. Despite these potential solutions, the general issue here is that if we are looking for surrogates of model fit and hypothesis testing, we are adopting an optimistic view of the Duhem-Quine thesis and trying to improve our understanding of macroecological patterns by exploring auxiliary hypotheses that could better delimit (or even constraint) the domains of the theory (see Laudan 1977; Diniz-Filho et al. 2023a). We are building a new, more general model by theorizing conditions in which it can be more successfully applied. Another interesting and related issue is whether historical contingencies in ecology represent “evolutionary accidents” or something “peculiar.” Are historical contingencies errors or deviations from a perfectly defined theoretical expectation derived from fundamental laws of nature, invariable in time and space? Or do they the expression of multiple factors in deep time that drives different and more complex patterns than we can anticipate? As Cartwright (1999) pointed out, if theories work only for restricted situations in which perfect conditions are found, these tests are hardly interesting in validating fundamental principles and supporting the existence of universal laws of nature that underlie ecological patterns. Teller (2008) argue that this idea quickly leads to a metaphysical discussion of accepting the fundamentalist idea that finding fundamental laws of the universe is the primary aim of science (or, in a moderate or ontic view, that although such laws may govern the world, the universe is too complex, and we will probably never be able to understand them). Moving beyond these metaphysical issues and thinking more operationally, these problems indeed define the difference between theory-based and model-based reasoning of scientific activity, as previously discussed in Sect. 2.1.2 and considering the differences between semantic and pragmatic views of theory (see Del Rio 2008 for a discussion in the context of MTE). Also, this is one of the points of discussion raised by Houlahan et al. (2015), in reply to Marquet’s et al. (2014) review of ecological theories, in terms of what it means to “understand” a theory. If it applies only to particular datasets, what exactly is the meaning of a theoretical explanation in terms of being a general theory? Going back to the Hawkins et al. (2007a) analyses with multiple datasets and under a more pragmatic point of view, it is safe to say that we are not “satisfied” (sensu Giere 2006) with MTE in terms of representing the diversity gradients because our hypothesis tested by comparing empirical data and Allen’s et al. (2002) model is frequently rejected. However, as previously discussed, it is difficult to generalize or predict patterns for different groups of organisms. Based on this idea, some would argue that it may be premature to discard MTE. Still, going back to the discussions about frameworks in Sect. 2.2.2, this depends on which research tradition the model is developed and evaluated. It would be easier to improve our understanding by building new models starting from MTE, adding more factors, and even

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thinking of integrating distinct theories or relaxing assumptions (as Gillooly and Allen 2007 indeed recognized). Thus, we do not necessarily need to discard MTE or even Allen’s et al. (2002) model. Still, the main question is why we need to be so attached and firmly committed to its axiomatic reasoning, even because other theories would lead to similar interpretive models (see Allen et al. 2007; Storch 2012). From a more pragmatic point of view, the answer is that this theory is not working well at the moment, as the interpretive model derived from it tends to fail in representation. It would be better to focus on the modeling approach, understand what went wrong, and improve its representation abilities in terms of generality (Hawkins et al. 2007b). Perhaps these improvements will lead, in the future, to a theory more appropriately coupling understanding (or mechanisms underlying richness) and generality (e.g., see the more recent work by Weiser et al. 2017; Storch et al. 2018; Arroyo et al. 2022 for interesting alternatives ideas). Thus, given the complexity of macroecological patterns involving patterns and processes operating at broad scales throughout deep time, it is unlike simple explanations based on simple variables and first principles, as proposed in MTE, would be helpful for the representation of richness patterns. So, moving on to a completely different framework for model evaluation and hypothesis testing may be interesting, akin to a pragmatic view of theories and model-based science.

2.4.3 Bayesian Inference Following the inductive reasoning of accumulating knowledge to support theories or models, some exciting recent advances are derived from a complete change in the statistical framework to analyze data. Bayesian inference may provide more satisfactory answers to those problems about generalization based on confirmation, at least from an empiricist point of view. It is beyond the scope of this chapter to provide a more detailed conceptual and operational description of Bayesian inference, and we provide here only a brief overview (Hilborne and Mangel 1997; Hacking 2001; Bolker 2008; Kruschke 2014; Ellison 2004; Banner et al. 2019; see Godfrey-­ Smith 2021 for deeper conceptual discussions). In classical hypothesis testing discussed in Sect. 2.4.2, the idea is to establish the probability of obtaining a result as extreme as the observed result by chance, given that the null hypothesis is true. This inferential strategy assumes that probability is a measure of the frequency of infinite trials (repetitions of an experiment or observation). The classical P-value represents the probability of the data given the null hypothesis. However, the departure from the null hypothesis is hardly what researchers want to know and does not represent how they interpret the results of classical statistical analysis in many cases (Dennis 1996; Ellison 2004; Clark 2005; Clark and Gelfand 2006; Manly 2006). We usually want to evaluate the “credibility” or “plausibility” of one or more alternative hypotheses. However, two conceptual shifts are necessary to make these more appropriate evaluations. First, it is required to change the interpretation of probability from a frequency of infinite trials to a

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degree of credibility. Second, we must invert the reasoning to estimate the probability of the hypothesis given the data. Indeed, it is more interesting to ask what the probability of the model parameters given the data, called “inversed probability.” More formally, the inverse probability is obtained by applying the theorem proposed by Thomas Bayes in 1763 so that

P  H | Y    f Y | H  p  H   / P Y 



in which P(H|Y) is the probability of a hypothesis given the data (the posterior probability), f(Y|H) is the likelihood of the data giving the hypothesis (see below for a more detailed discussion of likelihood, in the context of model comparison), and p(H) is the prior probability, which is essential to Bayesian inference, and holds the credibility in the hypothesis that was available before the analysis of the data. Finally, in the denominator, P(Y), is the marginal probability density of the data across all possible hypotheses (parameter values), which is a normalizing constant that allows the Bayes theorem to conform to the probability rules. The prior and posterior distributions of the Bayes theorem refer to the distribution of a parameter, such as the regression slope. Nevertheless, before advancing in Bayesian inference, it is essential to recall that, for instance, within the regression analysis framework, the linear relationship between response and predictor variables is a model. For MTE, Allen’s et al. (2002) model is given by linear relationship between species richness and temperature, and the hypothesis to be evaluated is that the slope equals a value of −0.65. However, an infinite number of alternative hypotheses could be plausible for a given data, each defined by their unique combination of intercept and slope values. In practice, the idea is to develop an algorithm that uses the Bayes theorem to iteratively update the probability of observing model parameter values given the previous knowledge accounting for its a priori distributions. Using the Bayes theorem, it is first necessary to understand how to calculate the likelihood of the data given a model and a hypothesis, which is the core of all modern statistical inference. Likelihood estimation is further discussed in the context of model selection addressed in Sect. 2.4.4. The idea was first developed by Sir Ronald A. Fisher between 1912 and 1922 (see Aldrich 1997 for a historical review), and there has been much discussion around its interpretation in the context of model fit. It is common to refer to this as the likelihood of a hypothesis given the data, but this is not entirely correct (Edwards 1972; but see Ellison 2004). From a practical point of view, estimating the likelihood of data requires the specification of a model, for example, a linear regression, and a probability distribution for its residuals (usually Gaussian). Thus, the likelihood of the data is simply the product of the probabilities of obtaining each observed residual under a given hypothesis (e.g., the intercept and the slope). However, because the product of many probability values is usually a very small number (successive multiplication of probabilities, which range from 0 to 1), it is more appropriate to obtain the sum of the log-transformed probabilities, which is called log-likelihood. The log-likelihood function of a linear regression with normally distributed residuals (Fig. 2.8a) indicates that observing real-world

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Fig. 2.8 (a) The negative log-likelihood function for regression slope of richness and temperature used to evaluate Allen’s et al. (2002) model, with the dashed line showing the maximum likelihood estimate of slope and solid line the expected slope, and (b) the posterior distribution of slopes for the same regression using a Bayesian framework, obtained using a MCMC algorithm using as a prior a normal distribution based on the slopes of 23 previous studies in which a linear model was fitted (see Latimer 2007). The insert in b shows the convergence of the chain

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global amphibian richness data is not the most likely under the hypothesis of slope −0.65 predicted by MTE. Maximizing the likelihood of the data requires a linear slope of −0.458, which is the same obtained with the standard OLS approach because OLS regression is a point estimate of the maximum likelihood. However, it is not satisfactory to estimate the probability of observing the data, given a hypothesis, under repetition of the sampling process. We want to evaluate the probability (interpreted as plausibility or credibility) of different hypotheses, including the one with a slope equal to −0.65, predicted by MTE.  However, to implement Bayesian reasoning, it is necessary to go further than the likelihood function and maximum-likelihood estimate. The next required step consists in shifting from the probability of the data given the hypothesis (f(Y|H), the likelihood) to the probability of the hypothesis given the data (P(H|Y), posterior). Estimating the probability of hypotheses requires specifying the prior probability distribution, which is the most controversial step in Bayesian inference (see Banner et al. 2019). The prior probability encapsulates what is known about the relationship between amphibian richness and temperature before the analysis of the data. So, one has to specify the probability value of each hypothesis (slope values) without using the global amphibian dataset. In this regard, it is essential to stress the distinction between Bayesians and Frequentists. In frequentist classical statistical tests, there is no need to incorporate prior information because it is an evaluation of the expected frequency of observing a result if the study is repeated. So, frequentist statistics, such as the likelihood approach (see next section), assumes that each new estimate is conceptually and statistically independent of previous studies and available knowledge. Conversely, Bayesian inferences challenge this idea and state that considering the uncertainty in knowledge and theory, the likelihood of the data given to the model should be weighted by prior information. Notice that some researchers apply a Bayesian approach using “non-informative priors,” such as a uniform probability function truncated at maximum and minimum plausible values. In this case, because a constant value weights the likelihood estimated for all hypotheses, the posterior distribution is the same as the likelihood function. Thus, this approach defies the very fundamental purpose of Bayesian statistics, which is to evaluate degrees of certainty using rational thinking. Going back to our example with MTE, we can use the slope estimates for all previous groups of organisms to build the prior statistical distributions based on the datasets available in Hawkins et al. (2007a). Following the earlier analyses, we can describe the variation in the more linear slopes by a normal distribution with a mean equal to −0.183 ± 0.446 (notice this would be an initial modeling exercise, i.e., to use empirical data – the estimated parameters – to define a theoretical distribution; in this case, using other distributions, like gamma, does not qualitatively change the posterior distribution). Then, we need an algorithm that generates the posterior distribution by combining the likelihood for the parameter and the prior distribution. The choice is commonly the Markov Chain Monte Carlo (MCMC) algorithm. There are many computational details, but, in short, the idea is to explore the parameter space (i.e., the possible values of regression slopes) and calculate the probability

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along it, but in such a way that most of the search tends to concentrate in the calculations of Bayes theorem. An important issue is that we do not have the denominator of the Bayes theorem. Still, because it is a normalizing constant, there is no problem in calculating a “non-normalized probability” if we are contrasting posterior “probabilities” of alternative hypotheses from the same model and data. Finally, we can use MCMC to obtain the a posteriori distribution of the regression slopes, and we can see that, in this case, the prior knowledge did not widely affect our initial estimate based on the OLS regression, with the mean a posteriori slope equal to −0.458. It is interesting to use this a posteriori distribution to obtain the credibility interval, ranging from −0.469 to −0.448. Thus, we can say that we have a 95% confidence (certainty) that the true slope falls within these limits. Again, this Bayesian estimate does not support Allen’s et al. (2002) model as adequate for representing richness. But this is a single example, and more general analyses may be required. Latimer (2007) also analyzed Hawkins et  al. (2007a) datasets using more complex hierarchical Bayesian regression models, fitting the slopes and intercepts to each dataset but allowing the slopes to help estimate a common slope and intercept, as well as quantifying the uncertainty around the fitted slopes as credibility intervals. Latimer (2007) did not find that these datasets support MTE under a Bayesian framework either. However, he found an interesting relationship between deviation from the expected slope and latitudinal extent (which may be related to geographically structured speciation rates; see Chap. 6). Bayesian inference is briefly discussed here in the operational context of parameter estimation, as commonly discussed in ecology and evolutionary biology (including in phylogeny reconstruction; see Chap. 3). Gotelli and Ellison (2013), for example, argue that we can infer parameters and evaluate hypotheses under three different frameworks (null hypothesis testing, likelihood, and Bayesian frameworks). However, as pointed out by Godfrey-Smith (2021), Bayesian reasoning is part of the more general strongly empiricist views based on inductive reasoning with deeper underlying philosophical issues. For instance, this neo-inductive focus on gaining credibility opposes the initial Popperian idea of knowledge increase by rejection, not confirmation, of theories and models discussed in the previous section. No doubt that Bayesian reasoning is today an important tool for generalization and from a pragmatic point of view, but it is interesting to highlight that this confirmation approach refers only to the empirical component. It does not (necessarily) improve our knowledge of the non-observed and theoretical components underlying the model, leading us back to the discussion of realism in Sect. 2.2.1. But within a strong empiricist background, this is not a serious issue as Bayesian inference is focused on observable components of reality and confirmation of models.

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2.4.4 Comparing Alternative Models If we return to Fig. 2.6a, it is clear that the relationship between richness and temperature for global amphibians is more complex than a linear (or log-linear) function. We can get the best-fit OLS model from a pure objective statistical criterion and show that the slope differs from the line obtained using Allen et  al. (2002) model. We do not have any ecological or evolutionary reasoning to explain this fitted parameter by an OLS, even if under a nonformal theorizing process, we can suspect that a relationship between richness and temperature exists. In addition, this is only one of the infinite ways to describe this relationship, and much more complex functions can fit this data using distinct criteria (i.e., “the curve-fitting problem, Coelho et  al. 2019a). Much more work in fitting would be required, using more complex regression models with more parameters (e.g., Zuur et al. 2009), and many alternatives are available. For example, a very popular modeling approach in macroecology now is the generalized additive model (GAM) (Hastie and Tibshirani 1990), which is a combination of local regressions fitted by alternative splines methods in knots along the X-axis (Fig. 2.9). In this case, the fit does not improve much

Fig. 2.9  Fitting a general additive model (GAM) to the relationship between richness and temperature for the global amphibian dataset (compare with Fig. 2.6a). The dashed line indicates a quantile regression at 95% upward limit, with a slope equal to −0.601 and much closer to the theoretical expectation

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(goes to 46%) and, despite oscillations, follows the decreasing linear trend by OLS. However, it would be challenging to biologically interpret the fitted curve. It is also curious that the relationship between richness and temperature can be better described as a polygonal relationship, a “constraint envelope,” according to Brown and Maurer 1987, 1989). If this is the case, perhaps Allen’s et  al. (2002) would be better tested based only on the upper limit on the envelope (see also Chap. 8 and below). Perhaps the theory predicts the relationship’s upward boundaries under energetic constraints rather than the overall relationship. Indeed, using a quantile regression allows estimating a slope equal to −0.601 at the 95% upward critical limit, much closer to the theoretical expectations (see Fig. 2.9). Each of these models would be viewed as an alternative empirical hypothesis for the relationship, even though using quantile regression to model the upward limit of the relationship changes the interpretive model derived from MTE. In the case of GAM, there is, in principle, no theoretical understanding underlying the curve fitting. So, suppose we only want to use this relationship for prediction or to test generalizations (i.e., to evaluate the best-fit model in other groups of organisms). In that case, as discussed later, it may be important to consider these models’ complexity (see Coelho et al. 2019a). Moreover, our goal is to use the relationship of Figs. 2.6 and 2.7 to “understand” the richness pattern in terms of the underlying mechanisms in a more general way to think on prediction and generalization to other groups of organisms (Houlahan et al. 2017). It is not common to try to improve the model fit by searching for different forms of relationship between temperature and species richness, despite the increasing popularity of using GAM, for instance. The common practice is to add other variables that can improve our understanding of the mechanisms and processes. In our example with the amphibians, given their physiology, it is intuitive that many warm regions on the planet are unsuitable for amphibians as some warm regions are arid. Although we do not have a formal theoretical model to generate a predicted slope for precipitation, adding another variable related to water availability (i.e., annual precipitation) to the regression equation and seeing how the model fit changes is possible. We can begin by thinking of simply building a statistical model keeping temperature according to MTE but now adding precipitation in a multiple regression OLS model. Some of the problems discussed in data statements remain, but the model fit, expressed by the coefficient of determination (the R2), increases from 44% to 61%. It is interesting to note that the fit of this model with temperature and precipitation is similar to one using actual evapotranspiration (AET) alone (r2 = 58.5%), following O’Brien’s (1998) “biological relativity to water–energy dynamics” previously discussed. This result is not surprising as AET is a composite variable expressing a combination of energy and water availability (Hawkins et al. 2003a, b). Notice that even with this model with two variables, we could still think about MTE and Allen’s et al. (2002) model and check if the partial regression slope matches predictions. Recall that the slope on this model is the effect of scaled inverse temperature alone, keeping all other variables statistically constant. Gillooly and Allen (2007) pointed out that the original MTE model never stated that temperature was the only driver

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of diversity and that other factors should also be considered. However, when including precipitation in the model, the temperature slope is far from expectations under MTE (now equal to −0.327), not supporting the ceteris paribus interpretations by Cassemiro and Diniz-Filho (2010) and in better agreement with recent analyses by Bohadalková et al. (2021) that effects of temperature happen throughout productivity (below). On the other hand, the coefficient associated with precipitation or AET is just a “free parameter” estimated to maximize fit with the empirical data. In principle, we can only compare them (after standardization) to determine which of the two variables is more “important” in a representational sense. Expanding the above reasoning, we can evaluate, using the same statistical tools, that the model including precipitation (or the model with AET alone) has a significantly higher R2 than the one based on temperature alone. In this case, the partial coefficient of the regression model is statistically significant, independent of the effect of temperature (see below), indicating that adding this variable improves model fit. We can also say that the coefficient associated with AET alone is statistically (P 2 or 3 is used as a criterion to define if that model is the best one or if different models are equivalent. Moreover, another interesting and informative approach is to transform the ΔAIC into an AIC weighting (AICw), given by

AICw  exp  0.5 AIC 



and this is usually expressed by the relative value of AICw with respect to its sum across the models compared. So, this is the probability that a given model is the best among those models under comparison, assuming explicitly that all relevant models are compared. Of course, there is no way of knowing if other possible models not included in the analyses would better represent the empirical patterns (see also Galipaud et al. 2014 for additional issues). Returning to the global amphibian dataset, we can think of alternative theories developed to “explain” the LDG and define variables, or sets of variables, that could represent them (see Rodrigues et al. 2005). A more detailed discussion of alternative theories that have been developed to explain the LDG appears in Chap. 6, but a few examples may suffice for now. Temperature can represent metabolic and energetic constraints, but water may also be essential, as previously discussed. The two factors could act together, expressing geographically structured effects of productivity and energy (see Hawkins et al. 2003a). But as AET also incorporates temperature, we evaluate productivity by net primary productivity (NPP) (e.g., see Bohadalková et al. 2021). Thinking of historical or evolutionary factors, we could also include topographic range in elevation as a surrogate of isolation and, thus, the chance of speciation. This process may also be associated with temperature shifts between the last glacial maximum and the present (expressing geographical patterns of climatic stability in the Quaternary), promoting recent diversification. On the other hand, deep time diversification could be expressed by analyzing phylogenetic patterns and calculating the mean diversification rate in each region (see Chaps. 6 and 7). It is common to generate OLS models or GAMs for each of these variables expressing representational models of alternative theories and compare their AICs, looking for the smallest one. However, considering the theoretical context previously discussed, it is more interesting to compare models based on theories that are not “mutually exclusive,” as combinations of these variables can explain “different parts” of data (Sect. 1.2.2). For instance, the temperature may be positively correlated with richness, but this relationship fails in deserts because of another factor (water availability). So, rather than fitting a single model for each variable, we can look for different combinations of variables that would improve the representation of the empirical data. It is possible to use an exhaustive search for multiple combinations of variables and search for the best model among all possible combinations. Although Burham and Anderson (2002) condemn this strategy as a kind of data dredging, in this case,

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it is important to realize that the theorizing component appears in the variable selection, as hundreds or even thousands of geographical and climate variables would be added to an entirely exploratory model. Moreover, underdetermination issues suggest that multiple paths would indeed be possible to link them under distinct ecological and evolutionary mechanisms (see Chap. 6). The model with all variables and the one with all variables but temperature stability are the minimally adequate models with ΔAIC smaller than 2. The model without temperature stability has an AICw of 66%, against 33% of the full model (so we can say there is a 66% chance that this is the best model among those selected). The model with all variables explains approximately 69% of the total variance in richness (the adjusted R2). It is also interesting to look at the standardized regression coefficients of the variables in the model to evaluate their relative effect sizes, and we see that temperature has the largest standardized effect (−0.447). However, NPP and precipitation also have higher coefficients, equal to 0.369 and 0.217, respectively (and the other variables have minimal effects). Notice that even without considering P-values, AIC-based model selection may also be affected by problems related to model misspecification and underestimation of errors due to autocorrelation, so these results are only illustrative (see Diniz-Filho et al. 2008a). For predictive purposes, it is also possible to estimate an average of the coefficients for each variable in all tested models, using the AICw as weights (i.e., multi-model inference). Still, in this case, as the two models are similar in terms of the selected variables, there is practically no difference between coefficients from the full model and the weighted-average coefficients (but in other situations, they can differ). Finally, it is also interesting to note that a multiple GAM model improves data representation, with an R2 = 75%, with higher relative importance of NPP and a much more significant effect of diversification. The use of AIC (or other related approaches) to select the model that better represents the data, comparing alternative models, consistent with many philosophical views. First, we have the idea of Lakatos (1978) of multiple competing hypotheses supporting one or more core theories that should all be examined and compared within their frameworks (see Hilborne and Mangel 1997). Multi-model inference can also be related to a popular framework called “strong inference” (Platt 1964). Platt’s idea is to develop a sequence of tests and experiments or observation tests so that hypotheses or theories are successively eliminated. The one that passes all tests must be true, in a “Sherlock Homes” approach. All these approaches contrast with more traditional views of hypothesis testing in terms of confirmation and refutation, in which hypotheses are tested individually. For instance, although “strong inference” has been widely viewed as a more generalized Popperian approach, it works in a cascade of tests to eliminate untruth or less likely hypotheses and confirm the final remaining one as true. However, this is not Popperian as there is no guarantee that these are all possible theories and because eliminating these other theories does not confirm the final one. Even so, Godfrey-Smith (2016) calls attention to the fact that model selection can be viewed not as a form of induction (confirmation) but instead as a methodological strategy to eliminate alternatives, more consistent with a Popperian view in a broad sense and particularly interesting in model-based

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reasoning. In addition, different models, including different variables, could be considered equally good when using multi-model inference. An interesting practical issue arises more explicitly when using AIC, concerning model complexity and parsimony. It is common to think in natural sciences that models should be as simple as possible, derived from “Occam’s razor” idea dating from the thirteenth century. The overall reasoning can be expressed as something like if simple explanations are available, it is pointless to look for more complex ones. AIC explicitly balances model fit (likelihood) and parameterization, so simpler models have an advantage if they have similar fits. But, as Coelho et al. (2019a) argued, important practical and conceptual problems underlying parsimony must be better understood. First, in a more practical and operational sense, AIC does not always produce the most parsimonious solutions, and there are other possibilities (e.g., Bayesian information criteria, BIC). Moreover, it is critical to pay attention that applying AICs for model comparison provides minimally adequate or more parsimonious. However, this minimally adequate model is not necessarily good (evaluated, for instance, by its R2) because, as pointed out above, AICw gives a chance that one is the best model within the set of models compared, so this is only a relative metrics. Indeed, there are some debates around the use of AICw and overestimating the relative importance of explanatory variables (Galipaud et al. 2014; Giam and Olden 2016). In a more general and philosophical sense, there is no epistemological justification for parsimony, at least not independent from other much deeper philosophical issues (Coelho et al. 2019a). Suppose one wants to use the models mainly for prediction. In that case, there is no problem with applying parsimony as a methodological criterion, as there is a tendency for more complex models to mix signal and error (the overfitting issue). However, suppose the goal is to understand a system. In that case, parsimony assumes that, from a fundamentalist point of view, nature is simple and governed by a few laws independent of anything, as pointed out above. This was a metaphysical approach defended in the eighteenth century from a theological point of view, but this is hardly a defensible assumption when most scientists and philosophers of science adopt a naturalistic view in the broad sense of the world. So, different interpretations and reasons for simplicity of nature are required (notice that this is part of the discussion between semantic and pragmatic views of theories, as pointed out earlier in this chapter). Thus, the debate on parsimony encompasses the issues of realism and instrumentalism in model building and interpretation, with parsimony making much less sense under realist view. Indeed, supporting this last sentence, and as discussed more extensively in Chap. 6, it may be nontrivial to use a single variable (i.e., temperature) to represent or to be used as a surrogate of alternative theories. In short, the temperature may drive richness in many different ways. For instance, the temperature may express the amount of energy available to organisms and thus limit the overall population density that, in turn, leads to smaller numbers of species by alternative mechanisms (see Lawrence and Fraser 2020; Bohadalková et al. 2021). Also, the current temperature may be correlated with its variation so that places with higher temperatures may have higher diversification rates and thus accumulate more species due to distinct

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mechanisms of increasing speciation or reducing extinction. Thus, a common approach in macroecology and community ecology is to combine these effects, try to provide general evaluations, and classify them into broader categories (say, ecological and evolutionary) (e.g., Borcard et al. 1992; De Bello et al. 2017; see Sect. 3.2.3). In the case of global amphibians, for example, we could say that 65% of the variation in richness is “explained” by ecological surrogates (temperature, precipitation, and NPP). In contrast, the effect of evolutionary variables is close to zero, with a 3% of overlap between ecological and evolutionary datasets. At these phylogenetic and geographical scales, variation in amphibian richness is better explained thus by environmental conditions (water-energy balance and productivity) in each region, and no evolutionary signal appears clearly, at least using these surrogate variables for diversification (see Chaps. 5 and 6 for more discussion regarding the underlying roles of speciation and extinction dynamics on diversity). Finally, “regression trees” represent another quite exciting approach for modeling that has been used more recently in some macroecological analyses (e.g., Lomolino et al. 2012; Mendoza and Araújo 2022), which is part of a family of techniques, including some incorporating artificial intelligence machine learning approaches. The idea is to sequentially (hierarchically) partition the explanatory variables based on optimization criteria and then find a sequence of effects that describes the response variable. For the amphibian dataset, the results are consistent with previous multi-model inference, although it can give some new insights (Fig. 2.10). The first partition was found for precipitation, separating regions with values higher (wet) and lower (dry) than 683.5 mm. Within the dry regions, with a small number of species, the second partition is based on diversification rate, with a

Fig. 2.10  Regression tree applied to global amphibian data, using an ANOVA partition and minimum increase of 0.05 in determination coefficient R2 in each step. The circles indicate the mean richness (at log scale) for each of the partitions in the three explanatory variables

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higher mean richness of 6.4 species per cell found in regions where DR > 0.03. On the other hand, for wetter regions with more than 683.5 mm, the second partition is temperature, with the highest mean richness of 33 species found in hotter environments. Thus, in dry regions, the difference between low and high richness is more related to diversification rates, whereas in wetter regions, the difference is then explained by temperature. In comparison with previous results based on multiple regression and AIC selection, the main issue is that NPP does not appear in these first partitions, probably because it correlates with precipitation (that, as shown in the next section, possesses both direct and indirect effects on richness). On the other hand, the diversification rate, which does not have a high coefficient in the multiple regression model, appears in the second level of partition, but only for dry regions (in the wet region, diversification effects may be confounded with those from temperature). This analysis suggests a more subtle, perhaps nonlinear, and spatially structured effect of diversification that deserves deeper investigation.

2.4.5 Causality, Explanation, and Understanding Following the above discussion, it is appropriate to discuss important issues related to “causality,” which has profound philosophical implications and is connected to many aspects of previously discussed issues on theory and models. For a long time, researchers and philosophers, especially within the empiricist tradition, have been hesitant to talk about causes due to metaphysical issues related to a fear of going back to Aristotelian final causes and, especially in biology, due to other teleological matters and to the problems associated to establishing “how” and “why” questions in an evolutionary context discussed above. Also, dealing with causes leads to discussions about hidden, underlying factors, which may be challenging to investigate and would lead to serious debates about realism and the meaning of unobservable entities or processes emerging from theories (see Sect. 2.4.6). Finally, it has been difficult to deal operationally with cause-effect relationships except for experimental data (as a good experimental design may effectively rule out confounding factors). The points raised above are only some of the complicated philosophical issues related to causality. Despite difficulties, it is important to briefly discuss causality here mainly because, especially in modeling, it is common to equate “explaining” with defining causal relationships among variables (Godfrey-Smith 2021). In a broader context, it is also possible to relate explanation with unification, considering that a theory or model covers or predicts a wide range of previously unconnected ideas (i.e., Darwin’s theory of natural selection or Newton’s mechanics or, in principle, Brown’s MTE discussed above). Coupling these ideas of causality, unification, and explanation leads to the vaguer concept of “understanding,” which, as pointed out by Giere (1988), really refers to an emotional or psychological state of satisfaction with a given theory or model when compared with empirical data. In practice, it is easier to understand why we can merge the ideas of “Inference to the

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Best Explanation” (IBE) with Cartwright’s concept of “Inference to the Best Cause” (IBC), as pointed out by Psillos (2008), under the equivalence between explaining and defining a causal structure. It is interesting that, in standard statistical jargon and usually in the context of regression, it is common to say that a given X variable “explains” a given percentage of the response variable (i.e., based on the r2, we say that temperature variation “explains” part of the variation in richness). Some people think that this expression is formally equivocal and prefer to think of r2 in a purely predictive context and even use the term “predictor variable” for X (in opposition to “explanatory variable”). Although we sometimes do not pay attention to these terms and use them synonymously, there are deeper philosophical issues here, even though there is not much difference between explaining and predicting in the empiricist tradition (see Godfrey-Smith 2021). However, at least in the example of LDGs and amphibian richness, it is more common to think causally, so when we say “explain,” we are assuming that variation in temperature “drives” or causes variation in richness based on the underlying theories in a mechanistic and realist sense. In principle, satisfied with this “lower level” of understanding of theories or models, in the sense of knowing that temperature and NPP drive richness, and only list several potential causes for this as a guide for future investigation. It may be, however, possible to enhance our understanding by finding surrogate variables that may help test complementary or auxiliary hypotheses that allow disentangling alternative mechanisms. We are back to the discussions about explanation in realism, and instrumentalism or empiricism, involving the unobserved components of the theory (see Sect. 2.4.1). The randomized experimental design by R.  A. Fisher and others in the early twentieth century allowed an explicit definition of cause-effect relationships in relatively simple situations. Nevertheless, it is well-known that experimental studies are rarely possible when working in macroecology and complex evolutionary systems based on observational data for several reasons. Indeed, we are usually conscious that the relationship between richness and temperature that we observe may be simply an “artifact” (in a causal sense), and our formal training in statistics consistently reinforces the mantra that “correlation does not imply causation.” However, when we are confident that a correlation is “statistically significant,” we frequently start thinking about the underlying mechanisms that could explain the relationship in terms of how and why temperature would drive richness. So, as convincingly pointed out by Shipley (2016), in most cases a strong or significant correlation indicates a non-resolved causal structure among the variables. This idea is especially valid in a macroecological perspective when we are fully aware that this kind of explanatory variable must be viewed, at best, as a surrogate of mechanisms and processes. We now have tools based on a set of practical, axiomatic rules that may allow us, in practice, to define causality within an empiricist framework by establishing hierarchical and sequential relationships among explanatory variables, enhancing model fit, and improving our understanding of the world. This goal can be achieved using different statistical frameworks developed in the last 30 years, despite its origins in the 1920s in the work of the geneticist Sewall Wright.

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We can begin to understand the reasoning behind causal analyses by thinking, returning to our global amphibian example, if temperature “explains” richness directly (for instance, because of its evolutionary effect on diversification) or only as a component of productivity, expressed by NPP. In this case, we can use the idea of partial correlation to evaluate the correlation between richness and temperature after keeping NPP constant and the other pairs of partial correlations (see Legendre and Legendre 2012). The original correlation of richness and temperature under MTE was equal to −0.665 and dropped slightly to −0.644 after accounting for the effect of AET. At the same time, the original correlation between richness and NPP of 0.653 reduces to 0.631. These simple analyzes suggest that, although there is a weak correlation between NPP and temperature, equal to −0.308, their effects on richness are independent and equally overlapping (unique and independent effects of temperature and NPP are 23.7% and 22.2%, and their overlap equals 20%). We can generalize this reasoning for several variables and create a much more complex causal structure linking all variables in a series of models that can be generally called structural equation modeling (SEMs) (e.g., Shipley 2016). SEMs are designed to simultaneously test multiple hypotheses within one network that can include a complex set of paths with variables having both roles of predictors and response (Lefcheck 2016). Unlike stand-alone models, SEMs allow evaluating the quantification of cascading effects with variables linked by both direct and indirect effects. In addition, SEM has been assumed to be a primary language for causal and counterfactual analysis (Pearl 2015; Pearl and Mackenzie 2019) given how path diagrams should be designed. Path diagrams are built based on observations, experiments, and theory that support the assumption of causal relationships between variables, with the direction of causality explicitly designed into the path diagrams (Pearl 2015). It is possible to add the effects of “latent,” unknown variables (which, in our case, would express unmeasured mechanisms and effects). There are many details in using SEM that go beyond the scope of this book and interested readers should consult the specialized methodological literature (e.g., Beaujean 2014; Shipley 2016; Fan et al. 2016). The application of SEM to the global amphibian dataset confirms that the two main effects driving richness are NPP and temperature, as shown above for the model selection using AIC. Although it is possible to design more complex paths to test explicitly for more sounding theoretical expectations (see Fig. 6.5), we use the same environmental and evolutionary variables used in the previous section. So, the SEM’s path diagram (Fig. 2.11) shows that the effect of temperature is, to a great extent, independent of NPP. However, the effect of precipitation previously shown is both direct and indirect on NPP (so we expect more richness in wet environments independently of its productivity as well). On the other hand, temperature affects diversification rates DR, but its effect on richness is not along this path, and the direct effect is much larger (as the effect of DR is minor). These simple results are coherent with previous partial analyses and model selection based on AIC. Notice that, when using SEMs, it becomes clearer that, from a conceptual and philosophical point of view, statistical models discussed in this section can be viewed from a pragmatic point of view. One adds more and more available variables

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Fig. 2.11  Path coefficients modeling the variation in species richness of global amphibians based on temperature, precipitation, productivity (NPP), range in elevation, diversification rate (DR), and climatic stability. The coefficients in bold indicate statistically significant relationships (P 5000 mammal species and its statistical distribution is “observed” data. These data are all theoretically conceived, are abstract objects and, as such, are excellent examples that may help to understand the concept of model of data. Under the above reasoning, we can conclude that we rarely (if ever) have “observed” data in macroecology. However, we can keep the more general idea of empirical data for operational purposes.

3.2 Statistical Issues on Basic Macroecological Data 3.2.1 Null Expectations of Community-Weighted Means There are other more complex ways to process the information in M based on the scheme shown in Fig. 3.2. For instance, one can calculate β-diversity in different ways, such as using pairwise similarities among cells and extracting axes using ordination techniques that are also descriptors of assemblages. Alternatively, each cell can be considered a “focal” cell, and several metrics can be applied to calculate the difference in composition between this focal cell and the surrounding cells (Sect. 7.3). Using a slightly more complex matrix manipulation, we can integrate Q- and R-mode and calculate, for example, the mean body size (or any other attribute of interest) for the cells. In community ecology, this is usually referred to as “community-weighted mean,” CWM) so that a trait originally paired with species can be “translated” into the level of assemblages. In matrix notation, the vector with CMW is given as

CWM  S 1 M Y t

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where Y is the vector with the species trait (i.e., body size) and S is the vector of species richness (i.e., the sum of columns of M). This equation expresses that, for the matrix product, we are multiplying the vector of body size by the vector with presence-absences in a cell, then summing, and lastly, when we divide this by the number of species in the vector S, we have the mean body size in the assemblage or community (CMW). If matrix M is row-standardized to sum 1, each presence becomes the frequency, so again the sum of the product of the rows (across columns or the matrix product MY) directly gives the mean of the trait. This operation allows the translation of a variable measured at the species level (a cross-species variable) into a variable at the assemblage level that can be analyzed in an explicit spatial context (see Olalla-Tárraga et al. 2010). There are, however, some important statistical issues about CWM to consider. First, there is rarely comprehensive geographical data for a given trait for all species (i.e., intraspecific variation across the species’ geographic range), so in most cases, the vector Y above is a general (i.e., mean, median, range) value for the species, such as mean body size. If this is the case, thinking in product MYt above implies that the same values of Y are used to compute the mean of the assemblages throughout the species’ geographic ranges. This approach is usually considered satisfactory for macroecological analyses, although it may not be enough for local communities and assemblages (e.g., Cianciaruso et al. 2009; Bolnick et al. 2011). Consequently, species with large geographical ranges contribute to the mean values across several assemblages. Jetz et  al. (2012) and Rabosky et  al. (2017) used a weighting scheme based on the inverse of geographic range sizes (i.e., rarity in a continuous sense) to calculate CWM, so that broadly distributed species contribute less to the mean in any cell. This approach is interesting because the averaged value of the trait in an assemblage would be more influenced by the values from species that are more akin to that cell, namely, by geographically restricted species. For instance, if one is thinking in the Bergmann rule (Sect. 8.4.1) and testing if the mean body size of species found in cold regions is higher than those in the tropical areas, this weighting scheme leads to the idea that only those species that are more “typical”, or better adapted, to that region used (or have more weight) when calculating the mean. Indeed, a species found everywhere, independent of being small- or large-bodied, is not very informative about how temperature could drive mean trait values in any region. In addition to this more sounding biological reasoning, this weighting scheme based on the inverse of geographic range size reduces the intrinsic spatial structure in data caused by repeating the same trait value for the species across large regions. It would also be possible to use a more complex, spatially explicit weighting system based on the distance of the cell to the center of the species’ geographic range so that a species would give more weight to the mean if the assemblage is closer to its geographic centroid. Another issue to consider when someone is interested in modeling mean trait values in assemblages is when CWM correlates with richness, which is indeed its denominator (e.g., Steven’s 1989 discussion of Rapoport’s rule being an explanation for diversity gradients, see Sect. 4.3.3). Important artifacts may appear because of this intrinsic inverse relationship, especially regarding the variance estimates,

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which may affect classical hypothesis testing and model selection using AIC. The problem, however, may be more general and potentially affect different ecogeographical rules, as many of the environmental variables associated with these patterns are also potential drivers of species richness (which, again, is the denominator of CWM). The problem is, of course, more severe if one is interested in using this assemblage variable as a predictor of richness or the other way around. Although the weighting scheme based on geographic range size can reduce this problem to some extent, it may be essential to evaluate this potential problem more carefully. Hawkins et al. (2017) warn that randomly generated traits show correlations with richness, especially when assessing patterns using complex statistical models such as regression and classification trees, geographically weighted regression (GWR), and others (e.g., Sects. 2.4.4 and 3.2.3). If one correlates this trait with environmental variables that are potential drivers of species richness, similar artifacts may appear, in different situations, although with a small magnitude. There are many possible solutions for this problem using various randomization tests. Conversely, it is also possible to extract from M the mean value for a given species for variables measured in the cells. For example, it is possible to calculate the mean temperature within the geographic range of a given species, providing a simple descriptor of the centrality of the species along this dimension of the Grinnellian niche (see Sect. 5.2 for more complex alternatives based on multivariate analyses). This is indeed a crude, macroecological indicator of the center of species niche along this dimension, and its biological or physiological meaning is not entirely straightforward. Another possibility is to do this for the geographical coordinates (i.e., latitude), so we can get an idea of the position of the species in the geographical space. It is possible to derive more sophisticated statistics than average coordinates depending on available data, such as the mean coordinate by weighting abundances or using more complex geometric definitions for the center of the extent of occurrence accounting for its shape. Nevertheless, the idea is to get the species’ geographical center, or “centroid.” In these examples, the idea is to translate a spatial variable, such as temperature or the own coordinates of the cells or of the occurrences in which species are found, into a species-level measurement analogous to a species’ trait. One of the main problems to consider in this case is that the geographic range size of the species in M may vary a lot (see Chaps. 4 and 5), so this averaged value is not necessarily meaningful across all populations. For instance, if most species have small ranges and we are dealing with latitudinal centroid across a continent, we can have a reasonable idea of which species are, say, temperate or tropical. For widely distributed species, however, the mean by a mathematical constraint falls into the mean of the geographic domain, which is the basis of the problems related to the mid-domain effects (MDE; Sects. 4.2.3 and 6.2.1). We must remember that other statistics from the geographical coordinates or cell variables (i.e., temperature) can be used to describe the species, including maximum or minimum values and their variances. These other metrics, for example, have been used in the analysis of the Rapoport effect. Moreover, this possibility of using more complex ways to describe patterns in M is the basis for the very interesting idea of diversity and dispersal fields.

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This idea of getting means for cross-directions in M can be generalized and expanded, forming the basis for the concepts of diversity and dispersal fields discussed in the next section. If the goal is to analyze the correlation between species’ attributes and environmental or any other variable measured in the cells of a grid, perhaps the best approach is based on a multivariate solution to what is called “the fourth-corner problem” (Legendre and Legendre 2012). The idea is precisely estimating the relationship among the “marginal” columns and rows paired with M, although this interesting approach is not commonly used in macroecology.

3.2.2 Diversity Fields, Dispersal Fields, and Regional Pools In the previous sections, we discussed the two dimensions of M as independent, dealing with spatial units in rows and species in columns and showing how they can be coupled with other variables of interest in cross-species and assemblage approaches. We showed how variables along one of these dimensions could be translated into each other’s direction, creating new variables that are analyzed independently from each other and paired with different variables to test hypotheses. Nevertheless, the situation becomes more complicated when considering geographic range size, which is an implicit variable calculated directly from the elements in M. At the same time, it offers more opportunities to explore the data structure. Can we say that these two variables are independent when we calculate, for instance, the mean geographic range size in an assemblage based on a given richness (which was also obtained directly from M)? Does the distribution of zeros and ones in a binary M create potential patterns or constraints in these variables that can inform some structure in ranges and richness to reveal co-occurrence patterns? These ideas open the possibility that more complex calculations may be necessary to deal with patterns in M. If we calculate, for a given assemblage, some statistics describing the geographic range size distribution for the species found there, we can obtain its “dispersal field” (Graves and Rahbek 2005). It is easy to understand the biological meaning of these statistics using the mean or median of geographic range sizes to define the region of influence of a focal cell in terms of species composition (notice that this idea relates to the concept of β-diversity discussed in Sect. 7.3). In Fig. 3.3, the dispersal field of locality A is larger than that of cell B, situated northern in the domain. A more consistent metric for the dispersal fields is the overall overlayed area of the geographic ranges of all species found in this place. However, this metric can be biased by the skewed distribution of geographic range sizes. Indeed, Graves and Rahbek (2005) mapped the skewness of the distribution of log-transformed geographic ranges in a cell as a metric for dispersal field in a more general modeled evaluation of the magnitude of influence. In this case, higher skews express a higher “influence region of the focal cell” regarding geographic distance (Fig. 3.4). Still, it may also be important to evaluate some measure of central tendencies, such as mean or median. There are thus several alternatives to assess the dispersal fields based on a description of

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Fig. 3.3  The definition of dispersal and diversity fields, based on the overlap of elliptical geographic ranges for six hypothetical species. For locality A, the dispersal field is defined as the combined overlap of the geographic ranges of species 1, 2, and 3. In contrast, locality B is defined by the overlap of species 3, 4, 5, and 6. If the richness patterns within the geographic range are analyzed, we can obtain the diversity field for that species. For instance, we can get a transect along the geographic range of species 6, and the mean richness of co-occurring species would be equal to 2 (ignoring the zero)

Fig. 3.4  Geographic patterns of skewness of log-transformed geographic range size of amphibian species globally, measuring each cell’s dispersal field (Graves and Rahbek 2005)

the distribution of geographic range patterns and their overlap. As discussed below, this is conceptually interesting to define regional pools or, more appropriately, under a macroecological perspective, the “biogeographic species pools” (see Lessard et al. 2011; Carstensen et al. 2013).

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Conversely, Arita et al. (2008) define the “diversity field” by calculating statistics for the variation in diversity within the geographic range of each species (richness or any other descriptor of the assemblage, such as phylogenetic diversity; Villalobos et al. 2013a and Sect. 7.1; see also Pie et al. 2023). Therefore, diversity patterns of co-occurring species become a trait of the species. For example, in Fig. 3.3, we can see that species six co-occurred with three, two, or one other species along a transect within its geographic range, resulting on average in two species for three points (i.e., cells) evaluated. We can calculate this average for many more assemblages in a grid overlaying the species’ geographic range and then obtain the mean richness for each species. It is interesting to realize that, in this case, the richness of cooccurring species turns into a species-level trait and could be used in further comparative analyses. For example, Villalobos et al. (2013a) generalized the diversity field to phylogenetic diversity and showed how it could change through time using paleontological data (see also Villalobos et al. 2016). Arita et al. (2008; see also Arita et al. 2012) proposed a general framework to display simultaneously the relationship between geographic range size and richness through “range-diversity plots,” which incorporates data on both dispersal (species) and diversity (cells) fields. Note that Arita et al. (2008) presence-absence matrix is transposed with respect to matrix M as defined above, so be aware that the notation in of rows and columns is inverted here. Range-diversity plots can be built by species or by sites. In the former, each point in the scatterplot refers to a species. The axis represents the proportional range size (i.e., the geographic range sizes divided by the total area of the domain, so a species that occurs throughout the entire domain has a proportional range size of 1) against the mean proportional species richness within the range (the mean richness within the geographic range divided by the total number of species). Arita et  al. (2008) added to this plot isolines of covariance among species, defined by co-occurrence patterns and limiting the distributions of points (Fig. 3.5a). In addition, Borregaard and Rahbek (2010a) proposed an easier way to understand the limits given by empirical data. For example, in Fig. 3.5, the upper limit of proportional species richness for geographic range size equal to 1 cell is given by the maximum richness in the domain (regardless of whether this exists in the dataset or not). For a geographic range size equal to 2, the upper limit would be given by the mean of the two cells with the highest richness in the domain, while for a geographic range size equal to 3, the value would be given by the mean of the three highest richness, and so on. Following the same reasoning, we can calculate the lowest possible limits so that for a geographic range equal to 1, the lower limit is given by the minimum observed richness in the domain. We can plot these two curves in the range-diversity plots and evaluate the distribution of points within these limits. Inverting the reasoning and the direction of analyses of M, we obtain range-­ diversity plots by cells (Fig. 3.5b). These plots show the proportional species richness (i.e., the ratio between richness in each cell and the total number of species) against the mean proportional range size, which is the mean range size in each cell divided by the total area of the domain, delimiting the upper and lower limits and constraints in the same way. In general, the idea is that if the points (cells or species)

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Fig. 3.5  Diversity and dispersal evaluation using the plots of mean proportional richness and geographic range size proposed by Arita et al. (2008) for global amphibians. Both plots show a large concentration of small ranges and low richness. Histograms show the frequency distribution of y and x variables. The solid black line delineates the upper limits for points, while the gray curves show the lines of equal covariance among species

are concentrated in parts of this limited space, ecological or evolutionary processes may drive the distribution of ranges and their relationship with richness. Alternatively, species can be distributed more or less homogeneously in this space, indicating that, in principle, the properties of range size can be explained by richness and vice versa. It is possible to use several distinct null models to evaluate the occupation of these spaces (Borregaard and Rahbek 2010a; Borregard et al. 2020). Despite the conceptual and applied interest in biodiversity conservation (see Villalobos et al. 2013b, c), the interpretation of range-diversity plots is complicated by several issues. Soberón et al. (2021) recently proposed a much simpler normalization for the range-diversity plot that may allow a more straightforward interpretation of the patterns. Finally, an important ecological issue widely discussed in ecology and appears in the context of dispersal fields is the relationship between local diversity and the regional species pool (e.g., Ricklefs 1987). There is a long debate in ecology about the saturation of local communities, so even when a given region contains many species, the local assemblages are limited to a smaller set of such species. Traditionally, the reasoning is that assembly rules (mainly discussed in biotic interactions) “filter” which and how many species can coexist locally. The sequence of local colonization events may determine these rules, and so on. Conversely, local assemblages may be defined randomly through a neutral process but are locally limited by environmental factors (so the composition varies at random, but richness is small). Regardless of the ecological processes defining the richness and composition of local assemblages, this is directly related to the β-diversity at that scale (Arita et al. 2008).

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However, from an operational point of view, all these issues are hard to evaluate because it is not simple to define the regional pool of species that would potentially colonize and compose the local assemblages. It is possible to think that the regional pool is the sum of all distinct species in any of the local assemblages or to define it by some external criteria (i.e., all species found in the continent, biogeographic region, or biome to which local assemblage belong; Kissling et al. 2012). However, an exciting application of dispersal fields previously discussed is precisely to provide a better way to determine the regional species pool. As the dispersal field of an assemblage can be defined by the total area given by overlaying the geographic ranges of all species found on it, the regional pool would be defined as all species found in this total overlaying area (i.e., whose geographic ranges overlap the total area of the dispersal field; Lessard et al. 2011).

3.2.3 Spatial and Phylogenetic Autocorrelation Recall that the rows of the matrix M (assemblages) can be paired with geographical coordinates, whereas its columns (e.g., species) can be paired with metrics of phylogenetic structure expressing species divergence throughout evolution. In both cases, the continuity of the ecological or evolutionary processes and their distance-­ dependence in space and phylogeny leads to autocorrelation patterns. In short, closely phylogenetically related species or nearby cells tend to be more similar for a given trait or variable because of these processes, regardless of the relationship with other variables. Ultimately, the observations may not be statistically independent from each other, thus violating a basic assumption of most classical statistical tests. It would be hard to review here all statistical and computational methods developed to deal with spatial and phylogenetic autocorrelation in ecological data in the last 30 years or so. However, there are many excellent texts and reviews about the different approaches available (e.g., Griffith 2003; Fortin and Dale 2005; Cadotte and Davies 2016; Paradis 2012; Mouquet et al. 2012; Legendre and Legendre 2012; Swenson 2019; Revell and Harmon 2022). Our goal in this section is to discuss the general ideas regarding these methods and characterize autocorrelation as an intrinsic statistical property of macroecological data. Thus, we can use different methods to describe the patterns that arise in geographic space and phylogeny and deal with inferential problems in hypotheses testing and model evaluation. The general idea underlying autocorrelation is that we can use methods to explore patterns generated by “contagious” processes in geographic space (e.g., higher dispersal possibility among neighbor cells or regions) and in the phylogeny (i.e., shared inheritance of trait value from a common ancestor by two species). Consequently, we can learn something about the ecological or evolutionary processes underlying trait variation and simultaneously consider the inferential problems created by such autocorrelation structures underlying the data. These two possibilities were epitomized by Legendre’s (1993) classical paper (in a spatial context) discussing autocorrelation as a “…trouble or new paradigm.”

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In the geographical context, it is common to refer to what is called Tobler’s (1970) “first law of Geography”, which says that “…everything is usually related to all else but those which are near to each other are more related when compared to those that are further away.” So, the first interesting question is to understand why this happens and why there are spatial patterns in data. Moreover, suppose this “law” applies. In that case, the problem is how we can distinguish if the association between two (or more) variables in a given region is due to a causal relationship among them or if this is only a coincidence created by shared stochastic spatial processes. For instance, we can find a region with high species richness not because it has high productivity (i.e., available water and energy) but because, regardless of its productivity, for some reason, the adjacent region has many species that disperse into the area under study. Thus, at a broad spatial scale, two effects may be confounded and jeopardize the test of the productivity effect on richness, inflating the Type I error (i.e., erroneously rejecting the null hypothesis) of any standard statistical analysis applied to this data. Also, autocorrelation causes problems even when using AIC approaches rather than classical hypothesis testing, as the origin of the problem is that errors of regression or correlation coefficients are underestimated (see Diniz-Filho et al. 2003, 2008a). Since it is nearly impossible to directly evaluate specific dispersal processes at broad scales, we can infer that this process creates a short-distance geographical structure that must be considered when analyzing productivity’s effects. Moreover, if the processes that generate high or low productivity are also spatially structured (at broad scales, we know that temperature and productivity have a strong latitudinal gradient and autocorrelation appears as trends as well, although technically, there are some more complicated issues here), autocorrelation in both variables may create geographic coincidences in patterns. Consequently, there would be an upward bias in Type I error of classical statistical analyses applied to this dataset. Notice that spatial autocorrelation also appears, in a more operational sense, by mismatches in resolution between data and cells due to scale issues, as discussed in Sect. 3.1.2, and because of the model of the geographic range we choose (Lichstein et al. 2002; Knegt et al. 2010). If we have, for example, very fine grains in a grid but species’ geographic ranges are not precisely defined at this same resolution, adjacent cells have similar species composition regardless of any other property of the cell. In this case, it becomes clear why we can also refer to autocorrelation as a pseudo-replication problem. Diniz-Filho et al. (2003) showed, for instance, that the discussion about how the relative magnitude of coefficients shift when using spatial and non-spatial regression methods is, to a great extent, due to these scale issues (triggering what we can call “the red shift” debate in geographical ecology, referring to the idea that spatially structured explanatory variables have an upward bias in regression coefficients due to autocorrelation effects; see Lennon 2000; Hawkins et al. 2007d; Beale et al. 2007; Bini et al. 2009; Gaspard et al. 2019; Currie et al. 2020; Kim 2021). From a phylogenetic point of view, the evolutionary diversification of a trait along the speciation-extinction dynamics creates a pattern because the two species branching from a recent common ancestor tend to inherit many of its characteristics.

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Thus, closely related species tend to be more similar for these characteristics than less related species. This relationship between the difference for a trait and the time since divergence among species depends on the evolutionary mechanisms that drive trait variation and how it responds to environmental changes. In such cases, divergence patterns may give some clues about the underlying processes of trait evolution (i.e., Hansen and Martins 1996; but see Revell et al. 2008). However, the main worry when thinking about phylogenetic autocorrelation has been that inflated Type I errors suggests several misleading adaptive processes inferred by cross-species comparisons and correlation between traits or between traits and environmental components (Felsenstein 1985; Cheverud et al. 1985; Martins and Garland Jr 1991; Martins 2000). It is somehow curious to see that this issue was intuitively pointed out by Charles Darwin in 1859, when he wrote that: We may often falsely attribute to correlation of growth structures which are common to whole groups of species, and which in truth are simply due to inheritance; for an ancient progenitor may have acquired through natural selection some one modification in structure, and, after thousands of generations, some other and independent modification; and these two modifications, having been transmitted to a whole group of descendants with diverse habits, would naturally be thought to be correlated in some necessary manner. (C. Darwin’s Origin of Species, 1859)

Operationally, we can now start by thinking about the patterns in data, focusing on a single variable. A common way to evaluate patterns both in space and phylogeny is to use Moran’s I autocorrelation coefficient, which is given by: I

n Sw

  W  y  y  y  y  y i

j

ij

i

j

 y

2

i

i



where y is the variable to be analyzed and Wij is the element of the matrix W with the weights expressing the relationship among n species or spatial units (i.e., neighbor or not, or some form of inverting distances). The SW is the sum of elements in W. Moran’s I is analogous to a Pearson correlation, varying between 1 and −1 for maximum positive (i.e., close cells or species are similar for y) and negative (close cells or species are very different for y) autocorrelation, respectively. There are some constraints and specific formulae for standardization currently available that better define these maximum values. Departures from the null expectation of absence of autocorrelation estimated by Moran’s I (i.e., equals to −1/(n−1)) can be tested analytically or by permutation approaches (see Sokal and Oden 1978a, b; Legendre and Legendre 2012). It is common in ecology and evolution to use not a single Moran’s I based on W to express the “global” autocorrelation but rather to partition this weighting matrix into several matrices W1, W2, W3 … Wk. These matrices describe the relationship of species or spatial units at increasingly distances, usually as binary matrices stating that the pair of species or cells are connected at that distance interval. We have a correlogram when Moran’s I coefficients calculated based on each of these matrices are plotted against the distance class. For example, the correlogram for bird

Fig. 3.6 Moran’s I correlogram for geographic patterns in species richness for South American birds (a) and phylogenetic patterns in body size evolution among the order Carnivora terrestrial mammals (b). For the geographical correlogram, distances are the upper limits of distance classes in kilometers, and solid circles represent the autocorrelation in richness. In contrast, the crosses represent Moran’s I of model residuals from a multiple regression model with eight environmental predictors that explain about 80% of the variation in richness. For the phylogenetic correlogram, crosses indicate Moran’s I for the residuals of body size against phylogenetic eigenvectors, with an R2 = 0.597. In both cases, autocorrelation patterns in the original variables were strongly reduced after modeling, although some data structure persists at the shortest distance classes. For the Carnivora, the matrix W comes for patristic distance in the maximum credibility tree from a Bayesian analysis based on molecular data

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richness in the Neotropics shows positive autocorrelation at short distances coupled with negative autocorrelation at long distances. However, at maximum distances, autocorrelation tends to be close to zero (Fig. 3.6). This is coherent with known latitudinal gradient in which adjacent cells have very similar richness, regardless of their position in the map, i.e., close cells in the Andes are similar because they have high richness. In contrast, adjacent cells in Patagonia are still similar as they have low richness. Simultaneously, the long-distance negative autocorrelation indicates that cells further apart have largely different richness, for instance, when comparing a cell in the northern Andes with one in Patagonia. However, at very long distances, there may also be cells with similar richness but situated much far apart (e.g., cells in the Atlantic Forest, Northern Amazon, or Central America, with high richness as well), so the differences in similarity cancel each other and autocorrelation tends to zero (see also Fig. 6.2). We can also calculate a correlogram for a trait measured for several species, in which phylogenetic distances define the matrix W. For instance, body size in terrestrial Carnivora mammals has a positive autocorrelation at short distance classes, which decreases with distance and then stabilizes at a given point (i.e., about 40–50 million years of divergence). Thus, in this case, although phylogenetically related species separated by a few million years (i.e., species within the same genus, subfamily, or alike) tend to have similar body sizes, when we are comparing distantly related species in the phylogenies, we can have combinations of highly different pairs of species. For example, a tiger is not that different from a bear in terms of body size, despite their long divergence, but at the same time, a bear is quite different from a small mustelid. Therefore, a correlogram provides a more comprehensive description of the phylogenetic structure in data and may be much more informative than a single Moran’s I. Many other autocorrelation coefficients, with slightly different properties, can be used in spatial and phylogenetic comparative analyses (in the latter, we usually talk about estimating the “phylogenetic signal” in data  – see Blomberg et  al. 2003; Münkemüller et  al. 2012). Moreover, in the context of phylogenetic comparative analyses, a widespread practice is fitting models to the data based on theoretical expectations of the relationship between species covariance in the phylogeny and a given trait (see Davies 2021). The basic evolutionary model is Brownian motion, which generates a linear relationship between these two covariances. If the relationship is not linear, it is possible to fit distinct models based on branch length transformations in the phylogeny. In some cases, the parameter used for this transformation is a metric for the phylogenetic signal, such as Pagel’s λ or the α from an Ornstein-­ Uhlenbeck (O-U) model, among others (see Pagel 2002; Hansen et  al. 2008). Another common metric is Blomberg’s et al. (2003) K, which indicates if a trait is evolving faster or slower than expected by Brownian motion. These metrics are further discussed in Chaps. 5 and 8 when evaluating phylogenetic niche conservatism and patterns in body size evolution (see Cooper et  al. 2010; Münkemüller et al. 2015).

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As previously discussed, when we have these phylogenetic or spatial patterns in data, it is more difficult to establish their correlation with other variables and to fit a statistical model. The problem is that we have an inflated Type I error, which is easily demonstrated in a phylogenetic context (it was indeed the main worry and motivated the application of phylogenetic methods in macroecology, e.g., Blackburn 2004). Suppose we use a given phylogeny to simulate the evolution of two independent traits under Brownian motion, which is usually done in practice by a stochastic process in which the trait “tracks” the phylogeny, evolving by small random changes along each of its branches. We can think algorithmically as if the trait starts evolving with a given starting value in the root and, at each time step, there are small random changes (the variance of the changes is the rate of evolution). When there is a speciation event (i.e., a node in the phylogeny), the trait starts to evolve in each of the new lineages independently but with the same starting value of the node that gave origin to the two lineages. The process “climbs up” to the tips of the phylogeny, with n species. Therefore, if we have, for example, two closely related species, they share the trait value that evolved from the root of the tree up to this last node and then have only a short time to diverge from each other, so they tend to be quite similar. This simple process generates the phylogenetic autocorrelation that can be evaluated by Moran’s I discussed above or by fitting an evolutionary model. Next, suppose that we have two of these processes along the same phylogeny, representing two traits, and all the stochastic process of trait differentiation along the phylogeny happens independently. We expect to have a zero correlation at the tips, and if we repeat this 1000 times and obtain the correlations, indeed, the average is close to zero (Fig.  3.7). However, the distribution of correlations has a much larger variance when compared to a simple distribution of correlations obtained by randomly generating the two vectors with size n. So, we can see that, although the two traits are independent, if they evolved along the same phylogeny, it is expected to have higher (positive or negative) correlations, exceeding the critical values under a standard null distribution of Pearson correlation. If we assume a typical Type I error of 5%, we expect that only about 50 in 1000 simulations are significant, but in our simulations, there are indeed 73% of significant (P  1 indicates evolution faster than Brownian motion along the entire phylogeny but does not consider variation in evolutionary dynamics within and among clades. So, if variation within clades is smaller than expected but clades are very different, this is consistent with ecological niches being close to clades’ adaptive peaks (optima). For instance, the idea is that we have two clades that diverged long ago, separated very early in the phylogeny, and are very different from each other in ecological niches (i.e., anurans and salamanders that tend to be more tropical and temperate, respectively). If niche evolved under Brownian motion, or O-U, we would expect much more variation among them because of the long time for divergence. However, suppose these clades tend to retain each of their ecological niches. In that case, there is a considerable variation among clades (as they accelerated early in time), but smaller than expected variation within each of them (i.e., if a model is fitted independently to each one, an O-U more likely shows a good fit). This pattern is indeed the pattern reported by Hof et al. (2010) in a first paper using K to evaluate PNC in amphibians at the global scale. It is always important to highlight that phylogenetic patterns in ecological niches are complex, and it may be challenging to get a high fit of simple models to data. In some cases, patterns may differ among distinct clades and thus violate the assumption of stationarity underlying these models. Thus, it is always interesting to have methods that allow a visual inspection of patterns and may help identify this complexity, such as the phylogenetic signal-representation (PSR) curves (Diniz-Filho et  al. 2012a, 2015). It is beyond the scope of this chapter to give details on the

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methodological development of the method, but, in short, the idea started with the possibility of describing the patterns using eigenvectors extracted from a pairwise phylogenetic distance among species, which we called phylogenetic eigenvector regression (PVR) (Diniz-Filho et al. 1998) (recall Sect. 3.2.3 for a general discussion on spatial and phylogenetic autocorrelation). In the first moment, the idea of PVR was to use phylogenetic eigenvectors to model trait variation to evaluate the magnitude of phylogenetic signal and take into account upward bias in Type I errors when correlating two or more traits and inferring adaptation. However, the PVR estimates depend on the number and relative explanation power of each eigenvector (its eigenvalues). Diniz-Filho et al. (2012a) then showed that if the R2 of the successive PVR models sequentially incorporating the eigenvectors is plotted against the cumulative explanation in the eigenvalues, it allows a visual inspection of phylogenetic patterns in a trait (see Fig. 5.9). For instance, under Brownian motion, a 45° PSR curve is expected, as the phylogenetic component of the trait (the R2) entirely depends on how the phylogeny is represented by the eigenvectors (the cumulative eigenvalues). Accordingly, a PSR curve above the 45° corresponds to a trait evolving faster than Brownian motion (with Blomberg’s K > 1), and a curve below 45° indicates a constrained evolution, coherent with K  S) is that it assumes that E directly affects J in a linear (or at least monotonic) way. However, more complex paths reflecting other

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ecological mechanisms are likely to occur in nature. For instance, the path depends on the shape of SAD, on how species niches evolve, and on how efficiently each species uses the available resources (so it is crucial to distinguish available and utilized energy). Therefore, it is necessary to consider how E drives population dynamics and triggers both speciation and extinction. Moreover, J and S are linked independently of E, as extinction (or emigration) of a particular species opens space for other species to increase their local abundances. All of this is mediated by variable levels of interspecific competition. There may also be more complex effects of productivity in speciation, although these are more difficult to quantify from macroecological data. Anyway, irrespectively, these more complex potential paths open additional possibilities to investigate and integrate or unify multiple theories to explain richness gradients. However, at the same time, it is difficult to evaluate and generalize such theories related to MIH due to the lack of detailed population data for each species. Moreover, some of these relationships of E with J can also appear under neutral dynamics, opening other opportunities for integration and unification pointed out in Sect. 2.2. As previously pointed out, the effect of temperature on richness can be traced back to the origins of biogeography, with von Humboldt in the early nineteenth century. Still, there are many different paths in which this effect would drive richness. Early interpretations of positive relationships between richness and temperature were usually based on the general idea of the “more energy hypotheses” and MIH previously discussed. However, there is also the idea that temperature increases overall metabolic rates and affects many life history parameters, such as reducing generation time (which may increase J, as expected by MIH) (Brown 2014). More importantly, higher temperatures may increase mutation rates, thus allowing higher speciation and diversification rates (see Rohde (1992) for an early proposition). As extensively discussed in Chap. 2, Allen et al. (2002) developed a formal model to explain latitudinal diversity gradients in the context of the metabolic theory of ecology (e.g., Brown 2004). The novelty of the model proposed by Allen et al. (2002) is that it predicts a slope for the relationship between the logarithm of species richness and the inverse of temperature, allowing explicit tests of the model. The rationale of the model starts by assuming that, in each assemblage, the total energy consumed by the population of a given species is independent of its body mass (the energetic equivalence rule, EER) and the temperature. As individuals in hotter regions have higher per capita energy consumption, local populations should have lower densities, and thus, species richness is higher to satisfy EER. Later, Allen et al. (2006) developed an alternative model coupling MTE and Kimura’s neutral evolutionary theory (and, consequently, also consistent with Hubbell’s NTE), in which a positive relationship between mutation rate and temperature explicitly explains richness variation. This model leads to the idea of higher speciation rates in hotter regions and arriving at the exact prediction of the original 2002 model (see Storch 2012 for a discussion of problems in defining abundance and density in the model and for a detailed comparison of 2002 and 2006 MTE models for richness gradients).

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Note that although the speciation rate in MTE models is correlated with energy (i.e., temperature), generating the latitudinal pattern, this is not an equilibrium model and does not involve a balance of speciation and extinction driving species carrying capacity. In principle, the number of species would increase exponentially everywhere, even though, at any given time, tropical diversity would be higher than in temperate regions (Fig. 6.6). Even if a minimum temperature in which equilibrium appears, the differences in richness along the gradient are not driven by different equilibrium points. It is also possible to produce another model by coupling MIH and energy-driven speciation rates, enhancing the patterns (e.g., Allen et al. 2007). In that case, a speciation-extinction equilibrium could appear because the link between MIH and richness gradients involves extinction rates. There have been much debate about these metabolic models, with some analyses supporting the idea of MTE applied to richness gradients (see Storch 2012). However, both Algar et al. (2009) and Hawkins et al. (2007a) initially showed that the model does not fit data well for many empirical macroecological datasets. For instance, Hawkins et al. (2007a) analyzed 46 datasets and showed that the distribution of slopes calculated for each of these datasets is widely distributed around zero (from both OLS and restricted major axis (RMA) regressions) and not aggregated around the expected slope of −0.65 (see Gillooly and Allen 2007 for a reply). More recent analyses support the overall conclusion that the effects of temperature are widely variable and not consistent for many groups of organisms and generally much lower than those of productivity (Bohdalková et al. 2021). Another idea is to generate a more hierarchically organized structure of the effects under MTE so that models fit data reasonably well under particular circumstances, turning back to the “ceteris paribus” argument when discussing the roles of theories and models (Cassemiro et al. 2007). Bohdalková et al. (2021) conducted a detailed empirical and comparative analysis of the statistical effects of temperature and productivity on richness gradients that they called species-temperature relationship (STR) and species-productivity relationships (SPRs). Their analyses were based on the datasets organized by Hawkins et al. (2007a) and on hierarchical analyses throughout the phylogenies of several clades of mammals, birds, and amphibians worldwide. In addition to measuring the relative explanatory power (R2) of each of the two variables (temperature and productivity), they evaluated the effects of taxon size, area, variation, and mean values of each variable on explaining the coefficients of determination. They showed that STRs are generally weaker and more variable than SPRs, which are stronger and more widespread. On the other hand, it is possible to explain patterns in STR by the amplitude of variation and mean temperature of the dataset, so STR is more context-dependent. STRs are stronger for lower mean temperatures and in regions where variation in productivity is higher. These results are partially in line with the proposal by Hawkins et al. (2003a, b) that the limiting factor in higher latitudes is energy (temperature), whereas in tropical regions, the limiting factor is water availability, measured by annual rainfall or AET (see also Vetaas 2006; Whittaker et al. 2007; Kreft and Jetz 2013). Nevertheless, even when STRs are significant in these regions, SPRs are also significant, suggesting that temperature drives richness

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mainly throughout productivity. Indeed, Barreto et al. (2021) supported this general “Hawkins conjecture” only for reptiles, analyzing global patterns of species richness for terrestrial vertebrates using nonstationary spatial analyses (GWR; see Sect. 3.2.3). The modal values of Spearman correlation obtained by Bohdalková et al. (2021) for SPRs in the datasets analyzed are between 0.2 and 0.6 for most groups (slightly higher for plants, insects, and reptiles). In contrast, STRs are much lower and close to zero, with many negative and nonsignificant correlations. Hawkins et al. (2003b) found that values of r2 for bird richness against AET can be as high as 0.8, depending on several methodological issues related to the extent, grain size, and the variable used as a surrogate for productivity (see also Kreft and Jetz 2013 for similar results for vascular plants). Even stronger correlations do not exclude the possibility that other ecological or evolutionary effects are involved in the richness patterns. So, although there seems to be a consensus that productivity drives (or most likely limits) the number of species in a region, it is important to consider other potential effects and to account for specific characteristics of the dataset and group of organisms under study. As shown in Chap. 2, patterns of amphibian richness at the global scale support these results, with coefficients of determination for NPP much higher than for temperature. Thus, there may be alternative ways to explain the roles of productivity and temperature in driving richness gradients based on equilibrium and non-equilibrium models and different abundance patterns. Whereas in MIH the richness gradient is driven by geographic (latitudinal, for simplicity) variation in J due to productivity, in the MTE models, J is assumed to be constant in geographic space, or at least independent of temperature. However, under MTE, the speciation rate varies geographically, and the theory does not assume equilibrium or even maximum limits for J. So, it is important to think independently with respect to these two possible abundance patterns, i.e., geographic variation in J tracking gradients and the saturation of local communities that are closer to a maximum J (regardless of its spatial patterns). The effects of productivity have usually been considered more clearly correlated with richness patterns, but this does not necessarily support MIH, as alternatives based on biotic interactions, ecological specialization, and niche partitioning remain, as discussed in the next section.

6.2.3 Climatic Stability, Biotic Interactions, and Ecological Specialization Rather than evaluating the effects of climate per se, as discussed in the previous section, it is also interesting to think about the temporal stability of the environment (more specifically, of the climate). This stability can involve both short (i.e., seasonality) and long-time scales (climate changes throughout the Pleistocene under Milankovitch cycles or even in deep time) and is the basis for several additional

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theoretical explanations for richness gradients. Interestingly, these explanations involve, in different ways, adaptive equilibria allowing populations of a species to persist in more stable regions, as the idea can be traced back at least to A. R. Wallace in the late nineteenth century. In addition, climatic stability is the basis for discussions of other macroecological patterns, including Rapoport effect previously discussed in Sect. 4.3.3 (see Tomašových et  al. 2016). The general idea of climatic stability also correlates to the overall effects of time and area, as stability promotes more area integration throughout time (Fine and Ree 2006; Fine 2015). The more direct models in which climatic stability affects speciation and extinction dynamics can be broadly divided into two issues. First, thinking in terms of seasonality, it is possible that species living in higher latitudes in which there are large variations in climate (mainly temperature) are well adapted to the more variable condition and have wider thermal tolerances and can have wider geographic ranges, as already discussed in the context of Rapoport rule (the climatic variability hypothesis; see Pintor et al. 2015). If coexistence reduces the likelihood of persistence of populations or species in these regions, richness tends to be lower (this is the link proposed by Stevens (1989, 1992) between richness and geographic range size patterns). Expanding the temporal scale and considering, for instance, climate shifts at the scale of thousands of years, such as during the Pleistocene, it is also easy to believe that a region with more changes would have higher extinction rates, as relatively more species are unable to track such changes (see Sect. 5.3). Complex orbital cycles (i.e., the Milankovitch cycles) generate what Dynesius and Jansson (2000) called orbitally forced range dynamics (OFRD), and the consequences of such geographic range shifts have been discussed in Chap. 4. This effect is much more accentuated in higher, especially northern latitudes, explaining the variation in richness between tropical and temperate regions. However, at the same time, Weir and Schluter (2007); see also Schluter and Pennell (2017) showed that in these regions, there may also be more opportunities for allopatric speciation due to OFRB and increasing isolation among fragmented ranges, so absolute rates of both speciation and extinction should be higher than in the tropics. In this case, richness patterns still depend on the relative balance between them, and the overall diversification rate is higher in the tropics (see next Sect. 6.3). Another impact of climatic stability, in terms of both seasonality and long-term historical stability, is related to physical aspects triggering habitat complexity, especially elevation. In the more stable tropical environments, climatic zones along elevational gradients will be more persistent and increase the isolation of populations and thus facilitate more frequent allopatric speciation, as previously described in Sect. 5.3.2 (see also Wiens 2004). This idea is synthetically expressed in Jansen’s (1967) influential paper “Why mountain passes are higher in the tropics,” and the process seems to be also involved in Rapoport’s effect and in LDGs (Hawkins and Diniz-Filho 2006; Tenorio et al. 2023) (see Chap. 4). This increasing isolation is also consistent with Weir and Schluter’s (2007) findings because, in more unstable regions, there is a greater chance of extinction by reducing area and complete habitat loss in warm periods.

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One of the ideas is that in more climatically stable environments, such as in the tropics, species can become more specialized and thus divide habitats and available resources more efficiently and therefore have narrower niches, allowing more species to share these resources, as previously discussed in Sect. 5.2.3. The richness gradient would then be explained by ecological specialization and finer resource partitioning by the species in tropical regions, regardless of abundance patterns. However, at the same time, higher productivity and warmer climates would promote more functional redundancy and decrease trophic specialization by promoting functional complementarity, especially at finer spatial scales (Luna et al. 2022; but see Sabatini et al. 2022). In this case, it is necessary to assume that J is limited and creates selective pressures for intraspecific and interspecifically specialization. Under MIH, these limits add even more species if selective pressures still hold with higher abundances. This effect is expected, for instance, if the strength of biotic interactions is also higher in the tropics, another idea developed by Theodosius Dobzhansky in his 1950 paper (see Schemske et al. 2009). Schemske et al. (2009) discussed multiple ways in which a higher magnitude and intensity of biotic interactions would drive richness patterns. Again, a higher speciation rate in the tropics is expected under habitat and trophic specialization, as well as coevolution, reducing extinction by allowing coexistence. Fine (2015), for instance, highlights the Janzen-Connell hypothesis developed in the early 1970s for explaining tropical diversification and involving stronger predation or herbivory driving multiple antipredator adaptations in prey or plants (see Comita et al. 2014). However, the evidence for stronger biotic interactions in the tropics is still inconclusive, especially in a macroecological context. There are many issues to solve, especially involving the type of interactions and the phenotypic adaptations involved (and if this leads to specialization or not), as well as evaluating scale and hierarchy issues that would entirely shift these relationships (see Martín González et  al. 2015). It is interesting to note that it may be challenging to evaluate paths of biotic interaction leading to higher speciation and lower extinction rates discussed by Fine (2015) because a past higher specialization due to stronger biotic pressures would reduce the intensity of interactions and allow coexistence reducing extinction rates. If this is the case, it would be important to have independent data for the strength of interactions and past and current selective pressures, which are very difficult to obtain, and evaluate both tropical-temperate differences and temporal dynamics (and eventually their interaction). It would be possible to assess past faunal and flora dynamics in terms of functional diversity and morphological indicators of interactions if good fossil data is available (Braga et  al. 2020, 2021). There would be statistical difficulties in separating the effects of the current environment (i.e., temperature or productivity) from historical stability or seasonality, as they are usually strongly colinear at macroecological scales. Theoretically, more stability is expected to be positively related to the strength of interactions (e.g., Luna et al. 2022), and its effect on biotic interactions is one of the possible paths to explain richness gradients.

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6.2.4 The Geography of Climate: Back to Hutchinson’s Duality Throughout this section we have emphasized the numerous ways that both present and past climate conditions (especially variations in temperature and productivity) can shape species richness. The processes mainly involve ecological and evolutionary processes stimulating adaptive changes that either increase extinction or speciation rates or drive geographic range expansion toward more suitable regions of the globe for a given lineage (Fig. 6.5). The effects of area and geographic isolation, on the other hand, are generally linked with stochastic processes at lower hierarchical levels, often leading to reductions in population sizes increasing local extinction rates or fostering population differentiation. The latter can gradually give rise to new species, causing species to accumulate at different rates around the world. Coelho et al. (2023), however, showed that this distinction between the adaptive effects of climate “per se” is not independent of the geography of climate, which is in turn a direct consequence of Hutchinson’s duality. Essentially, the following question arises: is the higher tropical richness a direct result of the climate itself, as previously suggested, or due to the larger area of warm and humid climates and the widespread isolation within them? To tease apart these effects, we must change our approach to analyzing richness patterns, focusing directly on the distribution of species in environmental space rather than in geographic space (e.g., Fig. 5.1). To differentiate between the direct effects of climate and its geographical aspects (area and isolation), Coelho et al. (2023) started by building a multivariate climatic space. For simplicity, they used the first two principal components of 12 climate variables from CHELSEA. They then mapped the richness patterns of tetrapods and the geographical aspects of climate (climate area and isolation) on this bivariate space, broken down into regular grid cells. Next, nonlinear models were then used to analyze richness in relation to climate (the first two principal components) and its geographical aspects (area and isolation), based on the cells in climate space. The patterns were strikingly similar for all tetrapods, and the model explained approximately 90% of the variation for each group. For amphibians (Fig 6.7a), climate area and isolation account for 9% and 5% of deviance, respectively, with an overlapping explanation of 12% (hence, the total explanatory power of the geography of climate is 26%). The first two principal components of climate (the direct effects) account for 16% of deviations with an overlap with climate geography of 45%. This gives a total explanatory power for climate and climate geography of 88%. It is important to note that previous results of nonlinear models based on direct effects of climate in geographic space (using AET alone, which synthetizes temperature and productivity; Fig. 2.9) were about 60%, revealing a confusion of effects between these two components of climate. The potential processes underlying the direct effects of climate, as well as the role of the area in driving diversity, have been discussed in the previous sections. However, when we turn our attention to the geography of climate, it brings a fresh perspective on how richness patterns emerge. In the area “hypothesis” championed

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Fig. 6.7  Exploring the influence of climate geography on global amphibian richness within the framework of Hutchinson’s duality. A bivariate space is defined using the first two principal components of climatic variation (a), based on 12 variables. This space maps richness and compares it against the principal components of climate itself and its geographical properties, namely, climate area and isolation (b). The geographical attributes of climate exhibit a non-uniform global distribution, with larger climate areas being more spatially fragmented and climate isolation increasing toward the poles (c). The nestedness and turnover aspects of beta diversity are also examined in relation to climate area and isolation (d) (see Coelho et al. 2023)

more recently by Rosenzweig (1995), the higher richness in the tropics is due to larger area in these regions, and this in turn means that populations would exist in more heterogeneous habitats. However, when shifting to climate space, the effects of area must be interpreted in a different way, because large areas in climate space are, by definition, more homogeneous (at least at a given grain size) but are scattered in geographic space (Fig.  6.7c). Higher richness in larger climate areas (Fig. 6.7b) would be due to MIH and other capacity rules, overlapping (or interacting) with climate isolation. At the same time, the effects of climate isolation are more correlated with expectations from geographic isolation, as similar climates more isolated will allow independent local adaptations (even if convergent ones) due to the reduced gene flow among diverging populations living in the same climate but that occur a given

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distance apart. It is interesting that the discussion about isolation between climates is usually focused on the latitudinal gradient, as both temperate and polar regions occur in distinct hemispheres and are isolated by intermediate tropical regions. Notwithstanding, it is weird that, for many patterns discussed throughout this book, effects are more intense in the northern hemisphere (i.e., Rapoport effect), which is usually interpreted because of distinct or asymmetrical historical events. However, Coelho et al. (2023) showed that the effects of climate isolation are more intense for the tropics (Fig. 6.7c), which is coherent with the findings about pantropical diversification patterns by Hagen et al. (2021a) and with an increase in turnover component for β-diversity (see Sect. 7.3.2). In fact, when analyzing community composition, Coelho et al. (2023) showed an increase in climate of turnover with climate isolation (Fig. 6.7d).

6.2.5 A Note on Spatial Autocorrelation and Richness Gradients Finally, it is interesting to highlight that the discussion about the relative roles of different environmental variables on richness gradients also involves statistical issues related to the effects of spatial autocorrelation in interpreting such effects. As pointed out in Sect. 3.2.3, the main issue of autocorrelation in data is that it disturbs the significance tests of models due to inflated Type I error rates and, consequently, a tendency to state that there are significant environmental drivers on richness when they are not necessarily prevalent in the literature. Lennon (2000) pointed this out and, moreover, called attention to what is called “red shift,” in which variables with effects at much broader scales, such as environmental variables, tend to have a relatively high effect that disappears or is minimized when proper spatial models taking into account spatial autocorrelation are applied to data. According to this idea, there would be a coefficient shift affecting variables with broad-scale effects when applying nonspatial and spatial models. So, the relatively high importance of such variables would be an artifact due to spatial autocorrelation. Thus, although some considered this issue a simple statistical problem, there are many implications for discussing the ecological and evolutionary drivers of latitudinal gradients. The details of the debate following Lennon’s (2000) paper (e.g., Diniz-Filho et al. 2003; Hawkins et  al. 2007d; Beale et  al. 2007; Kühn 2007; Bini et  al. 2009; Hawkins 2012; Kühn and Dormann 2012) are beyond the scope of this book as they involve many methodological and statistical issues, but it is important to highlight a few points to clarify the ecological and evolutionary implications involved. Diniz-Filho et al. (2003) showed that it is possible to use spatial correlograms to describe the structure of spatial autocorrelation in data (see Sect. 3.2.3). However, the interest here is not only the pattern “per se” but also how autocorrelation affects the interpretations of models relating richness to several variables. The idea, then, is to apply the spatial correlograms to the residuals of such models to evaluate at

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which spatial scale (distance) the environmental variables are explaining richness. Especially when dealing with refined grid cell data, where there is usually a significant mismatch between the grain size (resolution) and the geographic range size of species, it is most likely that spatial autocorrelation appears in model residuals of the richness-environment relationships. However, this significant autocorrelation appears primarily at short spatial distances, indicating that localities or assemblages within these distances tend to be autocorrelated – similar – despite the variation in the environment among them (for instance, see Figs. 3.6 and 6.2). In other words, environmental variation in the model is not enough to explain richness patterns at these short distances. As there is autocorrelation at short spatial distances, the statistical tests of the models are inadequate, and thus spatial models are needed. The main reason for this problem is that neighboring cells, for example, are not informative about the richness-­environment relationships. So, they represent an inflation of degrees of freedom (as only more distant cells are driving the patterns). A most straightforward and intuitive solution would be to avoid using close cells in the model or, more elegantly, to calculate geographically effective degrees of freedom considering the autocorrelation patterns (see Hawkins et al. 2007d). This approach implicitly shows that no shifts in coefficients would be expected, as the problem is in the Type I error rate and not in the coefficient estimate per se, and thus spatial models should not show the “red shift” discussed by Lennon (2000). The problem was, however, that some of the spatial models applied to analyze broad-scale richness gradients indeed showed the “red shift” and thus suggested that local variables (such as habitat type or elevation) are more important than the environmental variables in driving richness (Kühn 2007). These results triggered a methodological discussion about the modeling process, with implications for further debate on the role of environmental drivers of species richness (and if the apparent observed links between broad-scale climate and environmental variation and species richness at least sometimes are statistical artifacts, this reinforces the need for evolutionary and historical explanations) (Hawkins 2012; Kühn and Dormann 2012; see Currie et al. 2020 for a recent analysis and discussion). So, is it possible to conclude that broad-scale richness-environment relationships are an artifact of spatial autocorrelation? Not at all, because the spatial models, especially different forms of autoregressive models, are designed to capture the intrinsic relationship at short spatial distance by incorporating the spatial relationships among cells in the model. However, such models assume that we have stationary processes, so that the mean and variance are constant across scale, and the parameters of the models do not change across the domain. In the case of latitudinal diversity gradients, this is not true. Our best interpretation is that the “red shift” reflects both scale issues and potential violations in model assumptions and is not an artifact. Indeed, there is a considerable variation in the magnitude of “red shifts,” which depends on several dataset characteristics. Moreover, these models have different sensitivities to violations of non-stationarity assumptions, despite difficulties in evaluating these more complex and idiosyncratic effects (see Bini et al. 2009). Moreover, the “red shift” appears even when there is minor residual autocorrelation

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in data, a situation in which it would not be necessary to use a spatial model, as argued by Diniz-Filho et al. (2003). Recent development and application of more complex GWR approaches can also be a promising avenue to solve, at least in part, these statistical issues (Fotheringham et al. 2002; Barreto et al. 2019). Finally, when dealing with richness-environment correlations, there may be indeed problems related to the collinearity issues in terms of how to express geographic space (i.e., latitude) and environmental variables used, but solving this involves more background on theoretical and methodological evaluation of cause-effect relationships (which is tricky in observational data, as extensively discussed in Chap. 2) rather than autocorrelation issues alone.

6.3 Evolutionary Dynamics and Richness Gradients 6.3.1 Diversification Rates and Time for Speciation As pointed out by Ricklefs and Latham (1993; see also Ricklefs 2004, 2006; Wiens 2011; Etienne et al. 2019), the difference in richness between, say, two large regions must be understood by a combination of speciation λ and extinction μ in each region and reciprocal patterns of dispersal Δ between them (understood here in a broad sense, in terms of geographic range expansion and establishment of lineages in the new environment). Note that this idea is valid even under ecological limits because, as pointed out in Sect. 6.2.2, λ and μ will still be correlated with such environmental variables or biotic interactions that set such limits. For heuristic purposes, broad-scale evolutionary dynamics have been understood mainly using a simple scenario with two regions only (e.g., tropical and extra-­ tropical, or temperate for simplicity; it is common to refer to these regions as high and low latitudes as well), rather than using more complex and refined spatial patterns in richness discussed in the previous section and modeled based on the environmental and climatic variation. Moreover, some analytical tools developed for estimating these rates explicitly model scenarios with varying rates between two regions (see Sect. 6.4.2). Indeed, one of the challenges for advancing the coupling of available explanations for richness gradients is precisely how to match these ecological and evolutionary approaches. Some possibilities will be discussed later in this chapter, but we can keep for now the simple scenario of comparing patterns in tropics and temperate regions. We can start by considering two possibilities to explain differences between tropical and temperate regions based on the balance between λ and μ. We can assume, for simplicity, that no dispersal occurs among these two regions and that we have two subclades of large groups of organisms, one that originated in the tropics and now has 1000 species and the other that originated in the temperate region and has 100 species. We can explain this difference basically in two ways. First, it is possible to consider that the two subclades appeared at the same time (i.e., they may

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be sister clades starting with a single lineage each) in each of the two regions, say 20 million years ago. Without ecological limits, a straightforward measure of diversification would be given by log(S)/t, assuming thus also exponential growth. For the tropics, the diversification rate would be equal to 0.345, whereas for the temperate region, the rate would be 0.23 (see discussions between Rabosky (2009) and Wiens (2011)). These values of 0.345 and 0.23 are thus net diversification rates given by λ and μ and equivalent to the intrinsic growth rate in population growth models. In addition, it is necessary to consider that these two different diversification rates can be obtained by distinct combinations of balances between λ and μ in the two regions (again, this does not necessarily involve equilibrium and species-­density dependence). As discussed in Sect. 6.2.2, one can think that speciation rates in the tropics are higher than in the temperate regions, with similar extinction rates (Fig.  6.8a), as suggested by metabolic models by Allen et  al. (2006, 2007) and Gillooly et al. (2004) or by the effects of biotic interactions. On the other hand, it is also possible to think that extinctions will be higher in the temperate region due to climatic instability. In contrast, the speciation rate is more or less constant between regions (Fig. 6.8b). We can combine the two possibilities, and indeed most of the mechanisms discussed in Sect. 6.2.2 and shown in Fig. 6.5 would simultaneously generate higher speciation and lower extinction rates in the tropics (Fig. 6.8c). All three combinations of speciation, extinction, and dispersal would produce higher

Fig. 6.8  A higher diversification rate in the tropics, given by λ and μ (left plot) can appear by distinct combinations of spatial patterns in speciation (solid lines) and extinction rates (dashed lines). These possibilities include a higher speciation rate in the tropics but constant extinction in the two regions (a), higher extinction rates in the temperate regions coupled with similar speciation in the two regions (b), higher and lower relative speciation and extinction rates in the tropics (c), and higher speciation and extinction rates in the temperate region

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diversification rates in the tropics. However, it is also interesting to highlight that both speciation and extinction rates may be higher in the extratropical region, although the difference between them is still higher in the tropics, resulting in a higher tropical net diversification rate (Fig. 6.8d; Weir and Schluter 2007; Schluter and Pennell 2017). These different combinations of λ and μ can vary among groups and through time but, in the end, will result in geographically structured net diversification rates driving higher diversity in the tropics (see Pulido-Santacruz and Weir 2016). There is another obvious possibility to explain the tenfold difference between tropical and temperate regions in this example: that the time of origination of each subclade in the two regions differs. Following the previous example, suppose we assume that the group evolves with the same rate of 0.345 in the two regions. If the temperate subclade started its diversification about 13 million years ago, then the difference in richness can be explained by time alone. From an operational point of view, it is important to note that, in this case, time refers to the real origin of the group in each region, and this could be better estimated by a good fossil record, as molecular dating in phylogenies based on extant taxa could furnish the age of the most recent common ancestor rather than the real origination of the group (i.e., this is the difference between the crown age and the stem age of a clade). In short, the difference in richness between the two regions can be explained by differences in diversification rate and time since origination. In the hypothetical and enormously simplified scenario discussed above, it is straightforward to evaluate the roles of λ and μ. However, in practice, there are many complications involving the estimates of diversification rates and origination times, as pointed out above, as well as the additional effects of dispersal and range expansion between the two regions. Most likely, both time and speciation may vary (and covary) in different regions, as discussed in the previous section. Notice also that there is a complex integration among time, climatic stability, and area, so these three effects must be usually considered together for comparison between tropical and extratropical regions (Fine 2015). For instance, if larger areas reduce extinction rate because populations can be larger and if the tropics have more stable environments through time, its total integrated time-area is larger than a region in which higher climate instability changes the amount of effectively used area through time. In this last case, both time and area will be effectively smaller due to climatic instability. We can now move on to discuss some additional aspects of these two not mutually exclusive possibilities involving variation in the diversification rates (with different combinations of balances between speciation and extinction) and time since origination in tropical and temperate regions, as well as discussing the role of geographic range expansions, adaptive constraints, and phylogenetic niche conservatism in the origin of the richness patterns.

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6.3.2 Cradles, Graveyards, and Museums (and Casinos) One of the most exciting consequences of the scenarios discussed in the previous section, involving the different balances between speciation and extinction (and adding range expansion among regions and time), is that tropical and temperate regions will have distinct combinations of old and new lineages and species. As pointed out by Jablonski et al. (2006), the discussions started with A. R. Wallace in the nineteenth century of tropical climatic stability, which was later coupled with the ideas of fast evolution in the tropics by Theodosius Dobzhansky and others after the 1950s. Thus, the tropics can be viewed as a cradle or museum of biological diversity, a dichotomy popularized after the evolutionary biologist G. L. Stebbins (1974). Thinking of the tropics as a “cradle” involves higher speciation that would promote more novelty and rapidly evolving new species that could later spread toward other regions. On the other hand, a combination of climatic stability and deep time of origination would allow the tropics to harbor old, relic, and endemic species, viewed thus as a “museum” of diversity. As will be discussed in Sect. 6.4.1., the comparative evaluation of the distribution of branch lengths in a phylogeny can be one of the ways to estimate λ-μ balances (so the tropics would have, on average, longer branches in a phylogeny, or branch lengths would be left skewed, e.g., Hurlbert and Stegen 2014). These two ideas of the tropics as cradles and/or museums can be formally expressed by the alternative combinations of λ and μ in Fig. 6.8a, b, which can be more explicitly viewed as distinct growing phylogenetic trees (Fig. 6.9) (Jablonski et al. 2006). If there are higher speciation rates in tropical than in extratropical (temperate) regions (E; temperate) (λT > λE) and extinction rates are the same in both regions (μT = μE), tropics will have many new species, whereas in the opposite scenario (λT = λE and μT > μE), the tropics will accumulate old species and lineages. In these two scenarios, geographic range expansions are considered constant between

Fig. 6.9  Visual representation of the dynamics proposed by Jablonski et al. (2006) for distinct patterns of speciation, extinction, and dispersal in the tropics and temperate regions, including tropics as cradles (a), as museums (b), and “out of the tropics” (c)

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regions (so ΔT = ΔE = 0) (note that Jablonski et al. (2006) use the term “origination” instead of speciation, with O as a symbol, which is more common in the palaeobiological literature). Jablonski et al. (2006) proposed in this context the now famous “out of the tropics” (OTT) model, which is the combination of higher speciation and lower extinction rates in the tropics coupled with eventual and independent expansions and dispersal from the tropics to extratropical regions (λT > λE; μT  ΔE; this last term with deltas means that tropical diversity will be less impacted by dispersal or range expansion from extra-tropical diversity). Under OTT, the dichotomy between the tropics as cradle or museum disappears and can be viewed as both. Moreover, there are many other possibilities to combine the three rates of origination, extinction, and range expansion (and dispersal) (e.g., Roy and Goldberg 2007; Alves et al. 2017; Sect. 6.4.2). One could think, for instance, in a “into the tropics” (ITT) model simply by inverting the direction of dispersal (i.e., Pyron and Wiens 2013; Kennedy et al. 2014) so that the following combination of rates gives the pattern (λT > λE; μT  ΔE). The biological reasoning would be that assuming that niches of temperate species are broader, these temperate species could eventually colonize the tropical regions without many additional adaptations and successfully establish a new tropical derived lineage. In contrast, the colonization of the temperate region by tropical lineages will usually require more complex adaptations for cold tolerance (see also the next section for a discussion on the niche conservatism model). In addition to museums and cradles, we can also think of “graveyard” regions as defined by Rangel et  al. (2018). These regions would concentrate source-sink dynamics and aggregate many past extinction events, considering all the history of the clades within their regions. These graveyards of diversity were proposed using simulated data, and it would be challenging to detect such regions with macroecological data because an almost complete and geographically representative fossil record would be necessary. Moreover, Arita and Vázquez-Domínguez (2008), in the context of the discussion of MDE (see Sect. 6.2.1), suggested that we could also have “casinos” of richness, regions in which the survival of the species would be determined by chance alone, in the absence of ecological or evolutionary drivers (which, as already discussed, would not be the general case).

6.3.3 Tropical Niche Conservatism The time for speciation and the tropical climatic stability theories were more recently reframed within the more general idea of phylogenetic conservatism (Harvey and Pagel 1991), leading to the tropical niche conservatism (TNC) model, a particular case of PNC discussed in Sect. 5.3.3 (Wiens and Donoghue 2004; Wiens et al. 2010). The main idea is that, in addition to a simple difference between the two regions for time for diversification discussed in Sect. 6.3.1, the origin of the clade under study occurred in the older of the two regions first (i.e., in the tropics, for

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instance). Under niche conservatism, it is evolutionarily easier to speciate in the same region rather than develop new adaptations that allow colonization of the temperate region (also related to recolonization dynamics under climate change in short periods and deep time landscape changes; see Hortal et al. 2011; Cassemiro et al. 2023). However, speciation and extinction rates would be the same once a new lineage develops such adaptations. Thus, following the framework proposed by Jablonski et al. (2006), the tropical niche conservatism hypothesis would be given by (λT = λE; μT = μE; ΔT = ΔE) (even though in deep time it would be possible to think in some dispersal constraints from tropics toward temperate regions or geographic range contractions toward the tropics) (see Van Dijk et al. 2021). In practice, the differences between OTT or ITT and tropical conservatism are not that significant, especially if we consider that many adaptive failures in the temperate regions would simultaneously lead to higher (estimated) extinction rates. In addition, a higher speciation rate in the tropics due to stronger biotic interactions and niche partitioning is expected under niche conservatism, as it involves fewer complex adaptive changes. Although the same will be valid later for the temperate region, in short time scales and times of extra-tropical expansion of the derived clade, tropical niche conservatism would also reveal geographic variation in λ and μ. Further, over long periods, some old lineages that existed in broader tropical environments in the past (that shrank during the Cenozoic, as will be discussed next) would not disperse into the new tropical region and will appear in models as higher (past) extinctions. However, this may be more difficult to detect (see Sect. 6.4). In terms of the dispersal rate Δ, we can think that effective dispersal out of the tropics would not be frequent, but when it succeeds, the new lineages will diversify with rates similar to the ancestral tropical lineage. On the other hand, as pointed out, under climatic stability, temperate species with broader niches would more frequently occupy the tropics, but in both cases, the critical reasoning for niche conservatism is that no substantial differences in λ and μ are expected. The variation in richness is basically because of the time and constrained niche evolution. Moreover, in the case of richness gradients, niche conservatism can be viewed both as a process (as it is the mechanism underlying differences in dispersal rate Δ) and as a pattern for all expectations derived from λT = λE; μT = μE; ΔT = ΔE and similar models (Alves et al. 2017; see the debate between Losos 2008 and Wiens 2008 on this topics). Hurlbert and Stegen (2014) showed that niche conservatism could be distinguished from other models with higher differences of λ and μ along the gradients by its resulting more balanced phylogenies (see also Pyron et al. 2015; Pontarp and Wiens 2017; and Sect. 6.4) and by the absence of a relationship between estimates of these rates and richness. Indeed, several analyses have failed to detect strong gradients, especially in speciation rates (and it is important to note that extinction rates are usually hard to estimate using phylogenies, as discussed below). Considering the difference between tropical and temperate regions, it is important to think in tropical niche conservatism by considering climate dynamics during the Cenozoic, in which decreasing mean global temperatures reduced the extent of tropical environments and generated widespread temperate climates (even though

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these climates are not within the current formally defined tropics and temperate regions delimited by Tropics of Cancer and Capricorn). As pointed out by Fine (2015), this event created an intrinsic relationship between theories related to area and time, consequently driving more complex geographical patterns in λ and μ due to the many possible effects previously discussed. One of the consequences of this long-term temporal dynamics is that the richness gradient will appear for old lineages only, and new lineages could appear and diversify at approximately the same rate wherever they are. Indeed, Hawkins et al. (2006, 2007c) supported this general prediction and showed that gradients in bird richness were more pronounced for old lineages, even though this pattern was based on a now outdated DNA-DNA hybridization family-level phylogeny and more recent species-level analyses (i.e., Jetz et al. 2012) reveal more complex patterns. Moreover, it is interesting to note that we usually have a strong underdetermination for global richness patterns. For instance, despite the very high correlation and strong similarity of patterns for mammals and birds, the two groups differ in the predictions related to niche conservatism (Hawkins et al. 2011a). This difference may be due to differences in drivers of richness patterns (i.e., different pathways in Fig. 6.5) or methodological issues. Still, the main point is that explanations related to niche conservatism and its predictions of stronger gradients in older lineages do not hold for both groups. Furthermore, Buckley et  al. (2010) showed variation among mammal subclades, revealing a complex historical signal, even though there is some relationship between clade age, the environment of origin, and the steepness of richness gradients (and thus support to tropical niche conservatism). In a comprehensive study, Romdal et al. (2012) tested the relationship between the steepness of gradients using data from Hillebrand (2004) and ancestral environments of the taxonomic groups, showing that groups that initiated diversification in warmer climates tend to have more evident latitudinal richness gradients (see also Morales-Castilla et al. 2020). Note that the niche conservatism explanation for richness gradients does not necessarily involve latitudinal effects, and it mainly predicts that the ancestral environment will be richer (and this can be viewed in the time for speciation context because it is, by definition, occupied earlier). For instance, Hawkins et al. (2005a) showed that the eastern coastal region of Australia is occupied by a combination of old and new clades and that richness-poor areas of Central Australia, which is dominated by a hot and dry environment that requires new adaptations, are colonized by new lineages (revealing a triangular relationship between richness and distance to the root of the phylogeny; see Sect. 6.4.3). Although Hawkins et al. (2005a) did not use the term niche conservatism, it shows empirically precisely the pattern described by Wiens and Donoghue (2004). Moreover, niche conservatism appears in elevational gradients, as shown by Vetaas et al. (2018). The idea of explaining latitudinal gradients by niche conservatism following Wiens and Donoghue (2004) received enthusiastic initial support (e.g., Hawkins et  al. 2006, 2007c, 2011b; Hawkins 2010; Hawkins and DeVries 2009; Olalla-­ Tárraga et al. 2009; Buckley et al. 2010; Löwenberg-Neto et al. 2011; Smith et al. 2012; Qian et  al. 2013; but see Algar et  al. 2009; Boucher-Lalonde et  al. 2015),

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although in more recent reviews it is better viewed in a more integrated form with area and stability (e.g., Fine 2015). Consequently, there are mixed effects of variable extinction and speciation rates between temperate and tropical regions following many possible pathways shown in Fig. 6.5. We can better view niche conservatism more continuously, for instance, as a parameter capturing the dispersal constraints of lineages dispersing into or out of ancestral climate zones and their success in the newly colonized region (Pinto-Ledezma et al. 2017) (see Sect. 6.5.2). Thus, niche conservatism may appear more clearly at short phylogenetic scales, as when comparing and evaluating the distribution of closely related species and genera (Peterson 2011).

6.4 Phylogenetics and Estimates of Speciation and Extinction Rates 6.4.1 Basic Concepts and Methods Theoretical approaches to evaluate these patterns and estimate rates were available for some time and were well developed in the mid-1990s (i.e., Nee et al. 1994). Still, the applications were constrained by the generalized absence of fully resolved and time-calibrated phylogenies for a large proportion of species, even in the better-­ known taxonomic groups. However, the increase in the available information about phylogenetic relationships among species in the last 30 years, triggered by the technological advances in obtaining genetic and genomic data, opened the possibility of testing many of the theoretical ideas discussed in this chapter on how balances between speciation, extinction, and range expansion and dispersal could drive richness patterns, as well as how geographic variation in rates could be correlated with current and past environmental variation (which in turn has become possible via analogous advances in paleoclimatology). Estimating diversification rates based on molecular phylogenies and coupling them with the fossil record is one of the most active research fields in macroevolution and macroecology today, with many complex methodological discussions around estimating these rates. The current findings seem to be at least in part dependent on methodological choices, and there is much discussion about how the different scenarios described in Sects. 6.3.3 and 6.3.4 are supported for different groups of organisms or biogeographical regions using distinct methods. Moreover, there may be deeper issues related to the fact that the same combination of parameters can generate multiple phylogenies, creating a severe underdetermination issue that jeopardizes the basic assumption that these rates can be recovered using molecular phylogenies alone (e.g., Louca and Pennell 2020; but see Morlon et al. 2022). Thus, only a brief and overall discussion of how phylogenies can provide information about speciation and extinction rates, as well as of the most commonly applied approaches used to investigate richness gradients, will be given here (see Quental

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and Marshall 2010; Stadler 2013a; Pyron and Burbrink 2013; Morlon 2014; Mitchell et al. 2019; and Marshall and Quental 2016 for more general reviews). It has been recognized for almost 30 years (i.e., Nee et al. 1994) that molecular phylogenies could be helpful in estimating diversification rates, even though past speciation and extinction events are missing and only a fraction of the total diversity of species is extant. The balance between these processes leaves traces in the shape of the phylogeny and the distribution of branch lengths (Stadler 2011, 2013a, b). Thus, the starting point for estimates of speciation and extinction rates based on molecular phylogenies is to fit a birth-death process, in which random events of speciation and extinction through time occurring at a constant rate shape the tree. In this case, the net diversification rate (λ-μ) is the slope of the relationship between log-transformed species richness and time (or is simply the ratio log(S)/t for clades starting with one lineage, as pointed out in the previous section). However, it is possible to expand and evaluate this model fit in different ways and using maximum likelihood or Bayesian approaches. The simplest way to graphically understand the implications of the birth-death process and how both speciation rate λ and μ can be estimated from this process is to use the lineage-through-time (LTT) plots (Fig.  6.10) (see Ricklefs 2007 for a comprehensive review). The first important thing to understand is that when extant species are used to build a phylogeny, which is what Nee et al. (1994) called “reconstructed phylogeny,” it does not contain all species in the clade (to have all of them requires complete fossil record). It is also likely that not all species are currently known, as part of the Linnean shortfall discussed in Sect. 3.4.1. Irrespectively, the point is that under a constant birth-rate process, as extinction and speciation are random most of the time, the slope of the relationship is not biased, say, in the middle of the overall time span analyzed. However, when we approach the present, the probability of extinction is, by definition, downward biased, so we have a “pull to the present” toward the end of the LTT curve. In theory, because of the smaller effect of the extinction rate μ, this pull is precisely what is needed to estimate λ alone. It is also possible to use simple statistics to detect constant deviations from the expected branching pattern under a birth-death process, and a standard measure is the γ statistic. This statistic evaluates if, on average, the nodes are concentrated closer to the root (γ  2, indicating a high phylogenetic clustering)

point of view, as values higher than 1.96 (in module) indicate significant deviations from the null expectation of random assemblages at a 5% level. However, this test assumes a normal distribution of MPD under the null expectation, which is not necessarily true. So, applying randomization tests to evaluate the deviations between calculated and expected MPD values is more appropriate. For instance, for the Neotropical Furnariidae, the assemblages in the southern part of the continent, in Patagonia, and the dry diagonal of South America, with open habitats, tend to be more clustered (Fig. 7.3). The simple and intuitive interpretation by Webb et al. (2002) is that if NRI > |1.96|, there is some habitat characteristic that is “filtering” species that are phylogenetically similar, implicitly because there is a phenotypic trait that is “conserved” in the phylogeny (they mean a trait with a high phylogenetic signal, as discussed in Sects. 3.2.3 and 5.3.2). On the other hand, a negative NRI indicates that competitive exclusion makes the coexistence of phylogenetically close species more difficult (see Cavender-Bares et  al. 2009; Mason and Pavoine 2013 and Cadotte and Tucker 2017 for criticisms and more elaborate interpretations). Webb et al. (2002) also proposed another metric called “nearest taxa index” (NTI), following similar reasoning, but instead of using getting

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the MPD, it uses the minimum phylogenetic distance among species within the assemblage. Graham et al. (2009) applied the NRI in a macroecological analysis of Andean hummingbirds in Ecuador and found some dazzling patterns. They showed a significant relationship between NRI and elevation, with phylogenetically clustered assemblages (NRI > 2) above ca. 2500 m. On the other hand, a few lowland assemblages are overdispersed (although most are random across the phylogeny, with NRI > 2) for most assemblages, especially in South America and Australia. They then gradually reduced species pool size and calculated the NRIs using a division between New and Old World and then for more specific biogeographic realms (for instance, the species pool for an assemblage in South America is composed only by species found in this realm). There is a general reduction of average NRIs when reducing the geographic scale of the pool, and when using the biogeographic realms, there is no significant deviation of null expectations. These results suggest how clade history expresses at global and continental scales, with large clades occupying distinct biogeographic regions and defining their regional pools, but with phylogenetically randomly assemblages within these regions. Methodologically, notice that the MPD values calculated for each locality are the same regardless of the pool, but NRI changes because the range of possibilities to define random assemblages varies for different species pools. The null models traditionally applied to community phylogenetics and briefly described above are statistical realizations based on different sampling strategies of

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the regional pools, but more elaborated and informative neutral expectations can be established using diversification methods akin to those discussed in Sect. 6.4.2 (see Pigot and Etienne 2015). Another widely used divergence metric is Helmus’ (2007) phylogenetic species variability (PSV), which also has a direct relationship with MPD. However, PSV is theoretically interesting as it explicitly incorporates Brownian motion evolution in the concept of the metrics, which is an important step because of the relationship between phylogenetic and functional diversity (see also Pigot and Etienne 2015). The PSV starts by recalling that the mean neutral expected divergence between the species (i.e., for any hypothetical or empirical trait) has a linear relationship with the phylogenetic distances among them (Sect. 5.3.3). These phylogenetic distances can be measured in node depth and expressed as phylogenetic correlations. For instance, if two species diverged 1 million years ago and the tree’s total height (i.e., the age of the root) is equal to 10 million years, then these species have a phylogenetic correlation of 0.9 because they share 9 out of 10 million years of evolution. This value of 0.9 is exactly half of the patristic distance if the phylogeny is standardized to a depth equal to 1.0, so in this case, the PSV equals MPD. The last dimension proposed by Tucker et al. (2017), regularity, is not widely used in macroecology and community phylogenetics, although the γ-statistics of diversification models measures exactly this dimension (Sect. 6.4.1; see Kondratyeva et al. 2019). The metric for regularity reflects the asymmetry and stemness of the phylogeny, that is, how it departs from a “star phylogeny” (i.e., in which all species derived instantaneously from a unique ancestor, so there is actually no phylogenetic structure). It is straightforward to evaluate regularity based on pairwise distances, calculating the variance of these distances (or the variance or distance among nearest neighbor species) instead of means. It is also possible to evaluate regularity by the variance among tip rates such as DR (Title and Rabosky 2019). It is opportune to note that these phylogenetic metrics at the assemblage level capture some components of the shape of phylogeny that are, in turn, roughly related to diversification rates. Thus, in principle, they could be used as surrogate variables for diversification rates in models explaining latitudinal or elevation gradients in species richness (e.g., Brum et  al. 2012; Fritz and Rahbek 2012; Van Dijk et  al. 2021) or patterns in biotic interaction (e.g., Jorge et al. 2014). On the other hand, we started the description of such metrics by discussing more complex ways to express diversity patterns, adding more components to the simple idea of richness previously discussed in Chap. 6. If this is the case, it is more interesting to consider these metrics as response variables and evaluate their spatial patterns by comparing different clades or geographic regions and calculating correlations with other environmental and historical variables. Kissling et  al. (2012), for instance, discuss how phylogenetic clustering must change under distinct processes driving richness gradients, and their results with worldwide palm trees are consistent both with continent partial isolation coupled with limited long-range dispersal and habitat loss throughout the Cenozoic, reflecting a combination of OTT, niche conservatism, and time-area stability. They also pointed out that phylogenetic clustering can be associated with biotic interactions (Sect. 5.2.3) and that the few regions in which

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NRI identifies overdispersion most likely reflect regions of more recent biotic interchange.

7.1.3 Phylogenetic Endemism Rosauer et al. (2009) developed the concept of phylogenetic endemism by coupling PD with metrics for endemism, briefly discussed in Sect. 4.2.3. Recall that the weighted endemism is calculated by the mean of the inverse of the geographic extent in a region. This general metric for endemism can be modified into a metric for phylogenetic endemism by incorporating the idea of PD.  The phylogenetic endemism (PE) is then given by



PE =

Lc Rc

where Lc is the branch length of the phylogeny (sometimes standardized in respect to the total length of the phylogeny) and Rc is the total geographic extent obtained by overlapping all species descendent from this particular branch. So, high values of phylogenetic endemism are obtained if long branches, indicating deep time-­ independent evolution of the clades, are coupled with a small total range size of the species belonging to those clades. PE can be calculated for geographically varying assemblages, like any previously described metrics. There are several possible alternative null models to apply to PE, allowing evaluation of the different components (i.e., ways in which PE can vary among assemblages), as discussed by Rosauer and Jetz (2015). They showed that a first possibility is to use the more standard null model that they called the spatial null model, in which the recorded species in an assemblage are randomized over the tips of the phylogeny, but the geographic ranges are still fixed in the locality. Thus, the null expectation refers to the phylogenetic component alone. Another possibility, called the “local null model” by Rosauer and Jetz (2015), is to fix both the tips and the geographic ranges of the species in the assemblage but randomize the distributions and phylogenetic position of the other species in the pool, and in this case, the null model is focused on the relative metrics in the locality in respect of the other species that share ancestrality and geographic range patterns with the species found in the assemblage. They used these null models to investigate and map patterns of PE in mammals worldwide and, in addition, to identify the centers of phylogenetic endemism in tropical regions, islands, and some montane regions. They showed that PE correlates with energy available, elevation, isolation, and low variability in the current climate (but only weakly with climate stability since the last glacial maximum). Following the discussions on tropics as cradles, museums, or graveyards (Sect. 6.3.2), phylogenetic endemism can be defined by the concentration of old small-­ ranged species that may have been widespread in the past but whose geographic ranges now collapsed to the same region (paleoendemism, in “museum” regions)

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(e.g., Cassemiro et al. 2023). An alternative scenario is a concentration of recent species that diversified fast in a narrow region and did not expand their geographic ranges toward other regions yet (neoendemism in “cradle” regions). Mishler et al. (2014; see also Molina-Venegas et al. (2017) for application) proposed a new standardization of PD and PE to evaluate such patterns. Their idea was to generate relative metrics for PD and PE (rPD and rPE) by dividing the values of PD and PE by the same values obtained with a phylogeny with the same topology but in which the branches have the same lengths (and before calculating PD and PE, both phylogenies were standardized to a total length of 1.0). For instance, as a high PE is obtained by a long branch coupled with small geographic ranges, a low ratio indicates that the effect is a consequence of short branches in the observed phylogeny, so the assemblage is characterized by a neoendemism (whereas a high ratio indicates, on the other hand, a paleoendemic assemblage). Thus, before identifying a region or assemblage as paleoendemic or neoendemic, it is necessary first to identify it as endemic, which can be achieved by the null models previously described. Mishler et  al. (2014) defined a two-step protocol as CANAPE in which an assemblage is initially identified as a center of endemism if PE or RPE is statistically different from null expectation. In the second step, further analyses are conducted to define if the assemblage is classified as a center of paleoendemism, neoendemism, or both (a center with mixed endemism).

7.1.4 Genetics, Genomes, and Population Diversity Marske et al. (2013) argue that phylogeography provided, for a long time, a bridge between population genetics and patterns in species’ geographic ranges in a phylogenetic context. The idea was that most patterns of phylogenetic diversity can be also studied within a species, among its population, or dealing with continuous genetic variation, in a complementary approach between evaluating population processes discussed in Sect. 4.1 and biogeographical processes, such as geographic range shifts and responses to climate change in a scale of thousands of generations. Nevertheless, many other possibilities exist to combine these different research fields, and it is interesting to consider other possibilities to evaluate evolutionary patterns and dynamics using diversity estimates based on genetic and genomic data (i.e., Diniz-Filho et al. 2008b). The possibility of analyzing genetic patterns grew fast, thanks to the technological advances in molecular biology in the last decades, allowing relatively easy access to variation at the DNA level and the consequent accumulation of information in databanks like NCBI’s GenBank for genomes (www.ncbi.nlm.nih.gov/ genome/) and nucleotides (www.ncbi.nlm.nih.gov/nucleotide/), PhylomeDB (www. phylomedb.org), and BOLDSystems (www.boldsystems.org/), among others. This data increased the possibility of obtaining phylogenies for many groups of organisms and a more effective application of methods and discussion of concepts related to genetic diversity and population structure throughout species’ geographic ranges

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in ecology and evolution (Sect. 4.1). We provide below a relatively short synthesis of how these data may be integrated with macroecological data. Leigh et al. (2021) recently synthetized some ideas of the rapidly emerging field, which they call “macrogenetics,” which is analogous to macroecology. Firstly, it is curious to recall that most studies in genetic diversity up to the 1980s, with a few exceptions, targeted a few (or a single) species and local populations. These studies evaluated the magnitude of the genetic variation in (presumable) neutral molecular markers and how they vary among local populations. With the gradual advances in gene sequencing, allowing the development of refined molecular markers, it became possible to expand the analyses toward broader geographic scales and start investigations into more comprehensive questions. In short, geographical genetics (i.e., Epperson 2003; see also Diniz-Filho et al. 2008b) focused on using spatial statistics to infer microevolutionary processes underlying patterns in genetic variation among local populations in different scales. From a different perspective, phylogeographical analyses initially based on uniparental markers from mtDNA or cpDNA allowed a historical evaluation of lineage diversification among populations with the species’ geographic range. In both cases, the focus was to investigate patterns of intraspecific differentiation among populations. Suppose molecular data is available for a single species throughout its geographic range. In that case, it is possible to evaluate patterns of genetic diversity estimated based on distinct markers within local populations, usually by estimating heterozygosity and number of alleles. The same data allows evaluating the population structure and differentiation by estimating F-statistics or pairwise genetic distances that, in turn, are visualized using clustering or ordination techniques of multivariate analyses (e.g., Wagner and Fortin 2013). These analyses are analogous to evaluating α- (or γ) and β-diversity in ecology and macroecology (see next section), and there are straightforward interpretations for both patterns, in some cases coupling genetic and environmental variation (Sect. 5.3.2). On the one hand, if variation in molecular markers correlates with environmental or climatic variation, this may indicate adaptive processes that explain variation in the allele frequencies among populations. Thus, these correlations can help identify adaptive genetic markers a posteriori, which can be supported by understanding the methodological or genomic basis of the marker and the theoretical relationships with a mechanistic view of metabolic networks. On the other hand, even neutral molecular variation can also display apparent correlations with the environment due to autocorrelated population dynamics or reflect demographic patterns of changes in population abundance in response to the environment. For instance, these neutral patterns are important in discussing and testing central-peripheral population dynamics and niche variation (Sects. 3.2.3 and 4.1.3). There are, however, many other possibilities to discuss intraspecific genetic variation in a more comprehensive ecological context and better couple such patterns with macroecological analysis. One of the possibilities recently discussed by Lawrence and Fraser (2020) is to evaluate the geographic patterns of the number of populations (“population richness”) within species, defined by establishing a threshold in the FST pairwise distances among local samples, together with other estimates of genetic diversity. They

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used genetic data available for terrestrial vertebrates, providing expectations of patterns within species under the alternative ecological, historical, and evolutionary explanations for the latitudinal diversity gradients, previously discussed in Chap. 6. Thus, they established some exciting links between population genetics, ecology, and macroecology that may open many future research avenues. They showed that there is a relationship between geographic range size and the number of populations, but not with genetic diversity, which is interesting for the discussions about niche and models of geographic range dynamics previously discussed. Vellend (2003; see also Vellend and Geber 2005) pioneered an approach called “community genetics,” centered on the idea that the neutral genetic variation in populations of a focal, widely distributed species, would be positively correlated with species richness in the communities surrounding such populations. This pattern has been called species diversity-genetic diversity (SDGD) correlation. The reasoning is that stochastic processes driving genetic diversity among local populations within the focal species, related to genetic drift and limited dispersal defining meta-population structure, would also appear at the species level under stochastic metacommunity dynamics (Sect. 4.1). Defining the relative roles of adaptive and neutral genetic variation regarding environmental drivers and niche geographic delimitation allows the definition of a neutral expectation for SDGD correlations. If niche and adaptive variation at the species level are analyzed, similar reasoning based on “parallel effects” between the two hierarchical levels can explain the SDGD correlations (see Vellend et al. 2014; Lamy et al. 2017). Methodologically, it is possible to use species diversity or other related metrics, such as PD or other community or ecosystem metrics (e.g., Whitlock 2014), as explanatory variables of genetic diversity in the focal species together with other environmental and historical factor variables (Lamy et al. 2017). Although there seems to be a trend toward positive SDGD, there are many potential confounding factors, and indeed, meta-­ analyses of these correlations provided mixed results and revealed that there is still room for many discussions about the generality of patterns and processes (Vellend et al. 2014; Whitlock 2014). Lamy et al. (2017) proposed an interesting analytical and integrative conceptual framework incorporating distinct situations that could lead to positive, negative, or null SDGD correlations. The framework initially proposed by Vellend (2003) would allow some interesting inferences on ecological and evolutionary processes at the community or assemblage level, but the data available today allows expanding this idea to multiple species at global scales. Rather than correlating genetic diversity in populations of a focal species with richness in other related species in the same regions, it is now possible to evaluate patterns of mean genetic diversity within hundreds or thousands of species in different regions with richness and other metrics of diversity at a higher hierarchical level. Miraldo et al. (2016) were the first to use data from GenBank and BOLD repositories to evaluate genetic diversity from thousands of mtDNA sequences of mammals and amphibians worldwide (representing genetic diversity in about 38% and 27% of recognized species at that time for these two groups, respectively). In short, they calculated average nucleotide diversity for cytochromeb sequences within species and averaged them in a global equal area grid covering

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the world. Even with a clear upward bias of sequences availability for the temperate regions, it was possible to identify a peak of genetic diversity in the tropics, decreasing toward the poles, thus following the latitudinal patterns discussed in the previous chapter (but see Gratton et al. 2017). Theodoridis et al. (2020) expanded the previous analyses by Miraldo et al. (2016) focused on mammals and discussed how genetic diversity within species can support alternative theories for latitudinal diversity patterns. They showed that patterns in genetic diversity and their correlation with species diversity support the evolutionary speed model for richness gradients (see Figs. 6.6 and 6.7 in the previous chapter). However, they also indicate that the effects of productivity driving larger carrying capacities can affect the relationship (see also Storch et al. 2018). Genetic diversity is more correlated with PD than with species richness and thus reflects deep-time effects that may be related to both area and climatic stability effects. Finally, their findings are also compatible with enhanced biotic interactions accelerating adaptive rates reflected by high levels of genetic variation among populations within geographic ranges. Thus, their results are coherent with the multiple theoretical explanations for the latitudinal gradients and reinforce the difficulty in decoupling the relative roles of multiple processes and mechanisms driving complex macroecological patterns. Nevertheless, this approach is interesting and provides further and independent evidence of the ecological and evolutionary processes underlying richness patterns and tropical diversification. It also leads to meaningful discussions about reductionism and hierarchical emergence in macroecology. The main issue is how different processes and mechanisms related to population abundance could be distinguished (i.e., did they leave different tracks and spatial patterns in different types of genes) and how they could interact with speciation and extinction dynamics (Overcast et al. 2019). Finally, Leigh et  al. (2021) suggested that it is possible to classify studies in macrogenetics into three classes, defined mainly by the taxonomic and geographic extent of the study. Their Class I involves obtaining primary genetic data for species in the same region, usually involving a similar sampling design (i.e., sampling sites or effort at the regional level) for the same type of organisms. Depending on the level of endemicity and regional extent, it would be possible to correlate patterns of genetic diversity across species with life-history or ecological traits, an approach that has been sometimes called comparative genetics (and eventually, in a slightly geographically and historically broader context, as comparative phylogeography). For instance, it is possible to evaluate if plant species with different dispersal mechanisms or reproductive systems have higher levels of genetic diversity within a sample or more structured populations (see Epperson 2003). The same reasoning defines a Class II macrogenetics study, in which data compilation from the literature allows expanding the studies’ taxonomic and geographic extent, using meta-­analysis techniques to evaluate the relationship between genetic diversity and population structure with life-history traits and other ecological characteristics within species geographic ranges. Compiling primary information on genetic and genome diversity and reanalyzing then in an integrative framework, such as those developed by

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Miraldo et al. (2016) and Theodoridis et al. (2020), is classified at the highest level as a Class III macrogenetics study. In addition to these ideas provided by Leigh et al. (2021), there are many recent developments and possibilities to use new technologies of environmental DNA (eDNA) and metagenomics in both current and ancient samples to provide even more comprehensive data on diversity (Taberlet et  al. 2018; Wang et  al. 2021). Another interesting example is the use of genetic data to indirectly estimate effective population size that, in turn, can be used to track patterns of geographic range dynamics (see Fordham et al. 2022 for using these data to disentangle alternative extinction scenarios for the woolly mammoth). Based on these examples, we can easily foresee a better integration of genetic and genome patterns with other macroecological data in the near future, with an enormous potential to provide integrative explanations for diversity patterns at different scales and multiple hierarchical levels. From a more operational point of view, we can also highlight that there are tremendous challenges in obtaining and analyzing broad-scale population genomics data at macroecological scales, and the success of this emerging combined approach depends on how geneticists and ecologists interact and collaborate to answer new scientific questions.

7.2 Trait Diversity and Functional Biogeography 7.2.1 Divergence in Phenotypic Traits and Functional Diversity The discussion about functional diversity and, in a more general sense, “trait-based ecology” (see De Bello et al. 2021) has many theoretical and methodological convergences with the evaluation of patterns of niche differentiation discussed in Chap. 5 and with phylogenetic diversity discussed in the previous section. For instance, the maximum temperature that a species tolerates (the CTmax) can be considered a trait, whereas some of the metrics used to assess functional diversity are the same used in phylogenetic diversity (i.e., mean pairwise distance). Even so, perhaps it is more common to evaluate morphological, or even behavioral, traits (e.g., Cooney et al. 2022) when considering functional diversity. However, on a short historical note, it is curious to recall that functional ecology did not develop from an evolutionary view of ecology but instead derived from a physical and ecosystem approach in which species’ identity and their evolutionary trajectories are not explicitly considered. Only later, community phylogenetics and ecophylogenetics tried to provide more evolutionary-sounding integration between trait evolution, ecosystem function, and phylogenetic structure within and among assemblages (Mouquet et  al. 2012; Davies 2021). In the early days of macroecology, most of the discussions around traits focused on body size, building up on the justification that this variable would be a surrogate

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for many ecological processes and life-history traits and because it was readily available for many, if not all, species, including fossil ones. Given the importance of body size for macroecology, the patterns and processes related to this variable are discussed in more detail in Chap. 8. However, there are now many available databases that make several traits available for many species in different groups, out of which TRY (Plant Trait Database; https://www.try-­db.org/TryWeb/Home.php) is an initial reference for plants and PanTHERIA (Jones et al. 2009) for mammals (see DeBello et al. 2021 for a more comprehensive list). AmphiBIO is another example of a database for amphibians worldwide (Oliveira et al. 2017). A recent huge organization effort is AVONET (Tobias et  al. 2022), a comprehensive database with ecological and morphological traits for about 11,000 bird species measured in almost 100k individuals worldwide (see also Hughes et  al. 2022). There are still many missing data in all these databases, reflecting the Raunkiæran shortfall (Sect. 3.4) that requires several methodological strategies to overcome. One of the most important conceptual issues when considering functional traits to evaluate diversity is how these traits could mediate the relationship between ecological patterns (i.e., in abundance or richness) and the environment, with important implications for rewilding and restoration conservation programs (e.g., Santini et al. 2021). In this case, mediation means that traits are directly related to fitness, expressed by differential mortality or fecundity, so an individual in a given environment has higher or lower fitness depending on its value for the trait. As an evolutionary response to the environment, a high fitness given by the trait allows a population to achieve higher abundances and evolve toward the optimum (assuming genetic variance, although a similar response in the short term would apply by phenotypic plasticity). Under this process, traits are adaptively responding to selective pressures exerted by the environment, so they are called “response traits.” However, a trait may also cause a change in the environment and ecosystem functions, so they can be called “effect traits.” Depending on the situation, some traits can be classified as both response and effect, especially when considering multiple trophic levels. For instance, a large body in individuals from a given species found in low temperatures can be viewed as a response to the environment, but if this individual is a large herbivore, it can also drive vegetation shifts. The distinction between effect and response trait can also lead to a discussion about which environmental variables would drive interspecific variation (and consequently with other properties of assemblages). When considering a response trait, we usually consider climatic variation that may drive different optima across geographic space, as defined in the so-called ecogeographical rules for body size, shape, and coloration (Gaston et al. 2008). On the other hand, effect traits would lead to environmental variation related to ecosystem functions, such as productivity, and other more specific measures, such as carbon release. Note that the correlation between richness and productivity extensively discussed in Sect. 6.2.2 emerges because of increasing overall carrying capacity but is seldom considered, in a macroecological context, the potential feedback that this would trigger at more local scales.

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At this point, it is important to highlight that two slightly different ideas are involved when dealing with functional traits and diversity. When thinking about how traits are related to environmental variation, the focus goes to how different optima appear along a temperature gradient, for example. The response is a change in mean values that correlates with the gradient, such as large bodies in colder environments under Bergmann’s rule (Sect. 8.4.1). However, when expanding the reasoning for assemblages, it is worth asking how this gradient affects different species in terms of optima and tolerance around them. Depending on how correlated the responses are, different assemblages appear along this gradient so that we can think about functional diversity. It is also straightforward to expand the reasoning and think that, in practice, there are usually different traits responding in different ways to multiple gradients (and some of them are functioning as responses or effects, or both), requiring then multivariate approaches to try to disentangle patterns and processes (De Bello et al. 2010a, b, 2017). Although there is a relatively older tradition of evaluating patterns in community and metacommunity ecology (e.g., Lavorel and Garnier 2002; Pillar and Duarte 2010; DeBello et  al. 2010a, 2017), the increasing availability of large and more comprehensive databases of both functional traits and geographic distributions, coupled with the more general development of macroecological research program and broad-scale diversity analyses, allowed the development of a new field of “functional biogeography” (e.g., Violle et al. 2014). Mapping synthetic metrics of functional diversity along traits and species in assemblages and correlating the patterns with environmental variation is now a common theme in macroecology, as well as its relationship with phylogenetic diversity (as discussed in the next section) (Devictor et al. 2010; Safi et al. 2011; Brum et al. 2017; Mazel et al. 2018; Nakamura et al. 2018; Pigot et al. 2020; Leclerc et al. 2022; Trindade-Santos et al. 2022). As previously discussed, when evaluating niche overlap (see Sect. 5.2.3), traits can also mediate species’ coexistence patterns and thus create more complex relationships of richness and abundance with the environment. In this case, it is common to think in functional sets of traits more explicitly related to a function, such as feeding ecology. Other traits may be more associated with habitat occupation, foraging patterns, and dispersal ability, so constraints in sharing resources or space could be explicitly evaluated (e.g., see Pigot et al. 2020 for a recent example of the analyses at a global scale using bird traits in these functional contexts of feeding and locomotion). Some classical theories and models in early community ecology in the 1960s and 1970s usually focused on how trait divergence could drive coexistence. For instance, the famous “Hutchinson’s rule” states that there would be an average 1.3 ratio in differences among body sizes for coexisting species in the same trophic level and the more general limiting similarity theory (see McPeek 2019). Another interesting discussion is about character displacement, which refers to disruptive selection in sympatric populations of the same or closely related species, allowing coexistence by locally minimizing niche overlap (e.g., Stuart et al. 2017). In this sense, these traits can be viewed as effect traits as they drive a response in other populations or species.

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It is worthwhile to notice that the roles of traits in these classical theories and models can be directly associated with the early discussions in community diversity if we consider evolutionary models of trait diversification (see the following section on the relationship between functional and phylogenetic diversity). In short, as most phenotypic traits display strong phylogenetic signal, more closely related species tend to be more similar (note that Webb et  al. (2002) used the term “conserved traits” for this pattern). If this similarity limits coexistence, assemblages tend to be phylogenetically overdispersed (i.e., characterized by a negative NRI, for instance). On the other hand, under strong phylogenetic signal, the response of a trait to the environment leads to phylogenetic clustering assemblages (a positive NRI) because these similar species would be “filtered” by the environment. Notice that these two opposing processes could be potentially found for the same trait but at different spatial scales, with overall environment filtering generating the regional pools and limiting similarity at more local scales (leading to more complex patterns of β-diversity further discussed in Sect. 7.3). Moreover, although there is a trend to consider individual (i.e., intraspecific) variation in studies, it is more common to evaluate, especially in a macroecological context, overall species averages in a comparative sense or to generate the community weighted means (CWM; see Sect. 3.2.1) for assemblages and thinking about filtering processes discussed above and its phylogenetic implications (Duarte et al. 2018). So, we are usually considering analyses of aggregated traits and, as discussed in more detail for body size in the next chapter, there may be an interesting discussion of how these patterns can be a consequence of species sorting and environmental filtering (Jablonski 2008, 2017a, b). Finally, from a more operational point of view, the metrics used to estimate functional diversity are similar to those described in Sect. 7.1.2 to estimate phylogenetic diversity (Pavoine and Ricotta 2014; Violle et al. 2014). However, in some cases, it would be easier to understand because they are built in a traitspace, which may seem more realistic than those based on a more abstract phylogenetic space. As a multidimensional functional space is defined, obtaining several metrics for diversity analogous to those previously described for phylogenetic diversity is possible. For instance, it is possible to estimate a distance matrix among species after proper standardization of the traits and derive metrics from this, including MPD for different assemblages. It is also possible to calculate FD analogous to Faith’s (1992) PD using a dendrogram built using a clustering method on these distances (Petchey and Gaston 2006). It is common to use different metrics based on functional distances to define a hypervolume encompassing the species, using minimum convex volume and analogous techniques, as done for ecological niches and bioclimatic envelopes in SDMs. A similar approach is calculating the minimum distance between species in the hyperspace and then defining a “functional rarity,” which is also related to phylogenetic uniqueness.

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7.2.2 Phylogenies as Backbones and Proxy for Understanding Functional Diversity Investigating the expected relationship between functional and phylogenetic diversity can help understand ecological and evolutionary processes underlying functional patterns. However, there have been several discussions around this relationship. Nevertheless, incorporating phylogenetic information into the analyses of functional assemblage patterns related to trait evolution and ecological interactions brings several benefits to infer processes and mechanisms, providing an essential conceptual and methodological basis for integrating ecology and evolution (Mouquet et al. 2012; Gerhold et al. 2015; Davies 2021). Swenson et al. (2017) provides a helpful framework to understand how phylogenies were used in community ecology (which also applies to macroecology) and proposes at least two ways to think about this relationship. The first idea is to consider phylogenies as a “backbone” to understand trait evolution and patterns in functional diversity. Alternatively, it is possible to think of phylogenies as proxies or surrogates for FD. The two ideas are not mutually exclusive and adopting one of them actually depends on the fundamental question to be answered about the phylogenetic patterns in trait variation (see also Pavoine et al. 2011). Generally, phylogenies are used as a backbone for understanding biological patterns in comparative methods, as previously discussed in Sects. 3.2.3 and 5.3.3. The basic idea is that the phylogeny expresses a neutral expected divergence among species, so comparing observed differences for a trait, for example, reveals departures from this neutral expectation (Davies 2021). Even if most traits possess strong phylogenetic signal at broad scales, as previously shown for the Grinnellian niche in Sect. 5.3.3, it is possible to evaluate if some species diverge more or less than expected for different traits and, consequently, to help identify potential causes for this departure. This is the reasoning for identifying adaptive processes using comparative analyses (Martins 2000; Hansen and Martins 1996). The same reasoning can be applied when relating functional and phylogenetic diversity. For instance, Safi et al. (2011) proposed different interpretations for the deviation of FD with respect to PD (Fig. 7.4). Assemblages situated along the diagonal of the scatterplot of FD against PD would be composed of species whose functional differences are expected by phylogeny, reflecting thus purely “inertial” phylogenetic patterns or evolutionary constraints. More interesting are assemblages in which there is more FD than expected by PD, indicating competition creating more divergence, high environmental heterogeneity leading to more diversity of occupied habitats (which in turn is linked with more beta diversity), and rapid evolution. On the other hand, as previously described, strong environmental phylogenetic filtering or relaxed competition would lead to smaller FD than expected by PD. In one of the first global analyses of mammalian functional diversity, Safi et al. (2011) showed a gradient of such deviances, with more FD than expected by PD in the northern hemisphere. Santos et al. (2020) more recently discussed similar patterns for Europe, in which species-poor assemblages in the northern areas of the

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Fig. 7.4  Mechanisms underlying the relationship between PD and FD. The dashed line indicates the neutral expectation in which FD and PD are proportional and have a linear relationship. Notice that Safi et al. (2011) used the term “phylogenetic constraint” for this neutral expectation, with a different meaning from the classification by Cooper et al. (2010). (Modified from Safi et al. (2011))

continent have higher phylogenetic (and trait) clustering than southern areas, thus correlated to climatic instability. If evolutionary processes underlying the different traits generate strong phylogenetic signal, i.e., closely related species tend to be similar, it is possible to go to the second idea discussed by Swenson et al. (2017) of phylogenies as proxies. Indeed, this is the idea underlying the original propositions of community phylogenetics by Webb (2000) and Webb et al. (2002), when they state, for example, that phylogenetically clustered assemblages would be a consequence of a conserved trait, similar in closely related species that are adapted to the environment in that region and thus is the basis for filtering the presence or abundances of these species. As Cavender-Bares et al. (2009) argued, the assumption that there is a phylogenetically structured trait that controls the filtering process is rarely evaluated (see also Mason and Pavoine 2013; Davies 2021). However, the discussion of phylogenetic diversity as a surrogate for functional patterns (e.g., Cadotte et al. 2011) seems to be more explicitly related to the Raunkiæran shortfall and the need to understand the relationship between biological diversity and ecosystem function and conservation planning. Thus, because it is difficult to define which traits are more related to ecosystem functions and, even if this is known, the data is usually unavailable for many species, it is much easier to assume that phylogenetic distances are an adequate proxy for similarity in traits and associated functions. The main discussion on the similarity between FD and PD geographical patterns is whether this similarity is high enough to allow phylogeny to be helpful in

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environmental management and biodiversity conservation in practice (Winter et al. 2013; Molina-Venegas et al. 2021). Despite the empirical and practical discussions, the idea of proxy depends on the evolutionary models underlying trait variation (Diniz-Filho 2004b; Diniz-Filho et al. 2011; Mazel et al. 2017b, 2018). If functional traits have a strong phylogenetic signal (i.e., if there is a linear relationship between species differentiation for the traits and time since divergence, as discussed in Sects. 3.2.3 and 5.3.3), a strong correlation between phylogenetic and functional diversity emerges, so the idea of proxy may hold. However, even in this case, there may be several issues to discuss when adopting this surrogate strategy. A first important issue to consider is that a strong phylogenetic signal may be due to a stochastic variation under Brownian motion, so in this case, there is no apparent effect of traits on assemblage patterns. Consequently, the idea of the surrogate is better viewed from pragmatic scientific reasoning and should be carefully discussed more realistically, helping to infer ecological and evolutionary processes underlying patterns). Second, evolutionary models fitting ecological traits and niche dimensions are usually more complex and do not generate very strong phylogenetic signal and also depend on phylogenetic and geographical scales. If traits evolve under an O-U process instead of a Brownian motion, the proxy would only work at short phylogenetic scales. Early studies showed, for instance, that ecological traits tend to be “evolutionary labile” (i.e., Freckleton et al. 2002; Blomberg et al. 2003), and, as already discussed in Sect. 5.3.3, there would be many ways to think in phylogenetic conservatism under multiple models (e.g., Cooper et al. 2010). In short, it is still difficult to think in which specific situations the assumptions support the idea of phylogenies as a general proxy (Gerhold et al. 2015). Suppose the idea of proxies cannot be supported in a more general way due to the complexity of evolutionary processes underlying different traits. In practice, it is necessary to fill the gaps in the Raunkiæran shortfall by improving our trait databases across different groups of organisms and, in a more applied perspective, to better associate traits and functions. In the meantime, it is always possible to think that phylogenies can still be a way to capture hidden and unknown components of biological diversity. Thus, it is possible to use a different approach to combine phylogenetic and functional information to provide a more comprehensive measure of diversity. For instance, Cadotte et al. (2013) proposed that it is possible to combine the phylogenetic (PDist) and functional (FDist) distances among pairs of species based on a “traitgram,” combining phylogenetic structure and trait variation. The FPDist is then given by

FPDist  {aPDist p  1  a  (FDist p }1/ p



where a is a phylogenetic weighting parameter varying between 0 and 1 and p refers to the dimensionality of the functional diversity. For a single trait in a traitgram, p = 2, so the FPDist is a Euclidean distance that can be easily visualized (Fig. 7.5). Once that FPDist between pairs of species is calculated, it is possible to calculate all metrics previously discussed at the assemblage level, such as MPD and NRI.  In

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Fig. 7.5  The schematic calculation of Cadotte et al.’s (2013) functional-phylogenetic distances (FPDist) based on a traitgram (right) for a single trait. The FPDist between species 1 and 3 can be visually represented by the pairwise Euclidean distance them along the X and Y axes (the diagonal of the shaded area, with the arrow). In this case, with both axes at the same scale and the distance expressed simply by the diagonal, the phylogenetic weighting parameter a is equal to 0.5 (see text for detail). For instance, after obtaining the pairwise FPDist among species, it is possible to calculate the mean pairwise distances among the assemblages shown in Fig. 7.1. In this hypothetical example, the traitgram reveals two main departures from a stochastic divergence between species (Brownian motion), because the clade formed by the two species 1 and 2 are much more distant along the X-axis than expected by their relationship. At the same time, the sp6 is phenotypically too close to the clade formed by species 3, 4, and 5

addition, it is possible to evaluate the departures of neutrality in the functional dimension by the relationship between FPDist or the derived metrics at assemblage metrics (such as MPD) and the phylogenetic weighting parameter a. Neutrality, in this case, is the linearity between trait divergence and phylogenetic distances, which Cadotte et al. (2013) refer to as “conserved” (following the tradition in community phylogenetics). However, functional traits can be divergent or convergent with respect to this neutrality. For assemblage metrics, the discussion of mechanisms driving functional diversity patterns is the same as in Fig. 7.5. There is another approach to combine PD and FD based on a more explicit evaluation of the evolutionary models underlying trait variation or functional patterns among species. The idea is to warp the branch lengths of the phylogeny according to a given evolutionary model fitted for the trait (Diniz-Filho 2004b; Mazel et al. 2017b) (Fig. 7.6). So, calculating phylogenetic diversity metrics based on this phylogeny with warped branch lengths captures more adequately patterns of phenotypic variation among species. The main challenge with this approach is how to warp the branch lengths by fitting evolutionary models, especially considering that different functional traits can evolve under different processes and at distinct phylogenetic scales. Under Raunkiærian shortfall, it would be possible to evaluate the most common evolutionary patterns underlying important functional traits for

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Fig. 7.6  Warping the phylogeny according to the phenotypic divergence among species allows calculating an integrated PD-FD diversity and comparing assemblages. Following the example from Fig. 7.1, the difference between the two assemblages is now reduced because the basal species 6, which leveraged a much higher value of PD in the assemblage B, evolved slower than expected by Brownian motion (i.e., proportional to branch length) so it does not drive a high diversity in this assemblage. With the warped phylogeny, assemblage A now contains about 50% of the total possible diversity (similar to the PD in Fig. 7.1), whereas the relative diversity of assemblage B reduced from 73% to 67% of the total diversity

species with known values and then use this model to obtain a phylogeny with warped branch lengths for all species that could be used to estimate functional diversity. Another methodological alternative would be to obtain synthetic variables (i.e., principal components) and model phylogenetic patterns for these different complexes of traits. Some would argue that, under these distinct evolutionary models for trait divergence, this warping approach would be difficult to apply, but the problem, in this case, is not the method per se but the overall concept of achieving unique metrics for functional diversity in an assemblage. It would be better to think that different sets of traits may be related to different functions and should be evaluated and managed independently.

7.2.3 Dimensionality In the two previous subsections, we discussed how patterns in species richness could be compared with patterns in phylogenetic and functional diversity, with slightly different interpretations. However, it is possible to generalize these ideas by thinking that diversity is a much broader composition of surrogate variables for different ecological, physiological, behavioral, and morphological characteristics of

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the species and individuals that allow their coexistence in a given time and a particular set of environmental conditions. In addition, these traits may change according to different evolutionary models, so their patterns can be analyzed using distinct metrics that capture different properties of phylogenetic variation within and among assemblages, as discussed in Sect. 7.1.2. Thus, diversity is better viewed as a multidimensional concept and should be analyzed in an explicit multivariate way considering all traits and metrics simultaneously (Stevens and Tello 2014). So, in addition to interpreting some specific correlations between metrics (i.e., PD and FD) under alternative theoretical frameworks, it may be interesting to evaluate what has been called “diversity dimensionality.” If the metrics analyzed are correlated and possess, as previously discussed, similar spatial patterns, there is a low diversity dimensionality. Thus, a straightforward approach to evaluate diversity dimensionality is to evaluate patterns using a PCA and related multivariate methods. These ideas are relatively new, and we must highlight at least two issues from a methodological point of view. First, it is necessary to synthesize the information from PCA to measure dimensionality (Stevens and Tello 2014; Stevens and Gavilanez 2015; Nakamura et  al. 2020a, b; Richter et al. 2021). It is important to recall that the advantage of a PCA is that rotating multivariate space reduces dimensionality by maximizing variation among fewer orthogonal axes (the principal components). So, the first intuitive idea to characterize dimensionality starts with the scree plot showing the decrease in the eigenvalues from the correlation matrix among metrics. If, as pointed out above, the different metrics used are highly correlated, there is a low dimensionality and the first eigenvalue is much larger than the others. A simple comparative metric for dimensionality would be the amount of explanation of the first principal component, but this would be valid mainly for low-dimensional systems. A more comprehensive metric is to obtain an evenness for the entire scree plot by accumulating the differences between successive eigenvalues. This approach is related to the well-known sphericity criteria for selecting the number of axes in the PCA, which is a classical problem in multivariate analysis (see Legendre and Legendre 2012). A low evenness appears for low correlated diversity metrics revealed by a relatively large first eigenvalue, for instance (Stevens and Tello 2014). Nakamura et  al. (2018, 2020a) proposed another interesting metric that helps understand pattern dimensionality based on the results of the PCA, allowing determining which of the dimensions is more important to the system. This importance value (IV) is obtained by combining the loadings of each dimension (i.e., the squared correlations of each value and the scores of each principal component) with the relative eigenvalue of each principal component. Nakamura et al. (2020a) called the classical evenness metrics based on eigenvalues the “correlation component” of the dimensionality, whereas IV represents the variance component. They used simulations of metacommunity dynamics and trait evolution under O-U processes to show that different combinations of these two ways to approach dimensionality are related to different ecological and evolutionary processes underlying diversity patterns.

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The second important issue to highlight about diversity dimensionality is that it would be straightforward to translate the many discussions about the correlated patterns of functional, taxonomic, and phylogenetic diversity into the dimensionality framework (even with only three dimensions). However, most of the interest in dimensionality appeared only after the study by Stevens and Tello (2018) that discusses the geographical patterns in dimensionality. Rather than simply showing the multivariate correlations among diversity dimensions, they analyzed such patterns for latitudinal bands across the Neotropics and showed that evenness decreases from the equator to the poles (i.e., the dimensionality is higher in the tropics). From a theoretical point of view, Stevens and Tello (2018) highlighted that this approach is still in its infancy and argued that the current explanations for the latitudinal diversity gradients (see Chap. 6) do not account for these patterns in dimensionality. From a methodological point of view, it is still necessary to improve the approach used to evaluate such patterns, and an excellent way forward is to apply GWR to evaluate patterns in the metrics derived from the PCA (the evenness and the IV) more continuously in geographic space (see Barreto et al. 2021).

7.3 Beta Diversity 7.3.1 Scale Issues and the Concept of Beta Diversity Up to this point, we have been discussing richness and diversity defined for local assemblages or broader regions (in the context, e.g., of the discussion between local and regional diversity; see Sect. 3.2.2). However, we previously argued that understanding processes driving patterns evaluated using these different units might differ because of scale issues, leading us to the general idea of beta diversity. For instance, we start by considering how richness increases from a local assemblage (actually, several local assemblages) to a region. Suppose, for instance, a mean richness equals 20 species in many local assemblages for a given group of organisms. However, when analyzing a broader region encompassing these assemblages, a total of 35 species is recorded, indicating a different species composition for the assemblages. Thus, the decision about grain size to use in macroecological analyses of diversity patterns significantly affects understanding the processes underlying such patterns (see Sabatini et  al. (2022) for a recent evaluation and Sect. 3.1.2 for operational issues related to overlaying geographic ranges to calculate diversity). Following the classical definition of R. H. Whittaker from the 1960s, the mean local richness is the α-diversity, whereas the regional richness is called γ-diversity. The relationship between these two levels of richness defines what is called β-diversity, which measures the difference in composition of the assemblages and can be defined as a ratio (β  =  γ/α) or difference (β  =  γ  −  α). This definition of β-diversity is sometimes called “proportional diversity,” so furnishing a simple estimate for the region. A few years later, Whittaker proposed a more complex hierarchical scheme with successive diversity estimates (Tuomisto 2010a). Nevertheless,

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it is also possible to think of β-diversity as the difference in composition of the several local assemblages in a region, expressed as a pairwise matrix comparing their composition, an approach that is sometimes called “differentiation diversity” (i.e., Baselga 2010). So, a high dissimilarity (distance or difference) between the assemblages indicates different species’ composition or abundance patterns and, thus, a higher β-diversity. These different ways to deal with β-diversity were indeed suggested in the original paper by Whittaker (1960). It is possible to get the mean or median of the pairwise differences from the dissimilarity matrix among local assemblages to get a unique estimate of β-diversity for the entire region. However, the main advantage of using the pairwise approach is to get more flexibility to investigate different spatial and environmental patterns in β-diversity. β-diversity has been one of the hot topics in community ecology for a long time, both conceptually and operationally (see Tuomisto 2010a, b; Ellison 2010), and clustering and ordinating ecological assemblages based on several metrics to calculate pairwise similarities and dissimilarities is a usual starting point to evaluate differences in community composition using multivariate analyses (see Legendre and DeCaceres 2013). In a more operational sense, it is not common to explicitly think in α, β, and γ as traditionally defined when dealing with macroecological data, as framed in Sect. 3.1.3. Instead, it is more frequently to consider diversity for a set of spatial units (analogous to α-diversity in practice but more appropriately equivalent to γ, because of the relatively large grain) or as compositional differences among these units (β). As previously discussed in Sect. 3.1.2, it would be possible to evaluate richness, for example, based on distinct grids with varying grain sizes, but even so, this would rarely be defined as “local” as defined, for instance, in community ecology. This definition of local and regional scales is arbitrary and depends on the organism under study, considering its dispersal ability and other population parameters, which, in turn, could affect its response to the environment and the possibility of interaction with other species (see Sabatini et al. 2022). So, from the macroecological perspective, hereafter, we define β-diversity simply as differentiation among assemblages regardless of the grain size used to obtain the data. The β-diversity can be calculated for “focal cells,” in which composition is compared with neighboring cells (and the size of the neighbor can vary), or by a pairwise differentiation matrix among cells, and both approaches can use several distinct metrics (see next section). Finally, it is more common to define β-diversity based on species, based on occurrence or abundance, but it is straightforward to expand the reasoning and calculate it based on phylogenetic and functional data, as discussed in the previous sections.

7.3.2 Geographical Patterns in β-Diversity and Its Components Under the reasoning of the differentiation diversity, there are hundreds of metrics for estimating compositional similarity and dissimilarity (distances) among assemblages, varying in their statistical and mathematical properties, for distinct types of

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data (Koleff et al. 2003; see Legendre and Legendre 2012 for a review). The use of such metrics has a long history of application in community and metacommunity ecology, especially in the context of numerical ecology and application of multivariate methods, and only a very brief review is presented below. As pointed out in Sect. 3.1.3, the most common type of data available for macroecological analysis is the incidence matrix M, with the presence or absence of species in each assemblage. When comparing two assemblages (i.e., two lines of M; see Chap. 3), it is standard to count the number of co-occurring species (a), the number of species that only occur in each of the assemblages (b and c), and the number of species absent from both assemblages, considering the total number of species in M (d). The several formulae available for estimating β-diversity based on presence-absence data are defined by arranging these quantities a, b, c, and d in different ways. For instance, it is possible to define the Jaccard similarity (J) as J

a

a  b  c

which varies thus between 0 (no shared species between the two assemblages) and to 1 (when the composition of the two is the same). Thus, in this case with Jaccard, it is possible to use the complement of Jaccard so that 1 − J is a distance, or dissimilarity, metric (which allows an easier interpretation because it is better to have more dissimilarity directly associated with higher β-diversity). Notice also that in this metric, the common absence of species (d) does not affect the definition of the similarity. Several other metrics can be defined based on the counting a, b, c, and d. For instance, the Sorensen dissimilarity (complement of the original similarity metrics, differing from Jaccard just because the term a is multiplied by 2) is defined as (b  +  c) / (2a  +  b  +  c), whereas Simpson dissimilarity is given by min(b  +  c) / a + min(b + c). In practice, it is possible to calculate these metrics for all combinations of assemblages in M, so we have a similarity matrix between pairs of assemblages and 1  in the main diagonal (and the lower triangle is equal to the upper triangle). The patterns in this pairwise matrix can then be visualized with the help of clustering or ordination techniques. High dissimilarity indicates different assemblages (i.e., with different species composition) and thus a high β-diversity for the region. The pairwise dissimilarity matrices describe the overall patterns of variation among assemblages, and ordinating this matrix is a way to synthesize the multivariate space of species composition (or abundances) as previously described for ecological niches in Chap. 5 and phylogenetic and functional diversity in the previous Sects. 7.1 and 7.2. There are several ways to view the geographical patterns in biodiversity. For instance, Legendre and DeCaceres (2013) showed that we could evaluate the local contribution for beta-diversity (LCBD). In short, this metric is the distance of each cell to the centroid in the multivariate space of species composition (and it is also possible to evaluate the contribution of each species to beta diversity, SCBD, which may be correlated to niche metrics discussed in Sect. 5.2.1) (Fig. 7.7a).

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Fig. 7.7  Geographical patterns in β-diversity using different metrics for on the Furnariidae dataset, including LCBD (a), the principal coordinate of pairwise Sorensen dissimilarity among cells (b), and the mean Sorensen between nearest neighbor cells (c)

For the Furnariidae dataset, the LCBD correlates with the first principal coordinate of the overall Sorensen pairwise dissimilarity matrix, with both metrics showing higher β-diversity in the southwestern region of South America (Fig. 7.7b). Both analyses evaluate the overall patterns of β-diversity in M, expressing general patterns in assemblage composition, but it is possible to use more refined approaches to ask slightly different questions. For instance, it is possible to map the mean pairwise distance of each cell (the “focal” cell) and its neighbors (Qian and Ricklefs 2007; Melo et al. 2009), and with this approach, a different pattern appears, with higher β-diversity better following the Andean region (Fig.  7.7a). In short, these higher mean values for Sorensen dissimilarity indicate high β-diversity, so focal cells in this region tend to be more dissimilar to their neighbors than focal cells in the Amazon, for instance. The idea is then to evaluate the variation of composition at smaller scales within regions instead of evaluating the overall differences among assemblages throughout the entire domain (see Sect. 7.3.4 for regionalization approaches, for instance). The differences in species composition among assemblages expressed by these dissimilarity metrics have different components. There has much debate, for instance, on how differences in richness among assemblages affect such metrics and how to disentangle these effects to estimate the “pure” compositional differences. The problem becomes clear by considering a hypothetical example in which an assemblage A is composed of ten species and an assemblage B of 20 species. However, all ten species in A are also found in B, so A is entirely nested within B (see Sect. 5.2.3 for a discussion on nestedness in the context of species interactions). In this case, the difference in species composition is due to variation in richness between A and B and not because of the so-called turnover or replacement component per se. Under the above reasoning, Baselga (2010, 2013) proposed a now popular approach to decouple β-diversity into its turnover and nestedness components based on Sorensen dissimilarity, with the latter defined as the difference between Sorensen

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and Simpson indices defined above. As these quantities are additive, it is possible to evaluate the proportion of total dissimilarity among assemblages due to turnover (in comparison with richness effects). Almeida-Neto et al. (2012), however, pointed out that Baselga’s (2010) partition may be better viewed as reflecting the overall contribution of variation in richness to β-diversity rather than nestedness, in a stricter sense and as measured using more appropriated statistics such as NODF (see Sect. 5.2.3). The main issue is that NODF has an explicit directional component of richness variation in community composition, from poorer to richer communities (see also Carvalho et  al. (2012) for other criticisms and a reply to both criticisms by Baselga 2012). Even considering the valid criticisms by Almeida-Neto et al. (2012) about using the term “nestedness” for the richness, Baselga and Leprieur (2015) compared the alternative approaches and insisted that the 2010 framework allows separating the variation in species composition derived from species replacement independent of richness difference and the variation derived from nested patterns (see also Legendre 2014). Independent of this discussion about the meaning of the nestedness component and the differences in respect to more appropriate metrics such as NODF, we’ll keep using the term “nestedness” for Baselga’s (2010) original framework hereafter, because of its popularity in the current macroecological literature. Soininen et al. (2018) performed a meta-analysis to evaluate several predictions related to partitioning β-diversity in terms of turnover and nestedness or richness-­ derived components with respect to spatial extent, realm, and latitudinal gradients, as well as life history and ecological traits of the groups under study (body size, dispersal type, trophic level). Even though the overall fit of these explanatory factors on effect sizes was not high, they supported that nestedness tends to increase with increasing latitude, as Baselga et al. (2012) found in early analyses at global scales of amphibian assemblages. Indeed, Dobrovolski et al. (2012) analyzed New World assemblages and showed a pattern in the relative importance of the nestedness component, ranging from 53% for amphibians, 42% for mammals, and 30% for birds. Moreover, spatial patterns in this higher component of nestedness were also supported, and this component was correlated with the age of each region across the New World after the last glacial maximum, especially for amphibian assemblages. The turnover component tends to follow the opposite pattern, as recently shown by Sabatini et al. (2022). Soininen et al.’s (2018) meta-analysis also partially supported that the nestedness component increases with the overall extent and for large-bodied organisms for passively dispersed taxa. On the other hand, higher turnover is expected to be found at low latitude assemblages for studies at large extents but is lower for small-bodied organisms with active dispersal. For the Furnariidae data, turnover and nestedness components based on mean coefficients among nearest neighbors for each focal cell are correlated with total β-diversity estimated by mean Sorensen (r = 0.876 and 0.621, respectively). The higher total β-diversity in the Andean richness is due to the turnover component and relatively higher nestedness component appearing for Central America (Fig. 7.8). Across the entire Neotropics, the median β-diversity was equal to 0.24, with the

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Fig. 7.8  Geographical patterns of turnover (a) and nestedness (b) components of β-diversity calculated by the mean Sorensen dissimilarity between nearest neighbor cells for Neotropical Furnariidae

mean nestedness component equal to 0.09, and the distribution of ratios between nestedness and total β-diversity is indeed strongly right skewed, with a median of 39%. Another possibility to explore geographical and environmental patterns in pairwise matrices of β-diversity is to deal directly with the pairwise distances. The most straightforward approach is to use different forms of the Mantel test to correlate dissimilarity among assemblages with geographic or environmental distances (as discussed in Sect. 5.3.2, the Mantel test is the Pearson correlation between the elements of two similarity or dissimilarity matrices tested by randomization; see also Manly, 2006). A first neutral expectation in meta-communities and macroecology is that similarity among assemblages increases with increasing geographic distances, a pattern usually referred to as “distance-decay similarity” (see Bell 2001; McGill and Collins 2003). The theoretical function underlying this is usually exponential, so a log-transformation of geographic distances is recommended (see also Martinez-­ Santalla et al. 2022). It is also possible to detect this nonlinearity by applying Mantel correlograms and evaluating the correlation between matrices at increasingly distance classes. Soininen et al. (2007) performed a meta-analysis of such patterns and showed that geographic distances explained about 55% of the variance in dissimilarities, with rates varying as a function of scale (i.e., the extent of assemblages compared) and with a latitudinal pattern. The rate of decrease is higher at high latitudes than at low latitudes when dealing with larger extents, but short distance turnover was higher at lower latitudes (see also Graco-Rosa et al. (2022) for an update of a meta-analysis for decays in taxonomic and functional β-diversity in respect to geographic and environmental distances). For the Furnariidae dataset, there is a relationship between Sorensen similarity (i.e., the complement of the overall β-diversity discussed in the previous section) and the geographic distance among assemblages, but this does not appear as a linear

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Fig. 7.9  Relationship between Sorensen similarity (complement of overall pairwise β-diversity) and geographic distances among assemblages of Furnariidae birds in the Neotropics. The Mantel test indicates a strong negative relationship (r = −0.601; P 99%). The model with a parameter λ was the second best, with a parameter equal to 0.82

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(thus supporting a departure from Brownian motion). The O-U model, suggested by correlogram and by the PSR curve, was not a good description of data, even though its α = 0.0428 is coherent with patterns shown in Fig. 8.7. Cooper and Purvis (2010) explored the idea of variation in evolutionary rates from a more direct deconstruction strategy, fitting different models (Brownian, OU, and EB) for orders or mammals found in different ecoregions. The interesting aspect of this approach is that non-stationarity can be associated with geographic variation. For the entire mammal clade, the body size is better fitted by an EB model, but when evaluating the order and regions, the differences between the models are much more subtle (e.g., out of 23 orders, in 16, the body size variation is better described by a Brownian model). Cooper and Purvis (2010) then modeled the evolutionary rate σ2 from the Brownian model and showed that higher estimates were found in colder ecoregions, revealing a complex interaction among geography, climate, and history driving evolution in mammalian body size (see discussion on Bergmann’s rule below, Sect. 8.4.1). A more elegant approach to evaluate how these rates could change with environments or regions was proposed by Clavel and Morlon (2017), and they showed indeed that in colder periods throughout the Cenozoic, there was an increase in body size diversification rates (see also Velasco et al. 2020). Although these evolutionary models can give a nice clue about the general patterns, it is important to highlight that they all assume stationarity (in a broad sense), so that the parameters remain constant throughout the phylogeny (or at least their variation is constant). Thus, the same model applies to all subclades within a large clade under analysis. Depending on the phylogenetic scale of the study, this is very unlikely, and there are several ways to evaluate this issue. Diniz-Filho et al. (2015), for instance, showed that the PSR curve could be a useful exploratory tool to identify phylogenetic non-stationarity, although other methods such as AUTEUR (Eastman et al. 2011) and Castiglione’s et al. (2018) RRphylo, based on fitting ridge regression. More interestingly, fitting an O-U process with multiple adaptive peaks that may be related to habitats or environmental conditions is a first step toward avoiding this assumption. For instance, Godoy et al. (2019) provided an interesting example of fitting complex O-U models to understand patterns in body size evolution in crocodilians, including fossil species. A general conceptual discussion underlying these models is that these peaks reflect optimum body sizes for multiple combinations of environmental drivers affecting macroevolutionary dynamics. Pagel et  al. (2022) proposed a more general and flexible evolutionary model starting from a simple Brownian motion with two parameters, the standard evolutionary rate (σ) and another one for a directional change (β). However, the important novelty here is precisely that they allowed these parameters to change throughout the phylogeny. Fitting this model to mammalian body size reinforces several of the issues discussed above, particularly that parameters are not fixed throughout the evolution and that independent variation of β and σ can explain the patterns of interspecific variation. Even though the variation in the two parameters is not relatively high, it is interesting that directional shifts are more common than increases in evolvability (i.e., higher σ) and that they are more concentrated in the early branches, corresponding to the early diversification at the order level and most likely tends to

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occur in bursts (see also Raia and Meiri 2011; Raia et al. 2012). Adaptive peaks are not incorporated in Pagel’s et al. (2022) model, and again it may be hard to think of deterministic optima driving such directional changes in different moments, although it has been clear for a long time that life history and ecological patterns (e.g., diet or habitat preference) differentially constrain body size evolution (Sibly and Brown 2007; Smith et al. 2010). The models mentioned above have been widely applied to describe the phylogenetic patterns in body size evolution, but a fundamental (and related) issue is how these patterns can be modeled as a function of other ecological and life-history traits. Indeed, finding these evolutionary correlations was one of the main motivations underlying the initial development of phylogenetic comparative methods in the 1980s or earlier (see Felsenstein 1985; Harvey and Pagel 1991). The main issue was, at that time, that the Type I error of the correlation of two or more traits across species is inflated due to phylogenetic non-independence among species, as already discussed in Sect. 3.3.2. This estimation issue, rather than understanding body size evolution as discussed above, was the initial motivation for applying phylogenetic comparative methods in macroecology (e.g., Blackburn and Gaston 1998; Blackburn 2004). However, the magnitude of this inferential problem depends positively on the magnitude of the phylogenetic signal, and the higher biases in Type I error occur when evolution is Brownian. Although body size usually has a strong phylogenetic signal and can be frequently modeled by Brownian motion, as discussed above, other ecological or life-history traits tend to be more labile (e.g., Freckleton et al. 2002; Blomberg et al. 2003). So, in practice, biases in Type I errors are not that serious (Diniz-Filho and Torres 2002). Even so, the more interesting issue when applying comparative methods to correlation or regression problems is what parameter is estimated. Martins and Garland Jr (1991) argue that the correlation of interest is the “input correlation,” which is the intrinsic correlation of changes of one of the traits in response to the other throughout the entire tree. This parameter differs from the standard correlation among traits across the tips (species) of the phylogeny. This interpretation is explicit when applying the popular Felsenstein’s (1985) PIC method, in which correlation is calculated between the rates of changes for two traits for different contrasts of nodes or tips throughout the phylogeny. So, this interpretation of the parameter reveals that adaptive inferences based on correlations among traits that have been proposed at lower levels (within species or closely related ones) can be inferred based on interspecific data if comparative methods are applied, as be discussed for Bergmann’s rule, in the following Sect. 8.4.1. However, this is only strictly valid under the stationarity assumption, which is not usually the case at broad phylogenetic scales, as shown by Pagel et al. (2022) for body size.

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8.3.2 Cope’s Rule Phylogenetic patterns in body size have been widely applied to evaluate macroevolutionary dynamics, but there is an important limitation as the fitted evolutionary models discussed in the previous section rarely take the explicit extinct species into account. So, although it is possible to evaluate how body size is correlated with phylogenetic proximity, it is much more difficult to infer evolutionary trends, such as an increase in mean body size in time. Even though the fossil record is assumedly biased and poorly known, body size for at least some of the extinct species in a clade can be helpful to improve the fit of evolutionary models (Slater et  al. 2012). Moreover, adding fossil data may provide a more comprehensive picture of body size evolution, especially for evaluating macroevolutionary trends. Due to all these reasons, these comparative analyses of body size have been a very active field in paleobiology (e.g., Damuth and McFadden 2005). In the early twentieth century, Darwinism was in crisis, and the newly established evolutionary thought was dominated by several competing theories that proposed all sorts of mechanisms and processes that could explain biological diversity (Bowler 1992). In this context, paleontologist Edward D.  Cope developed and championed a broader view of evolution called “orthogenesis,” a mixture of mutationism and neo-Lamarckism, marked by intrinsic (and metaphysical) trends to change the species by accelerated ontogenetic development. This view of evolution was mainly derived from Cope’s evaluation of morphological trends he observed in the North American mammalian fossil record. A few decades later, in 1944, G. G. Simpson published the classic “Tempo and Mode in Evolution,” in which he inserted paleontology into the developing framework of the modern synthesis and reestablished the role of adaptation by natural selection as the primary driver of changes (vanishing the neo-Lamarckian and mutationist views, including orthogenesis). Even so, the broad-scale trends in morphological variation, in particular the tendency to increase in body size through time, became known as Cope’s rule (but see Polly 1998 for a more complex historical view and a debate with Alroy 1998). Despite Simpson’s reasoning that it was possible to explain body size trends by standard adaptive explanations without inviting metaphysical explanations, talking about trends in evolution and the almost inherent association with “progress” became suspicious, and it is not surprising that non-adaptive (neutral) explanations quickly developed for Cope’s rule. More recently (i.e., MacFadden 1986; Alroy 1998), it was possible to go back with general explanations for this trend in body size based on more sounding data and analyses. It is also interesting that, at least in part, this resurged interest came together with the early developments of macroecology (e.g., Brown and Maurer 1986; Maurer et al. 1992). Thus, although Cope’s rule has been mainly investigated in the paleontological context, there are several important interfaces with macroecology, for instance, when dealing with BSFDs as shown in Sect. 8.2.1 and the comparative phylogenetic analysis of body size data discussed in the previous section.

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Fig. 8.8  Patterns in body size evolution along a phylogeny, showing the resulting BSFD and patterns of change through time for simulations under a standard Brownian motion (a), a Brownian motion with a trend toward increasing body size (driven trend, b), and Brownian motion with a boundary close to the minimum ancestral value (passive trend, c). The BSFD tends to be normally distributed in a and b, but strongly right skewed in c

The discussions around Cope’s rule have been focused on at least two main related issues. First, is it possible that patterns of body size variation in time are just an artifact and are generated by stochastic processes? If not, how can it make sense of adaptive patterns driving variation in the same direction for so long? This second issue involves evaluating the generality of Cope’s rule and if the potential mechanisms are driving variation within or among species, balancing anagenetic cladogenetic processes and leading to the question of how body size is associated with speciation-extinct dynamics. The idea that macroevolutionary trends in body size are due to stochastic process involves a first recognition of what has been called passive trends (in opposition to active, or driven, trends) (Fig.  8.8), which Steven Stanley and Stephen J.  Gould earlier conceptually championed (Stanley 1973; Gould 1988). Passive trends appear when ancestral species in a clade are small-bodied, and there is a minimum limit to body size for a particular group, given morphological, ecological, or physiological constraints (a lower “evolutionary boundary”). Thus, the evolution of body size would inevitably lead to an increase in the mean body size due to an increase in variance (see McShea 1988, 1994; Gregory 2008). This proposition of the passive trends is also related to broader conceptual discussions around evolutionary progress and the evolution of biological complexity, reflecting a more profound change in the more orthodox view based on adaptive evolution (McShea 2016). This diversification in the absence of general adaptive trends is what we expected under Brownian motion.

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On the other hand, active trends would represent Cope’s rule in a “strict sense” and are based on the competitive advantages of being large. As early pointed out by Brown and Maurer (1986) in a macroecological context, this competitive advantage would appear, for instance, if large species use a disproportionally high number of resources or energy from ecosystems at local scales (but see Damuth 1993). Large species also tend to possess broader niches, large geographic range sizes, and increased longevity. There are, of course, some disadvantages in being large as well, including longer generation time and high absolute energy and resource requirements, leading to small abundances that may drive populations to extinction with a higher frequency. Kingsolver and Pfennig (2004) showed that selection coefficients for body size are positive for about 79% of studied populations, suggesting a positive balance of advantages that could lead to Cope’s rule by active drive (see also Hone and Benton 2005). However, the situation is more complicated, and these positive selection coefficients at local scales do not always translate into higher diversification rates in macroevolutionary dynamics. The main issue is that, at least for mammals, an increase in body size is also associated with specialization (usually in diet), which also leads to a high extinction rate and to counteracting effects on body size evolution at different hierarchical levels (Valkenburg et  al. 2004; Raia et al. 2012). Disentangling these alternative processes and understanding active and passive trends are thus more complicated than anticipated, requiring information on other ecological characteristics of the species that could reveal specialization trends in time, thus based on an extensive and relatively detailed fossil record. Moreover, it is essential to consider the balance between anagenetic and cladogenetic effects on body size changes among species leading to Cope’s rule, which must also lead to known patterns in BSFD, coherent with simulations by Maurer et  al. (1992), Kozłowski and Gawelczyk (2002) for Clauset and Erwin (2008) (Fig.  8.3). For instance, McShea (1994) proposed what he called the “subclade test,” which predicts a correlation between the skewness of BSFD and the distance from the minimum body size (or some description of the central tendency of BSFD). Under a passive trend, Cope’s rule appears because of the small-bodied ancestor close to a lower boundary for body size. Thus, clades of small-bodied species have a right-­ skewed BSFD, but as evolution stochastically generates larger bodies as ancestors of new clades, the BSFD in these larger groups would tend to a normal. Maurer (1998b) showed, for instance, that for birds, there is not a clear positive correlation between mean and skewness among orders, not supporting thus a passive trend and reinforcing the role of energetic explanations driving body size increase (see below). However, this result depends on the definition of subclades (i.e., orders), with some leverages in the relationship between mean and skewness. Wang (2001) proposed a very interesting and more elegant method derived from the subclade test to evaluate passive trends, following the reasoning of ANOVA and based on partitioning the skewness within and among clades. Wang’s (2001) method (which we could call ANSKEW) is interesting because rather than classifying a trend into two discrete categories, it allows evaluating the relative balance between driven and passive components of variation. For distinct subclades within a large

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clade, Wang’s (2001) method defines that an active system can be characterized if the total skewness is due mainly to skewness within each one of the clades, whereas a passive system is more characterized in the total skewness, which is due to skewness among the means of groups plus a heteroskedasticity component. Using data from bird orders with more than 100 species, ANSKEW suggests that about 19% of the body size variation would be due to active trends (within-order skewness) and 81% due to passive diffusion. However, again this result someway assumes phylogenetic equivalence among subclades (orders), and it would be interesting to compare this with some form of neutral (Brownian) model for a reference (see also Diniz-Filho et al. 2007a for an application of Wang’s 2001 method to evaluate niche evolution in the context of LDGs). From a more methodological point of view, the idea of cross-species and assemblage-­based macroecological analyses in geographical space discussed in Chap. 3 (the matrix M) can be extended to time to be used with paleontological data by replacing cells of spatial units by time bins. For Cope’s rule, most analyses were cross-species, but as time is unidimensional, the associations between the two approaches (i.e., cross-species and assemblages) are much easier to understand and to combine them for a more general evaluation of patterns and processes. A first and straightforward cross-species test for Cope’s rule is to correlate body size of each species with time, usually considering the time of first appearance (different from the spatial evaluation, in which mid-range metrics are preferred). Under Cope’s rule, in a strict sense, a positive linear correlation is expected between body size and time, but as pointed out by Jablonski (1997), it is possible to use this simple scatterplot for a more comprehensive evaluation. For instance, an active trend is characterized by an increase in both maximum and minimum body size along time bins, whereas passive trends are characterized by stability of minimum and even medians or means coupled with an increase in maximum (i.e., there is then strong heteroscedasticity in the relationship between body size and time; see below on the subclade test). Notice that it is also possible to compare different taxa using cross-­ species approaches under a deconstruction approach (i.e., Hone and Benton 2007). In addition, it is possible to evaluate the mean or median evolution of body size for assemblages at each time bin, and in this case, it is interesting to weigh the species by the inverse of their temporal ranges to minimize autocorrelation issues. Finarelli (2007) and Raia et al. (2012) used more sophisticated approaches to comparing species’ body size following different events of origination and extinction in each time bin, which also allows correlating shifts in body size with diversification. Alroy (1998), in a first comprehensive analysis of mammal fossil record in North America, showed that despite the overall increase in variance (with body size starting indeed from early small-bodied species in the Cretaceous), there are strong suggestions of a bias in the diversification toward large bodies through time. Moreover, there seems to be an increasing gap between large- and small-bodied lineages, which would explain suggestions for a bimodal BSFD. Smith et  al. (2010) later showed these patterns in more detail and that this increase in maximum body size is associated with other environmental trends during the Cenozoic (including changes in available continental area, temperature, and oxygen concentration in the

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atmosphere). The approach by Alroy (1998) is also interesting because it is based on coupled ancestor-descendent pairs, even though these pairs were not phylogenetically explicitly, as this would be extremely difficult, or even impossible, for this scale and using fossil data. Nevertheless, interestingly, Alroy (1998) showed that although these pairwise differences were approximately normally distributed, there was a significant but small bias toward increasing body size, with new species being, on average, about 9% larger than their assumed ancestors. With this approach, Alroy (1998) accounted for broad-scale phylogenetic effects of body size increase and focused on shifts at small phylogenetic scales. It is interesting to note that the slope of this relationship measures the overall rate of evolution of body size, assuming an active trend (Cope’s rule in a strict sense). Suppose that several species are distributed in a wide interval of time (say, 50 million years), with the ancestral having 10 kg and evolving to a much larger species of 100 kg in this time interval. This comparison between extremes in time gives a slope of 0.046 from a linear regression fitted to the logarithm of body size against time. This slope is equivalent to an intuitive metric for estimating evolutionary rates called “darwins,” given by log(Mi/Md)/t, where t is the divergence time, in millions of years, between the ancestor (Mi) and descendent (Md) species (see Gingerich (2019) for a review of metrics for estimating evolutionary rates and their interpretation). However, two substantial improvements to this simple metric must be considered. First, a high or low rate depends intrinsically on the amount of within-population variation. Second, the time since divergence must be better expressed by generations to be comparable among distinct organisms. So, an improved metric for evolutionary rates is given in “haldanes,” so log(Md)  – log(Mi)/s/tG, where s is the pooled within-population standard deviation (at log scale) and tG is divergence in number of generations (e.g., see Sect. 8.4.2 on Island rule). Evans et al. (2012; see also Polly (2012)) proposed an alternative way to think about evolutionary rates and to evaluate the maximum rate of body size evolution of a clade, independent of the more traditional way to calculate rates along lineages. They showed that, for mammals, this maximum evolutionary rate is much slower than those usually observed for lineages, as expected. Indeed, one of the interesting points is that the relatively high evolutionary rates estimated for populations or lineages are not sustained at macroevolutionary scales, reinforcing the punctuated mode of evolution in body size, as well as the variation in rates across lineages discussed in the previous section (e.g., Kingsolver and Pfennig 2004; Pagel et al. 2022). Evans et al. (2012) also reinforced that evolution toward smaller body sizes occurs at a much higher rate than those toward large body sizes, which is associated with evolution in island environments (as discussed later in Sect. 8.4.2). It is important to realize that, in general, estimating evolutionary rates assumes that evolution is constant and linear, which is not always the case except in relatively short phylogenetic or temporal scales. Thus, it is also interesting to evaluate more complex patterns in body size fit alternative and more complex evolutionary models for the time series (analogous to models for phylogenies discussed before in Sect. 8.3.1). These models are usually classified into stasis (stability), random walks, or directional changes, and it is relatively straightforward to evaluate the statistical fit

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of time series of body size data to such models. However, it is also interesting to think in more mechanistic models and evaluate, for instance, how O-U processes with single or multiple optima for body size would improve the model fit of punctuated patterns. For instance, Hunt and Rabosky (2014) comprehensively reviewed such models based on time series and discusses several important issues, including the ecological and genetic processes underlying the stasis (leading to punctuated equilibrium patterns and coherent with macroevolutionary analyses by Evans et al. (2012) and Pagel et al. (2022)), as well as drivers within and among species gradual changes associated with Cope’s rule. As Cope’s rule has been mainly supported for mammals, it is also interesting to briefly mention that other related morphological traits may display similar patterns, but this is not necessarily due only to intrinsic and general size correlations. For mammals, brain size is one of such traits of interest, given the high level of encephalization and larger brains’ behavioral and cognitive advantages. For instance, Mondanaro et al. (2019) showed that, for primates (especially hominins), Cope’s rules apply to body size and brain size and that these trends toward large sizes are associated with higher diversification rates. In another recent example, Bertrand et al. (2022) showed that in early mammals, there was a decrease in relative brain size due to an increase in body size (because the allometric scaling coefficient is  1 indicates gigantism, whereas nanism is indicated by S 5%) are larger than H. sapiens. So, a large geographic range and relatively low local population abundances are expected for the species (Fig.  9.1). Indeed, mammals in body size similar to humans, say 60  kg, usually have geographic ranges larger than 300 km2. Although it may be complicated to calculate the

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Fig. 9.1  The relationship between geographic range size (a) and population density (b) with body size for mammals worldwide, highlighting the relative position of Homo sapiens (black spot in a). In (b), the vertical line indicates population density for different human populations, ranging from hunter-­gatherers (solid line) to industrial societies. (Data from PanTHERIA (Smith et al. 2014) for mammals and Stephens et al. (2019) for H. sapiens)

geographic range of H. sapiens, the extent of occurrence of hunter-gatherers would be larger than 120 million km2, slightly larger than the maximum for mammals of similar size and much larger than the minimum expected geographic ranges. Using the allometric models proposed by Stephens et al. (2019), we get population density for humans between 2 × 10−4 and almost 500 individuals/km2, and indeed the abundances of hunter-gatherer human populations range from approximately 0.02 to 3 individuals/km2, slightly below the average for mammals but quite well within the average for carnivores. Densities for urban societies go close to the productivity

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limits proposed by Stephens et  al. (2019), but maximum urban density is much beyond such limits and would be well characterized as an outlier in this relationship (with consequences discussed in Sect. 9.1.4). There is an interesting discussion on how these abundance estimates would reflect “natural populations” of H. sapiens. As indicated above, these abundances already reflect cultural (technological) and social characteristics of populations, which are inherent characteristics of our species. However, they can also vary among traditional hunter-gatherer societies because of dietary balances (e.g., Stephens et al. 2019). Although this is most likely a continuum, it is usually considered that these hunter-gatherer societies have a shared limited capacity to overcome more severe environmental constraints. This limitation arises because the technological advances that improve agricultural practices that resource management are not entirely independent of the environment. As revealed by patterns shown in Fig. 9.1, hunter-gatherer population densities match expected values for carnivore mammals, below the average for a given body size. Moreover, from a macroecological perspective, the geographic variation in local abundances is correlated with environmental patterns, especially productivity (e.g., Eriksson et al. 2012). Favorable environmental conditions that allow higher abundances also seem to be one of the key aspects of social innovation, including the origin of agriculture (Kavanagh et al. 2018; see Sect. 9.1.4). These macroecological patterns in abundance also make sense in light of other characteristics of H. sapiens. For instance, it is possible to scale down this a bit and make sense of patterns by considering how the abundance at more local scales is driven by resource availability within the home range of individuals or groups (Burnside et al. 2012). Indeed, it is important to recall that the abundance-body size model by Stephens et  al. (2019; Fig.  9.1) assumes patterns in how individuals explore local resources related to allometric energy use patterns. The same reasoning applies to humans, and the foraging strategy used to acquire necessary energy by different groups of hunter-gatherers, as well as decisions about which resource to use (see below), depends on the distribution and type of resources available in the region. This distribution, in turn, depends on environmental drivers, especially productivity. These patterns in the home range are also correlated with other more complex behavioral and life-history patterns that reflect in social structure and networks (Burnside et al. 2012). As Gavin et al. (2018) argue, all these factors and their interaction are also correlated with decisions in adopting, for instance, agricultural versus animal husbandry subsistence strategies. There is another outcome of this first initial expansion of H. sapiens out of Africa. Going back to our social and behavioral inheritance, at the time of leaving Africa, H. sapiens was an efficient hunter and, during geographic range expansion, had contact with indigenous species of large mammals and birds that were quickly converted into prey (and it is interesting to realize that, in this context, H. sapiens can be considered an invasive species). There is an old debate about the impact of the arrival of human populations into different parts of the world, more specifically if population densities and technological hunting abilities of hunter-gatherers were enough to drive local populations of large mammals and birds (i.e., the megafauna)

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to extinction, in several forms of the so-called “overkill” scenarios (see Barnosky et al. 2004; Koch and Barnosky 2006). One of the difficulties in evaluating such patterns is that there are some coincidences of climate change (warming) during the late Quaternary and the arrival of humans in different parts of the world, but several analyses have tried to decouple these effects (e.g., Nogués-Bravo et al. 2008, 2010). In general, different from the initial debates during the 1970s and 1980s, the current idea is that both factors had a synergic effect of triggering the late Quaternary extinctions, although their relative contributions are still under debated (e.g., Prescott et al. 2012; Lima-Ribeiro et al. 2012; Sandom et al. 2014; Araújo et al. 2017; Carotenuto et al. 2018; Prates and Perez 2021). Alroy (2001) pioneered using more elaborated macroecological approaches and computer simulations based on predator-prey models to evaluate the plausibility of the overkill scenario. His model correctly predicted the extinction or survival of 32 out of 41 large mammalian species in North America during the late Quaternary. An interesting aspect of this pioneering study is that it can be viewed as a general population model in which parameters for the multiple species are macroecological generalizations based on allometric equations. It is also possible to expand this model and explicitly incorporate other macroecological generalizations, including more complex relationships between geographic range size shifts estimated by ENMs, abundance, and body size to build more elaborate and specific demographic and predator-prey models and to evaluate the effects of geographic range shifts under climate change (Martínez-Meyer et  al. 2004; Lima-Ribeiro et  al. 2014; Lima-­ Ribeiro and Diniz-Filho 2017). In addition to direct hunting effects, it is also possible to consider indirect drivers of extinction driven by biotic interactions and habitat shifts (Pires et al. 2014; Lim et al. 2020; Sales et al. 2022). Other pioneering macroecological analyses used paleoclimatic reconstruction and ENMs to project geographic distributions in the past, showing that the distribution of wooly mammoths most likely oscillated a lot during the last 100 ky, tracking the temperature variation of glacial cycles and consequently reducing and expanding its geographic range size (Nogués-Bravo et  al. 2008; Nogués-Bravo 2009). However, the significant reductions after the Last Glacial Maximum make the species more vulnerable to hunting by the relatively dense human populations that occupied northern Europe and Siberia in recent times. This pattern would be the effect expected under the reasoning that both climatic shifts and hunting interacted to drive some species to extinction. Lima-Ribeiro et al. (2013) coupled predator-­ prey models with ENMs, showing that, for South American mastodons, these synergic effects also had a geographical and environmental component. They found a replacement between open and closed habitats in glacial and interglacial intervals (the “broken zig-zag” model) and the geographic structure of human occupation patterns. In northern regions of South America, climate change effects modeled by ENMs were most likely enough to trigger wide reductions in geographic range and, consequently, abundance, whereas in mid-latitudes and Patagonia, these shifts are much smaller. On the other hand, the coexistence between humans and mastodons is more likely, so additional effects of hunting seem to be necessary to explain extinction in these regions. Interestingly, these macroecological patterns are also

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present in the current extinctions, so understanding these past changes can help define better strategies to deal with the ongoing biodiversity crisis (Dirzo et  al. 2014; Sales et al. 2022).

9.1.2 Genetic and Phenotypic Variation in Human Populations The relatively fast expansion of the geographic range of H. sapiens in the last 70 ky or so and the associated patterns in population structure, balancing variation in abundance in response to environmental variation, population density, migration waves, and geographic isolation, generated genetic and phenotypic divergence among local populations worldwide. On the one hand, considering the large amount of data available for our species, this divergence opens the possibility of studying how adaptive and stochastic processes can drive genetic and phenotypic variation, as well as how patterns of isolation and dispersal throughout history create much more complex geographical patterns in different scales. On the other hand, it is impossible to ignore the potentially undesirable consequences of studying and mapping this variation, as a lack of understanding of how evolutionary dynamics happened to generate distortions that quickly become an excuse for racial discrimination and all forms of social, sexual, and ethnic discrimination, as briefly highlighted at the end of this section. As previously pointed out, all available evidence suggests an African origin for H. sapiens, although several events of genetic introgression from other independently evolving populations are known (which does not mean that a model of multiregional origin is supported; see Templeton 2002; Bergstrom et  al. 2021). The primary and first genetic evidence for this early African origin comes from comparative genetic analysis of local human populations based on mitochondrial DNA (mtDNA), as in the classical study by Cann et al. (1987). Since then, several studies have supported much more complex patterns, but at global scales, we have two overlapping gradients of genetic and phenotypic differentiation generated by historical migration pathways and isolation-by-distance process (Handley et al. 2007; Cramon-Taubadel 2014). First, local populations become more different as they become more distant from east Africa. Second, regardless of the region where these populations are found, closer populations in geographic space tend to be similar. Thus, to a great extent, genetic and phenotypic variation patterns reflect the historical dynamics of geographic range expansion and thus do not generate well-defined and phylogenetically consistent groups of populations. Instead, we see long-range continuous gradients, as shown by early pioneering studies by Cavalli-Sforza’s group (see Cavalli-Sforza et al. (1994) for a synthesis). These patterns tend to appear not only for genetic variation, and more recently, comprehensive analyses showed that craniometric variation could be better understood based on a neutral perspective (Cramon-Taubadel 2014; see also Lynch 1990). Of course, at the same time, several more detailed analyses of particular regions using now more refined genetic and genomic data showed complex patterns of

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dispersal and migration through time influencing current patterns of genetic variation. Even the difference among types of molecular markers used reveals distinct ecological and life-history patterns in population expansion (in our case, social and cultural factors as well) and how they interact to generate currently observed patterns of genetic divergence (Harcourt 2012). For instance, an exciting debate happened in the early late 1970s about the association between several gradients of allele frequencies and historical/archaeological knowledge about the expansion of agriculture from the Middle East to Europe, as pioneered by Cavalli-Sforza’s group (e.g., Menozzi et al. 1978; see also Sokal and Menozzi 1982), even there are some complex and potentially problematic statistical issues involved in showing gradients based on principal component analysis (Sokal et  al. 1999; Novembre 2012; Novembre and Stephens 2008). These patterns are also widely investigated as they are related to Paleolithic against Neolithic origins of current European populations (e.g., Richards et al. 2000; Chikhi et al. 2002; see Hofmanová et al. 2016; Lipson et al. 2022 for more recent evaluations). These complex geographical patterns of neutral genetic variation are coupled with other phenotypic patterns of adaptive variation. Some of these patterns, mainly in morphology, may be more directly associated with previous discussions on ecogeographical rules like Bergmann’s, Allen’s, and Gloger’s rules that were already discussed in Chap. 8 (see Goldenberg et al. (2022) for a review). For instance, it is interesting to highlight that the first discussion about the validity of the thermoregulatory mechanisms associated with Bergmann’s rule by Scholander (1955) was actually based on analyses of human geographic variation. Even so, more recent studies seem to support that human populations in northern regions were heavier (Bergmann) and with proportionally shorter limbs (Allen) than warmer tropical populations (Ruff 1994, 2002; Perez and Monteiro 2009; Betti et al. 2010, 2015) (Fig. 9.2). In the context of thermoregulatory explanations for such patterns, there is still some discussion about these patterns as they seem to be influenced by some extreme observations. For instance, shape variation may not be adaptive in some cases and reveal mainly allometric relationships (Cramon-Taubadel 2014). In addition, there are other adaptive drivers of body size, including the dwarfing observed in pigmy populations in the tropics that may reflect advantages associated with the shorter growing season in environments with higher adult mortality (Migliano et al. 2007; Perry and Dominy 2009; see also Sect. 8.4.2 on Island rule and dwarfing of H. floresiensis). Thermoregulation is an essential adaptive component underlying these morphological patterns, and indeed human populations also vary in terms of basal metabolic rate. There is also an inherent demographic effect on high mortality rates associated with temperature, even in modern human populations (Gasparrini et al. 2015). Even so, it is not easy to decouple thermoregulation and other significant effects related to productivity driving broad-scale patterns in body size, such as diet. Cramon-Taubadel (2014) reviewed more specific cranial variation patterns and discussed several interesting macroecological patterns related to adaptive and neutral diversification in human populations. These patterns tend to reinforce the adaptive patterns in body size expected under Bergmann’s rule based on a generalized

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Fig. 9.2  Bergmann rule in H. sapiens, visualized by plotting mean body weight for males (gray dots) and females (black dots) against latitude for human populations. (Data from Ruff 1994)

morphometric approach (see Sect. 8.1.2). However, other patterns in craniometric variation, for instance, in facial morphology, usually considered adaptive to temperature, seem allometrically related to body size. In this context, it is interesting, however, that Cramon-Taubadel (2014) discusses how post-World War II physical anthropology, to avoid racist interpretations of human variation (i.e., supported by non-adaptive, historical divergence among groups that were characterized as “races”), tried to reveal adaptive processes underlying all morphological variation. In addition, previous authors assume that, in the absence of natural selection (i.e., neutrality), there would be no reason to observe variation in populations living in colder or hotter environments. We know today that this is not true, of course, as neutral dynamics of expanding populations can also generate complex patterns of morphological variation, and it may be challenging to disentangle spatial correlates of morphological and environmental variation. In the end, although there may be signs of an adaptive relationship between cranial variation and temperature (supporting both Bergmann’s and Allen’s rules), Cramon-Taubadel (2014) concluded that, generally, craniometric variation among human populations is a consequence of neutral microevolutionary dynamics. Another important phenotypic trait that varies among human populations and always attracts much attention is skin color, which is also the basis for some ecogeographical rules such as Gloger’s rule. More descriptive approaches traditionally

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recognized that darker skins were found in tropical regions, whereas lighter skins were found in temperate regions, suggesting a relationship with the environment. However, alternative adaptive explanations for these associations exist (Goldenberg et al. 2022), and more detailed and recent investigations of this association revealed a much more complex and exciting story (Jablonski and Chaplin 2000). Large tropical primates closely related to Homo, such as chimpanzees and gorillas, have light skins. Nevertheless, the loss of fur associated with several adaptive processes in positive feedback involving water-balance mechanisms, diet changes, and thermoregulation most likely triggered evolution to darker skin in the tropics at the early stages of hominin evolution. The main potential driver of this process is to avoid the dangerous effects of UV driving degradation of folic acid, which causes high infant mortality and infertility. However, as humans dispersed toward the northern region, lighter skin with less melanin most likely evolved because of the need to keep a high production of vitamin D (and there may also be additional effects related to skin cancer; see Lopéz et al. 2014). These selective agents then created a broad-scale continuous gradient in skin color, although diet effects can keep relatively darker skin in northern populations. It is inevitable to point out that all these discussions on human phenotypic variation in both morphology and skin color, and about the adaptive and neutral divergence patterns associated with them, although tracking some of the ecogeographical rules such as Bergmann, Allen, and Gloger’s rules, have been historically giving support to misleading racial politics and are the basis of several forms of discrimination. Current scientific understanding of these patterns and processes does not support these politics and discrimination for several reasons. Most of the morphological variation among the human population is a product of historical processes of expansion and stochastic divergence, so by definition, there is no adaptive value associated with this variation, and thus it is impossible by definition to state that part of this variation in “better” or “worse.” However, when we observe clear clines associated with the environment, such as skin color, advantages for survival depend on the environment, and there is no association (by the way, this is the most emblematic morphological trait when discussing racial discrimination). Moreover, as previously pointed out, both adaptive and neutral processes generate broad-scale gradients in genetic and phenotypic variation. No “natural” groups of populations could be defined as “races” that, in turn, would have inherent superior or inferior status. What we see, in both cases, are complex geographical patterns that respond to continuous environmental gradients or multiple historical events of dispersal and isolation through time. Even these gradients are usually not too steep, and there is a relatively low proportion of variation among populations compared to total variation (see Edge et al. (2022) for a recent review and discussion on Richard Lewontin’s 1972 classical paper on the subject). Although following similar reasoning, more complex discussions appear if we consider cultural and behavioral (social and sexual) patterns in a macroecological and macroevolutionary context. Thus, the challenge of modern physical anthropology is, as discussed by Cramon-Taubadel (2014), to understand the biological variation among populations and always highlight that, regardless of patterns and

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processes of divergence, this does not support any racist interpretations. On the other hand, arguments against the biological existence of biological races should be used with caution because there is always a risk of misinterpretation that would lead, someway paradoxically, to a denial of the existence of racism. Although there is no biological support for “races,” we must acknowledge that this concept became a genuine social construction. Thus, it is important to keep fighting racist and discriminatory attitudes and to support the political movements toward a more egalitarian ideal of society. It is beyond the scope of this book to go deeper into these complex anthropological and sociological discussions about human variation and racism. However, even so, it is always important to keep these issues in mind and avoid a naïve attitude of “objective” discussion about human genetic, morphological, and cultural variation.

9.1.3 Human Cultural and Social Diversity Despite the potential ideological issues related to the phenotypic patterns of genetic and morphological variation in H. sapiens discussed at the end of the previous section, these patterns are also found in several other species, as discussed, for instance, when thinking Bergmann’s rule (Sect. 8.4.1). Evaluating such patterns is interesting to show that humans also follow these more general biogeographical patterns, helping us to understand patterns and processes in other species (and the discussions on processes underlying geographic gradients in color skin may be an excellent example of this potential of knowledge feedback). The geographic gradients in more complex social and cultural characteristics that emerge from the more complex behavioral patterns unique to our species are even more interesting than these genetic and morphological variations. Macroecological analyses of behavioral patterns are still in infancy (e.g., Machado et al. 2016; Fontoura et al. 2020), and one of the main limitations is the lack of populational data at broad spatial and taxonomic scales for most groups of organisms. Nevertheless, this is not a real hard limitation for H. sapiens (despite difficulties in collecting data and defining some cultural patterns), so available datasets and platforms on cultural, ethnographic, and linguistic aspects of human diversity at the population level, such as D-place (Kirby et al. 2016), provide an important for theoretical improvements in our overall understanding of behavioral macroecology. At the same time, the discussions around these gradients and the underlying processes parallel many of the more general aspects involved in the origin and maintenance of the richness and diversity gradients discussed in Chaps. 6 and 7. Collard and Foley (2002) pioneered the study of latitudinal gradients in human cultural diversity and showed, for distinct continents, that higher cultural diversity appears for regions closer to the tropics. The data used by Collard and Foley (2002) define “culture” based on the classification available in Price’s Atlas of World Cultures, and they counted the number of cultures for different latitudinal bands (assigning them to each band based on midpoints). As expected, they found

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significant statistical correlations (i.e., r > 0.8) with temperature and rainfall, which could provide the first set of ecological explanations for these patterns based on higher population density that could coexist and, under higher environmental heterogeneity, would also develop alternative behavioral ways to deal with abundant and variable resources. Alternatively, the more unstable environments and lower availability of resources would constrain how humans deal with them (see Chap. 6). However, at these broad scales and considering the coarse definition of data (i.e., “culture”), it is difficult to disentangle the many potential drivers of such patterns. More recent analyses, based on more refined or specific cultural and ethnographic data, better coupled with historical data, help to identify processes and mechanisms generating such patterns. For instance, Botero et al. (2014) showed that belief in moralizing gods is well explained by social and political complexity, including the capacity of farming and animal husbandry, and that triggers social cohesion that may be ecologically adaptive in harsh and unstable environments. Kavanagh et al. (2021) also showed that another social and cultural trait, land ownership, is also related to environmental characteristics, predicted by what is traditionally called “resource defensibility theory,” especially in mountain regions (and there may also be indirect effects of environment driving land ownership via population density, which is also an important explanatory variable). It is interesting that in both studies, the spatial structure also accounts for significant parts of variation in the response variables, leading to discussions on how these cultural traits diffuse throughout the societies by a combination of cultural transmission and higher persistence of societies that, in some particular environmental conditions, adopt these practices (this later idea would match an adaptive Darwinian process at demic level). An excellent example of recent macroecological analyses of cultural variation involves evaluating linguistic patterns (see Gavin and Sibanda 2012; Gavin et al. 2013; Hammarstrom 2016; Hua et  al. 2019 for reviews). There have been many studies that applied techniques of phylogenetic reconstruction to understand the diversity of languages, and, despite some differences in respect to species divergence (i.e., due to reticulation), they have been successfully used to track historical differentiation among societies and human populations based on linguistic diversity (Greenhill et al. 2017). Moreover, it has been discussed for a while in geographical genetics how linguistic boundaries among populations are correlated with genetic barriers, reinforcing how cultural variation may constrain gene flow and evolve unique local characteristic under isolation (see Harding and Sokal 1988; Sokal et al. 1989). These genealogical and historical processes at distinct time scales led to divergence in several aspects of the structure and organization of languages among populations. Moreover, this divergence is also geographically structured and, as previously discussed for other cultural patterns, tend to generate broad-scale latitudinal gradients (i.e., Mace and Pagel 1995) (Fig. 9.3). These patterns appear both in the number of languages (richness), diversity based on phylogenetic patterns (and a different way to show these patterns is by mapping richness of linguistic families), and linguistic disparity akin to functional diversity and evaluating the magnitude of structural differences among the languages in the same region.

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Fig. 9.3  Map of linguistic diversity for H. sapiens overlayed on a grid of 3° of latitude and longitude. (Adapted from Coelho et al. 2019c)

Because of the overall similarity between patterns in linguistic and cultural diversity and species diversity at broad geographical scales, it is common to assume that similar ecological and evolutionary processes (e.g., see Fig. 6.5) underlie both patterns. However, it is necessary to highlight at least two conceptual and methodological particularities when comparing macroecological patterns of species richness and cultural and linguistic diversity. First, when evaluating diversification dynamics and responses to the environment, it is common to invoke adaptive and neutral processes, so it is advisable to consider how cultures or language characteristics respond to the environment and how they are inherited. This question is related to the more general issues involving the levels of selection in evolution and genetic-­ cultural dynamics. A second interesting and more methodological issue is that although we can establish the geographic ranges and rarity of cultures and languages, they would not overlap. Thus, linguistic richness is usually investigated by counting the number of languages in grain sizes usually larger than its mean geographic range, such as grid cells, nations, continents, or biogeographic regions. Explaining the geographical patterns in linguistic diversity and richness follows, in general, the same reasoning discussed in Chap. 6 for richness patterns, but a few more specific characteristics related to the way language and culture deserve some comments. For instance, thinking first in the set of mechanisms related to ecological limits, we can think about how area and environmental factors constrain the number of individuals in local populations. The interesting aspect related to the potential carrying capacity of languages is that testing this also involves (due to the non-­ overlapping geographic ranges) how each language would expand in time and space because of the human population and meta-population dynamics. In highly productive areas, for instance, it is expected that human populations would have a small home range to acquire necessary resources, allowing more languages to coexist (Gavin et al. 2017). Thus, a similar area in more productive (i.e., tropical) and less

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productive (i.e., temperate) environments would support a variable number of individuals and thus drive small and large linguistic geographic ranges. Consequently, a Rapoport effect (see Sect. 4.3.3) is also expected in linguistic ranges, as Mace and Pagel (1995) observed. The more individual mechanisms, as discussed in Sect. 6.2.2, are now better understood by how they would affect diversification patterns. In this case, it is interesting to think about geographic and social isolation processes that can also be related to population density. On the one hand, akin to what happens in neutral models of genetic diversification, one can think that diversification would be faster in small populations due to stochastic gain and loss, for example, of new words or meanings. However, it is also possible to think that the social networks and familiar links in such small populations would constrain conservative forces, and linguistic innovations are more likely to appear in large populations. In practice, these two explanations would converge under social factors creating population structure at increasingly geographic scales (which is also related to the area and part of the explanations related to ecological limits). For instance, if there are more intrinsic limitations in social networks due to cultural characteristics (i.e., shared trust, communications and cultural transmission facility, and probability of reciprocal altruism), there can be an intrinsic correlation between population size and structuring factors, generating thus positive relationships among abundance, isolation potential, and area leading to high diversification rates. There may be other mechanisms associated with lower population densities in regions with lower productivity, related to how more social cohesion and stronger familiar links that can constrain linguistic and cultural diversification may improve the probability of persistence in more unpredictable, unstable, and harsh environments, reducing ecological risks (as pointed in a more general context by Botero et al. (2014) and Kavanagh et al. (2021), discussed above). In addition, from a more historical perspective, there may be some associations of linguistic diversity with the origin of agriculture and an increase in political complexity (both of which can drive social isolation). However, it is difficult to disentangle the effects of these cultural and social innovations “per se” and related effects of increasing population density. More detailed analyses of linguistic diversification have also been investigated using more recent methods that allow a more comprehensive evaluation of the spatial structure and evolutionary dynamics by simulations (see Sect. 6.5). For instance, Gavin et al. (2017) used simulation approaches to model linguistic diversification in Australia. In short, the idea was to develop a stochastic simulation in which the geographic ranges of simulated languages expand in space according to the carrying capacity of the human population in a grid cell (which was, in turn, determined by productivity) through time. The model correctly predicts the mean number of languages and gives a reasonable approximation of the spatial patterns in linguistic richness, with an r2 of around 56%. Coelho et al. (2019c) used the same approach to model linguistic diversity in North America but also used geographically weighted (local) path analyses to investigate spatial patterns of language diversity. They showed that the ecological drivers of language diversity vary across regions, with

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distinct balances of direct and indirect effects of previously recognized variables such as population density, density, resource diversity, and carrying capacity, with group size explaining between 40% and 86% of the variation in linguistic diversity.

9.1.4 Toward Global Civilization and Ecosystem Domination There is a long jump in time from the origin of agriculture and domestication that triggered sedentarism and the early establishment of urban centers worldwide to the industrial and technological revolution after the nineteenth century. There are interesting more conceptual discussions about the validity of gradual and progressive stages of social complexity established in more orthodox anthropology and sociology from hunter-gatherer to post-industrial societies, mainly in terms of their abstract cultural values and way of life (and indeed, we most likely should abandon these progressive views, as we already did for a while in evolutionary biology; see Graeber and Wengrow (2021)). Even so, from a purely ecological point of view, there have been a more-than-exponential increase in population density and even faster increases in per capita energetic demands. The origin of agriculture, in general, increased human population growth density (Kavanagh et  al. 2018), but an increase at unprecedented rates occurred after the industrial revolution, most likely following a model of combinatorial innovation increasing carrying capacity (Steel et al. 2020). In the first instance, this accelerated growth triggers many troubles and threats for persistence for both human civilization and the global ecosystem, and solutions to these two problems are not independent (Tilman 2022). It may be interesting to call attention to the magnitude of this increase with some helpful numbers in addition to a visual inspection of the growing global human population (Fig.  9.4). As shown by Cohen (2003), the human population experienced a tenfold increase from 600 million people in 1700 to 6.3 billion in 2003. In 2022, halfway through the time interval of the predictions by Cohen in early 2003 (i.e., that the global human population would achieve about 8.9 billion in 2050), we are already approaching 7.9 billion people. Based on these numbers, it is possible to infer that the arable area necessary to supply essential food demands now clearly exceeds the available area by 50% or more (Tilman 2022; see also Brown et  al. 2011; Gavin et al. 2018). For the first time in history, more than 50% of the global human population lives in urban centers of variable sizes, and this strong aggregation creates a more complex network of interactions and nonlinear effects on food and energy demands. However, we have increased per capita consumption beyond this enormous increase in global population size, as demonstrated by different indicators. For instance, the demand for calories per capita increased from an average of about 1500–2000 kcal day−1 in hunter-gatherer societies and considered about the minimum for healthy human subsistence to up to almost 9000 kcal day−1 in the industrially developed countries by the end of twentieth century (even though, at the same time, there are generalized nutrition problems in many regions of the world,

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Fig. 9.4  Historical patterns of human population growth and human footprint in the early twenty-­ first century (Sanderson et al. 2002). (Population growth data from OurWorldInData.org)

revealing, of course, that other social, cultural, economic, and political issues are involved in the food supply at the global scale; see Gavin et al. (2018)). Burnside et al. (2012) also point out, in similar terms, that the basal metabolic consumption of a human being, equal to 120 W, was about 300 W in hunter-gatherer societies and now may be as high as 11,000 W in developed nations, with extra energy surplus fueled by different energetic sources, ranging from burning fossil fuel up to solar, nuclear, and hydroelectric power. Some of these patterns, which have been studied for a while by geographers and economists, are also well explained by ecological models that control the optimum or near-optimum flow of energetic requirements. Thus, the primary outcome from all these models is that the current demand for resources at a global scale tends to exceed the available resources, and we are now bounded, in several important dimensions, by what has been called “planetary boundaries” (see Brown et al. 2011; Steffen et al. 2015). There is evidence that we have already trespassed at least some of these limits. It is not unexpected that these impacts are not random or uniform in geographic space and tend to concentrate in the northern hemisphere, where we can find most

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urban and wealthier industrial societies with more intensely and older settlements in Europe and North America. However, there are also significant impacts on the eastern coast of South America, India, Eastern Asia, and Indonesia in the colonized tropics. The “human footprint” allows visualizing these geographical patterns, combining surrogates of direct and indirect human impacts based on remote-sense metrics and local survey data for eight variables, including built environments, human population density, infrastructure (electric, roads, railways), area of croplands and pasture, and navigable waterways (Sanderson et  al. 2002). Keeping this map in mind is essential for discussing global biodiversity conservation strategies in Sect. 9.2.4. In addition, it is now well established that the direct and indirect impacts of human activities, mainly in the last 250 years or so, are driving unprecedently fast climate changes at the global scale, as have been continuously pointed out by successive reports of the Intergovernmental Panel for Climate Change (IPCC) (see Hausfather et al. (2022) for a recent discussion). In short, in the late 1990s, different climatologists started developing a series of complex simulation models on atmospheric dynamics, the coupled Atmospheric-Ocean Global Circulation Models (AOGCMs) producing end maps of expected temperature and precipitation at a global scale under different scenarios of human development that would increase or decrease the emission of CO2 and other greenhouse gases. These models have been continuously upgraded and become more complex, involving other factors, and at the same time, better dealing with many uncertainties. Based on these more recent models from IPCC, a mean increase in temperature between 2 and 6 °C is predicted for the year 2100 under more optimistic and pessimistic future scenarios of human activity, respectively. There is a lot of variation among different forecasting models and, of course, among the emission scenarios. However, in any case, these changes at global scales are adding much more complexity to all scenarios of human persistence up to the late twenty-first century, ranging from associated sea level changes that would displace a massive number of people from large urban centers in the coastal regions of the world up to shifts in the areas necessary and adequate to keep food production necessary for human subsistence (de Vrese et al. 2018) (Fig. 9.5). As discussed in the next section, all these global changes are also important threats not only to humans but also to the persistence of the entire ecosystem, thus being widely important for defining strategies for biodiversity conservation. It is widely argued that these two issues (i.e., human persistence under global changes and biodiversity conservation) are not independent. There have been many discussions about how more sustainable strategies for dealing with natural resources should be implemented and improved even further, which requires better ecological theory, data, and analytical approaches, as proposed by Burger et  al. (2012). However, at the same time, they call the attention that most successful sustainability projects are developed at local (or regional at most) scales. However, it is crucial to consider the global patterns of human occupation on the planet and the entire complex networks of energy flow and food demands, as well as more general economic issues related to international trade and social politics, to expand our reasoning and explicitly think in sustainability in a macroecological context. In this context, it is

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Fig. 9.5  Global patterns of climate change in temperature in a 1 degree latitude and longitude grid, showing the relationship between baseline modern temperature (1950–1999) and projected to 2080 using CCSM model and emission scenario RCP85 (a). Map (b) shows the difference between the two layers, with red tones showing larger increases in temperature in 2080

interesting to use detailed data on human occupation through time and better evaluate the complex relationship between human development and other metrics for welfare and ecosystem loss related to agriculture expansion (see da Silva et  al. (2017) for a discussion in the Brazilian Amazon). In this context of the profound global changes affecting our species, it is also inevitable to mention how new pathogens and infectious diseases may also threaten large urban aggregated populations, currently an important topic in human macroecology. There are many interesting macroecological and biogeographic aspects of human host-pathogen interactions, some of which deserve mention. From classical compartment population models (i.e., SIR models; see Anderson and May (1979)), it is possible to infer that more aggregate host populations would allow faster dissemination of pathogens, whose dynamics follow a logistic curve with attack rate (i.e., the proportion of a population infected) depending on the ability to infect new hosts (which in turn depend on host susceptibility) and lethality rate. So, it is

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expected that large human populations are more susceptible to these infections and are associated with a high richness of pathogens, as shown by Dunn et al. (2010). However, they also showed that richness in human pathogens is highly correlated with the richness of mammals and birds and offered at least three explanations for these common patterns. First, richness patterns of mammals, birds, and pathogens could all be related to the same overall environmental patterns driving diversification, as discussed in detail in Chap. 6. A second possibility is that regions with more mammals and birds have more diversity of pathogens, increasing the likelihood of spillover events to humans. Finally, the correlation would appear because human pathogens would be a surrogate for the average pathogen richness within a single host and that, in general, a high richness of pathogens could lead to higher host diversification (Allen et al. 2017). Another important issue refers to more general aspects of coevolution between pathogens and humans, and in turn, a recent important aspect is the macroecology of spillover events. There is currently evidence that although the chance of spillover events is geographically widespread and depends on the effective probability of interaction between human and reservoirs, the expansion of these infectious diseases would be correlated with densely occupied regions nearby high urban centers (see Ribeiro et  al.  2022b for a discussion in the coronavirus spillovers in the COVID-19 pandemic). These patterns reinforce the links between the need for more effective practices in biodiversity conservation and the preservation of natural areas to prevent future pandemics (Vora et al. 2022; Gatti et al. 2021) and evaluate the relatively economical cost-benefit of improving biodiversity conservation and environmental monitoring programs to mitigate future health issues (Dobson et  al. 2020). In the case of the ongoing COVID-19 pandemic, there is also a clear connection between the routes of spread of the virus and networks of air traveling and transportation at global and national scales (Ribeiro et al. 2020; Coelho et al. 2020; Kraemer et al. 2020). Finally, from a more methodological point of view, in the context of global climate change and warming, it is possible to use the SDMs discussed in Chaps. 4 and 5 to predict the northward expansion of the geographic ranges of some species of health interest that are now endemic from tropical to temperate regions, which require attention for the health risk for northern populations which have been usually isolated from such pathogens for a while (see Peterson 2007). More complex models at biogeographic scales also allow understanding dynamics of specific pathogens and how they interact with other components of human occupation (e.g., Aliaga-Samanez et al. 2021). The more pessimistic view of the excessive human population growth in the last 250 years or so, as well as economic and social politics discussed to solve the problems (and usually widely questionable), has usually been framed in what is called Malthusian (or Neo-Malthusian) view, in reference to the famous English economist from the early nineteenth century Thomas Malthus. In a more recent reference, much of the debate was triggered in the early 1960s by the famous book The Population Bomb by Ehrlich and Ehrlich (1968), now with a more explicit link with

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the emerging field of conservation biology. However, all discussions about the Malthusian pessimistic view have been dampened by events that frustrated the more recent predicted population collapses. For instance, the global production of food and goods in the late nineteenth century would be barely enough to support a population of, say, 1 billion people, but as we got close to these thresholds, scientific and technological developments allowed a further expansion of the population. At the same time, most models (see below) now suggest that global human population will achieve equilibrium late in the twenty-first century and is already showing signal of decline in some parts of the world (with debatable political and economic implications). These marks provide the conceptual basis for more optimistic views of the future, in terms of nature conservation, paving the way for a more scientifically and educationally oriented society. The reasoning behind this more optimistic view of the future was pointed out and discussed in a modeling context by Cohen (1995a, b). We can start by recalling the basic logistic population growth model in which dN/dt = rN (1 – N/K), where K is the carrying capacity defined by the equilibrium of birth and death rates that are, in the last instance, regulated by the available resource (see Chap. 4). As already discussed, at a global scale, the carrying capacity K of the human population would be determined by the amount of food production and potable water, among many other factors. However, what if this equilibrium is not a constant but depends on the scientific and technological developments that reduce mortality and increase fertility? We can think that K varies in time, so we can also write the equation for its growth rate as dK/dt = c (dN/dt), which can then be added to the original logistic model forming what Cohen (1995a) calls Malthus-Condorcet model with the “technological constant” c, a homage to the more optimist French illuminist philosopher, Marquis of Condorcet (1743–1794). In this more general model, if c > 1, each additional person increases the human carrying capacity beyond his or her uses, so the population grows faster than exponentially. If c = 1, each person’s consumption is self-sufficient, so the population increases exponentially (in this case, the models converge to a purely Malthusian model). Finally, if c