Geographical modeling: cities and territories 9781119687290, 1119687292

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Geographical Modeling

Modeling Methodologies in Social Sciences Set coordinated by Roger Waldeck

Volume 2

Geographical Modeling Cities and Territories

Edited by

Denise Pumain

First published 2019 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc.

Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address: ISTE Ltd 27-37 St George’s Road London SW19 4EU UK

John Wiley & Sons, Inc. 111 River Street Hoboken, NJ 07030 USA

www.iste.co.uk

www.wiley.com

© ISTE Ltd 2019 The rights of Denise Pumain to be identified as the author of this work have been asserted by her in accordance with the Copyright, Designs and Patents Act 1988. Library of Congress Control Number: 2019949917 British Library Cataloguing-in-Publication Data A CIP record for this book is available from the British Library ISBN 978-1-78630-490-2

Contents

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Denise PUMAIN

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Chapter 1. Complexity in Geography . . . . . . . . . . . . . . . . . . Denise PUMAIN

1

1.1. A first bifurcation in the epistemology of geographic modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.1. “Vertical” explanations for the “science of places, not people” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.2. “Horizontal” explanations for the science of the spatiality of societies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.3. The discussed status of modeling . . . . . . . . . . . . . . . . . 1.2. Modeled regularities . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.1. Proximity and distances . . . . . . . . . . . . . . . . . . . . . . . 1.2.2. The scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.3. Concentration and accumulation: geographical inequalities and scaling laws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.4. Spatial change and trajectory dependence . . . . . . . . . . . 1.2.5. Territorial drifts, space-time compression, and globalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3 4 5 7 10 11 15 19 21 25 29

Chapter 2. Choosing Models to Explain the Dynamics of Cities and Territories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lena SANDERS

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2.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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2.2. Explaining by reasons or laws: choosing an epistemological framework . . . . . . . . . . . . . . . . . . . . . . . . 2.3. The modeling approach: diversity of models . . . . . . . . . . 2.4. Explaining through statistical relationships or mechanisms . 2.5. Choosing the level of abstraction for the phenomenon to be explained: general versus particular. . . . . . . . . . . . . . . . . 2.6. Choosing the level of abstraction for the model: stylized or realistic, KISS or KIDS . . . . . . . . . . . . . . . . . . . . . . . . . 2.6.1. Modes of representation of space: from a stylized space to a realistic space . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6.2. Formalizing spatial mechanisms: from stylized to realistic. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.7. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Chapter 3. Effects of Distance and Scale Dependence in Geographical Models of Cities and Territories . . . . . . . . . . . Cécile TANNIER

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3.1. Three fundamental principles for modeling cities and territories. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.1. Effects of distance . . . . . . . . . . . . . . . . . . . . 3.1.2. Effects of scale dependence . . . . . . . . . . . . . . 3.2. Role of distance in spatial simulation models . . . . . . 3.3. Modeling scale dependence . . . . . . . . . . . . . . . . . 3.3.1. Scale dependence as a result of processes acting at different scales . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.2. Scale invariance for the description of geographical phenomena . . . . . . . . . . . . . . . . . . . . 3.3.3. Scale dependence as a generative mechanism for simulated spatial configurations . . . . . . . . . . . . . . . . 3.4. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Chapter 4. Incremental Territorial Modeling . . . . . . . . . . . . . Clémentine COTTINEAU, Paul CHAPRON, Marion LE TEXIER and Sébastien REY-COYREHOURCQ

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4.1. The map and the territory . . . . . . . . . . . . . . . . . . . . . . . 4.1.1. Modeling as one map: selection and schematization . . . . 4.1.2. The representation of territory as an input of the model . . 4.1.3. The representation of territory as an output of the model . 4.2. Generality and specificity: explaining by ways of geographical models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.1. Historical contingency and non-ergodicity . . . . . . . . . .

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4.2.2. General/specific/singular . . . . . . . . . . . . . . . . . . . . 4.3. Incremental territorial modeling . . . . . . . . . . . . . . . . . . 4.3.1. Identifying the object, scale, configuration, and stylized facts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.2. Gathering the different theoretical explanations . . . . . . 4.3.3. Hierarchizing the interaction processes between agents . 4.3.4. Hierarchizing the interaction processes between agents and their environment . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.5. Implementing mechanisms and their formal alternatives 4.3.6. Combining, simulating, and comparing . . . . . . . . . . . 4.4. Challenges and limits of multi-modeling . . . . . . . . . . . . 4.4.1. The combinatorial curse. . . . . . . . . . . . . . . . . . . . . 4.4.2. Human and technical costs . . . . . . . . . . . . . . . . . . . 4.4.3. Subjectivity in the choice of building blocks. . . . . . . . 4.4.4. Comparing models of different structures . . . . . . . . . 4.4.5. Sharing and accumulation of knowledge . . . . . . . . . . 4.5. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Chapter 5. Methods for Exploring Simulation Models . . . . . Juste RAIMBAULT and Denise PUMAIN

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5.1. Social sciences and experimentation . . . . . . . . . . . . 5.2. Geographical data and computer skills . . . . . . . . . . . 5.3. New generation simulations. . . . . . . . . . . . . . . . . . 5.3.1. A virtual laboratory: the OpenMOLE platform . . . 5.3.2. The SimpopLocal experiment: simulation of an emergence in geography . . . . . . . . . . . . . . . . . . . . . 5.3.3. Implementation of SimpopLocal, from NetLogo to OpenMOLE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.4. Calibration and validation . . . . . . . . . . . . . . . . 5.4. Other examples of OpenMOLE applications: network–territory interaction models . . . . . . . . . . . . . . . 5.5. Perspectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5.1. Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5.2. Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.6. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Chapter 6. Model Visualization . . . . . . . . . . . . . . . . . . . . . . Robin CURA

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6.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 6.2. Visualization as modeling . . . . . . . . . . . . . . . 6.2.1. Visualization as a tool for interdisciplinarity . 6.2.2. Visualization and reproducibility . . . . . . . .

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6.2.3. Visualizing a model means learning . . . . . 6.3. Visualize to evaluate . . . . . . . . . . . . . . . . . 6.3.1. Visualize before modeling . . . . . . . . . . . 6.3.2. Visualize during the simulation . . . . . . . . 6.3.3. Visualizing after the simulation . . . . . . . . 6.4. Visualizing to compare . . . . . . . . . . . . . . . . 6.4.1. Which models should be compared? . . . . 6.4.2. How should visual comparison be done? . . 6.5. Visualizing to communicate . . . . . . . . . . . . 6.5.1. Visualizing to disseminate . . . . . . . . . . . 6.6. Some obstacles inherent in model visualization 6.6.1. Producing and visualizing massive data . . . 6.6.2. Visualization of aggregated data . . . . . . . 6.7. Conclusion . . . . . . . . . . . . . . . . . . . . . . .

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162 163 164 166 169 172 172 174 178 179 182 183 187 191

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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List of Authors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Introduction

Never has geography been so present in our societies. For centuries, stimulated by the curiosity of travelers, the appetite of merchants, and the greed of powers, knowledge about the planet, its resources, and the riches of its cities and territories has never ceased to increase while remaining the privilege of the powerful. Precise knowledge of the terrain was an essential prerequisite for the great strategist Sun Tzu, in his famous book, The Art of War, published in China’s warring kingdoms during the Spring and Fall period in the 5th Century BCE. The French geographer Yves Lacoste confirmed, as recently as 1976, the strategic capacities of the discipline by showing in his provocatively-named book, La géographie, ça sert, d’abord, à faire la guerre (Geography primarily serves to make war), that it was supported in France by a nationalist and imperialist state power. In France, geographic learning has been a requirement for all students in school curricula since 1870. However, it is especially since the emergence of mobile phones in the early 2000s that geography has been a factor in daily life. Even in the poorest countries, a very large majority of people are able to connect to the Internet, see images and maps from around the world, use satellite positioning services, GPS, Galileo, Glonass, or Baidu, to mark routes, navigate the world, geolocate, or make themselves visible to nearby “services” and “friends”. This revolution surpasses, by the number of applications it generates and the extent to which they are shared, the one that has occurred more discreetly since the 1970s with the widespread use of geographical information systems (GIS), in administrations, for spatial planning, and in companies, for logistics management. The limited capacity                                         Introduction written by Denise PUMAIN.

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of the computers of the time and the insufficient competence of the services in the analysis and modeling of spatial data have long slowed down the effective integration of these tools into many activities (Goodchild 2016). One of the current challenges in fully exploiting the new major computer capacities and democratizing geographical information is to make judicious and appropriate use of the knowledge and skills accumulated about cities and territories, not only through geography, but also by all disciplines that have sooner or later integrated the “spatial turn” into their research approaches, from agronomy to archeology and from history to epidemiology. These disciplines share the construction of models, which are above all summaries of knowledge, simplified in relation to the diversity and complexity of individual cases, but communicable and improvable because they are codified, at a given moment in the state of knowledge, by mathematical or computer formalizations. The knowledge integrated into a model represents sets of recurrent facts in empirical observations, which have been selected according to the hierarchy of their effects on the problem being studied, with more or less parsimony depending on whether we focus on the generality or precision of the results. Calculation or simulation is used to propose predictions, or to explore possible scenarios, as part of the model assumptions. According to appropriate granularities and levels of resolution, all forms of modeling can be used with extremely variable objectives: laboratory hypothesis tests for theoretical models, serious games with a didactic function, support models designed to solve difficult situations including contradictory or even conflicting issues, models inserted in interactive applications intended for information or decision support, commonplace models generally used for location choices or infrastructure templates, and so on. Critics of models often denounce oversimplification, or selection bias, and question the quality of the data used to validate them. Admittedly, each model has its shortcomings and deficiencies, but the great advantage of modeling, compared to the subtleties of written or spoken rhetoric, is that it requires very detailed clarification of the assumptions of discourse and intentions in order to better share them. Modelers are informed of the defects and deficiencies of their models; they are the first to deplore them and are constantly trying to overcome them. The uses and functions of the models are multiple. They are often designed for prediction (meteorological and financial models), more broadly

Introduction

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data mining models, for the validation of an analytical theory (economic models) or, in geography, for the planning and discussion of territorial issues (decision support models and companion models), but social science modeling develops practices that are much broader and richer than those anchored in the traditional scientific imagination. Models are also used to deepen and test explanations using an abductive approach (Besse 2000) that interacts with conceptual constructions and empirical data, as will be shown in several chapters of this book. Several publications have already proposed more or less ambitious syntheses of geographic modeling. For this expression in French, the Google Scholar algorithm offers some 40,000 references, which are mainly journal articles. Collective books or textbooks are less common. The book published by Lena Sanders in 2001 is pioneering in this field. The work of Yves Guermond (2005) compiles the productions and practices of the laboratory of the University of Rouen. Others have focused on the important processes of spatiotemporal change (Mathian and Sanders 2014) or only deal with certain urban models (Antoni et al. 2011; Bonhomme et al. 2017). Most recently, two books by Arnaud Banos (2013, 2016) and one by Frank Varenne (2017) laid the foundations for epistemological and philosophical reflection on geographical models. The book we propose here is part of a multidisciplinary collection. It is designed to provide didactic information on the modeling process, in its particularities justified by the handling of geographical concepts and information, and illustrated with examples representative of the major innovations that have taken place over the past decade. Chapter 1 recalls the foundations of the geographical discipline on which models can be based to take into account the complexity in the organization and evolution of cities and territories. Chapter 2 deciphers the crucial choices for modeling, which are at the root of the diversity of models and their uses: we examine to what extent the complex can be simplified or, on the contrary, how can we try to integrate it into the models. Chapter 3 describes the models that establish explicit relationships between contrasting spatial morphologies, which present inequalities on different scales, and the social processes that generate them, according to “micro–macro” dynamics. Chapter 4 explores the construction stage of city and territory models and proposes a new incremental multi-modeling method. Chapter 5 introduces various possible uses of a simulation platform, OpenMOLE, which uses evolutionary algorithms and provides access to HPC equipment. Finally, Chapter 6 is

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devoted to the new visualization tools that are so important for model exploration and validation, as well as for communicating their results. At the end of the book, the index brings together the main concepts that characterize geographical modeling. For the concepts that are already precisely defined in the chapters devoted to them, the multiple page numbers that testify to their appearance throughout the book make it possible to understand how they also apply to widely shared intellectual and practitioner approaches. Moreover, essential concepts such as “space”, “simulation”, “territory”, “city”, and “visualization” do not appear in the index because they are used and enriched many times by all of the authors. It is also because of the great coherence of these texts that the bibliographical references, which often appear several times, are grouped into one list at the end. This provides an original and updated state of the art on the major parallel and convergent directions in geographical modeling.

1 Complexity in Geography

The last three or four decades have completely renewed the modeling practices of geographers. Two major changes, one epistemological and the other technical, are at the origin of these transformations. Technological change is the tremendous expansion of information processing capabilities, which has made work that could previously only be sketched as thought experiments possible, or work that has been carried out wholly incompletely due to a lack of powerful computing resources. This technical change has made it possible since about the 2000s to fully implement a major epistemological change that occurred sometime earlier in the 1970s and 1980s. This is the introduction of paradigms and models from the natural sciences into geography, whose keywords are self-organization (the dissipative structures of Prigogine and Nicolis (1971)), synergetics (Haken 1977; Weidlich 2006), and complexity and the notion of emergence (Bourgine et al. 2008). We will not recall here those filiations that are already mentioned in several works (e.g. Dauphiné 2003; Pumain et al. 1989; Sanders 1992). We want to show not so much how these forms of modeling can be applied in geography, but how to proceed for real model transfers, since many theories of the discipline had already largely anticipated the need for the newly proposed formalizations. Transferring scientific language, concepts, methods, and instruments from one discipline to another is only a fruitful operation if it meets an expectation, a real need for innovation. In this case, it is not so much the paradigm of complexity as such that has been the novelty for the human and social sciences since they have always been confronted with the                                         Chapter written by Denise PUMAIN.

Geographical Modeling: Cities and Territories, First Edition. Edited by Denise Pumain. © ISTE Ltd 2019. Published by ISTE Ltd and John Wiley & Sons, Inc.

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irreversibility of the trajectories of their objects, the near impossibility of prediction, and the phenomena of emergence in the systems studied. It is because complexity sciences provide complementary methods, means to process information and to formalize knowledge. Many geographers have adopted these references to work on their models. These have contributed to building cumulative knowledge when previously acquired intuitions could benefit from the transfer. This is why it seemed useful in this introductory chapter to remind geographers as well as readers trained in other sciences of the disciplinary fundamentals on which geography modeling can be based, particularly to deal with the complex objects that are cities and territories. We quickly retrace the successive postures of geographers faced with the possibilities of modeling, and then, we outline a set of regularities that can be more easily modeled among the objects that geography studies. These regularities partly lead to specific modeling practices by geographers, which are largely motivated by the multiplicity of observation scales, but also practices that have been much more in demand over the past two decades by the influx of geolocalized data, which opens up considerable development opportunities. The general idea is that the complexity of the objects and processes observed by geographers is always constructed, not so much in formulating universal “laws”, but more often by including spatiotemporal elements, like in other human and social sciences, which are fundamentally “historical sciences” (Passeron 1991). These disciplines share with the natural sciences certain forms of nonlinear relationships, processes of self-organization, morphogenesis, dynamics oriented by attractors, or emergence phenomena characteristic of complex systems, which are formalizable on specific case subsets or segments of their trajectory. Geography adds to this complexity of nonlinear processes the specific feature of being interested in a very wide diversity of variables and levels of observation, including natural and social elements, in an attempt to formalize the evolution of landscapes, cities, and territories, which gives an additional dimension to the complexity of the systems that geography models1.

                                        1 A few other disciplines such as archeology or social and environmental epidemiology also deal with indicators relating to the natural sciences as well as the humanities and social sciences.

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1.1. A first bifurcation in the epistemology of geographic modeling Geography appears among the humanities and social sciences as one of the most practiced in modeling (Banos 2013; Sanders 2001). Geography has often been identified as a pioneer in the use of digital tools. It is no coincidence that a philosopher has chosen to test his conceptions of modeling with this discipline (Varenne 2018). This is a paradox: indeed, until recently, geography seemed to be a “soft science”, insofar as it does not assert theories as powerfully unitary as the so-called mainstream economy, and does not export its concepts as much as sociology, if we think, for example, of the French theory in vogue in the United States for at least 30 years. However, the theoretical and quantitative “revolution” that began in the 1950s in Sweden and the United States and then developed in France in the 1970s (Cuyala 2014; Pumain and Robic 2002), probably explains, to a large extent, why a certain “spatial turn” took place in most human and social sciences in the 1990s. Concepts and methods, software tools such as geographic information systems (GIS), and research questions brought by geographic space modeling practices (Banos 2016; Bonhomme et al. 2017) have been successfully imported into almost all disciplines. However, in everyday language as in many representations of common sense, the “geography” or description of the Earth sometimes seems to be summed up in terms of nomenclatures, knowledge of locations (latitude, longitude, and altitude), and place names, the toponyms that societies have associated with them, whether they are mountain ranges, rivers, islands, or cities. However, academic geographic science – once the era of exploratory journeys and the “discoveries” of the regions of indigenous peoples by colonizers had passed – relied in the late 19th Century on questions designed to unpack the reasons for the diversity of the imprints shaped by societies on the Earth’s surface. Agrarian landscapes and forms of habitats, the exploitation of mining resources and industrial production, arrangements of villages and cities, traffic routes, and tangible or intangible flows have been examined at all scales, in a diverse range of geographical environments and according to their evolution over the course of history. Two main types of explanation successively dominated the research. In the first half of the 20th Century, the main focus was on the relationship between a society and its environment, speculating on the more or less favorable or constraining nature of natural conditions and the social capacity to develop them,

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according to a somewhat “vertical” interpretation of its relationship with the resources offered locally by the planet. In the second half of the 20th Century, another, more “horizontal” way of producing explanations emerged, which tends to interpret the characteristics of a territory or a city from its situation in the world, i.e. from its relations with other territories and other cities. In truth, these two explanatory forms, which lead to very different models, are complementary and are necessarily articulated in any geographical interpretation of a particular city or territory. 1.1.1. “Vertical” explanations for the “science of places, not people” 2 In its academic history, geography has long been at the interface between the natural and human sciences. Taking into account the description of the planet (Robic et al. 2006) and its transformation into environments and landscapes by societies (Robic 1992), it had built a few general models. The relationship between the material organization of societies and natural resources, mediated by climatic and altitudinal zones, had been well observed and described, revealing some regularities. In particular, they highlighted the fairly close interdependence between ancient societies and the local character of mineral and plant resources used in housing and agriculture, which did not, however, exclude long-distance trade in less common commodities. When such regularities were systematized to excess (e.g. “limestone votes left, granite votes right” to caricature the positions of André Siegfried, founding geographer of electoral sociology in the 1930s, who actually linked the hydrography of these environments to their form of habitat, grouped, or dispersed and to the degree of dependence of the inhabitants on the domination of landowners), the corresponding statements were quickly rejected on the grounds of “determinism”. Conversely, noting the great diversity of selections and combinations of resources made by societies under more or less equivalent physical conditions could also, on the contrary, lead to “exceptionalism” (Schaefer 1953). This expression covers Schaefer’s criticism, both of the claims, which was frequent at the time, of a specificity of the geographical explanation, based on the genetics of the places, and of its consequence consisting in highlighting the uniqueness of the places. Regional                                         2 The expression in quotation marks is by Vidal de la Blache, with the intention of characterizing the geography project to distinguish it from that of Durkheimian sociology, which became institutionalized at the same time, between the end of the 19th Century and the beginning of the 20th Century.

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idiosyncrasies have been the subject of numerous demonstrations denying the possibility of a rise in generality, the authors insisting sometimes on the strong constraint exerted by local resources and sometimes on the social free will with regard to how using and transforming them, as well as to the diversity of their creations in terms of the forms of their political, social, and cultural organizations. In the early days of academic geography, it was, therefore, physical geography in the fields of geomorphology or climate, which allowed modeling. Thus, since the early 1960s, the English geographer Richard Chorley (1962) advocated the transposition of von Bertalanffy’s general theory of systems into geomorphology and advocated the design of open systems, both for physical and human geography3. In such systems, the second law of thermodynamics does not apply and evolutions are not directed toward the maximum entropy and homogeneity, but other processes generate all kinds of configurations, formalized in models, which were listed five years later in a book written with Peter Haggett about these two branches of geography (Chorley and Haggett 1967). 1.1.2. “Horizontal” explanations for the science of the spatiality of societies Some other types of regularities had indeed been observed since at least the early 19th Century in the organization of cities and territories and gave rise to various attempts at formalization, through mathematical models or iconic representations. The regularities of the spacing of cities, the hierarchy of their functions, and the interlocking of their catchment areas had been described since 1841 by the Saint-Simonian Jean Reynaud as “the general system of cities” strongly constrained by the use of the nearest service and thus generating forms of circular or hexagonal service areas, interlocking according to a hierarchy of rarity of urban services (Reynaud 1841; Robic 1982). This concept and the derived spatial models had little immediate impact, but the principles of a theory associating the size of cities with the rarity of their economic functions and the extent of their clientele in the surrounding region were rediscovered and systematized by the German geographer Walter Christaller (1933) in a “central place theory”, which was the subject of multiple tests in all parts of the world (Berry and Pred 1961).                                         3 “Open-system thinking, however, directs attention to the heterogeneity of spatial organization, to the creation of segregation, and to the increasingly hierarchical differentiation which often takes place with time. These latter features are, after all, hallmarks of social, as well as biological, evolution” (p. 10).

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This theory actually included the previous model known as the “Reilly law of retail gravitation” (Reilly 1931), which explained the location of commercial activities by competition between businesses and services frequented by consumers under the constraint of proximity. In both the Reilly and Christaller models, travel costs are borne by the consumer and are added to the price of goods, encouraging people to buy from the nearest place. This determines, in the cartographic representations, more or less circular-shaped catchment areas, which fit together in the form of hexagons in the spatial diagrams drawn by Christaller. In fact, these early geographic models validate what American cartographic geographer Waldo Tobler (1970) later referred to as “the first law of geography” (“everything interacts with everything, but two close things are more likely to interact than two distant things”). This law summarizes many of the previous observations made about the movement of people in space. The first formalizations can be attributed to the geographer Ernst Georg Ravenstein (1885), who published several articles from 1885 onward which summarized the main characteristics of population movements in a period of high rural exodus under the title “Migration laws” in a British statistical journal. It was the American geographer Edward Ullmann who, in 1954, proposed defining geography as the science of spatial interactions. In his work Geography as Spatial Interaction, he certainly introduces the same “physical” model as the astrophysicist Stewart (1948), namely, a “gravitation” model (the flows between two geographical units are proportional to the product of their masses and inversely proportional to the distance that separates them) but he truly transposes this idea to the social sciences. He specifies the geographical conditions that are likely to explain the exchange and the movement: there must be a complementarity between a demand for a given product from a certain place of origin and the resources available in a place of supply, and travel must be possible, and therefore not too costly, for the exchange to take place. The characteristic principle that organizes geographical space is, therefore, the constraint of proximity; it includes the “sociological” principle that puts it into practice, stipulating that the nearest destination is chosen. There must also be no closer places offering the same product, or intermediate locations, which the sociologist Stouffer (1940) calls intervening opportunities. The geography that is built on these foundations (Abler et al. 1977) is then conceived as a science of the organization of space. This expression

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was coined by the French geographer Jean Gottman (1961) about the Northeast megalopolis, the group of cities that stretches from Boston to Washington. Although it is made up of distinct urban entities, whose urban structure is not continuous, this large regional complex appears to be a functional unit due to the multiplicity of communication and exchange networks that connect these cities together and make them complementary in a differentiated territory. The concept of a region then gradually emerged from the criteria of landscape homogeneity or historical delimitation that had hitherto underpinned it and was enriched by the concept of a functional region, defined by the polarization of traffic flows and the strong economic and social interdependencies between the cities and countryside that constitute it. This new form taken by geographical investigation then makes it possible, under the designation of “locational analysis” (Haggett 1965), to identify all kinds of regularities in geographical space and to build canonical models, whose ancestors are often shared by economists specializing in the emerging “regional science” (Isard 1960). The translation into French of Peter Haggett’s book (Locational Analysis in Human Geography) by Hubert Fréchou in 1973 converted the title to “spatial analysis”. This expression, which was used in subsequent manuals (e.g. Pumain and Saint-Julien 1997), is the subject of one of the three main entries in the online encyclopedia Hypergeo, entitled “the spatiality of societies”, alongside the entries “societies and environment” and “cities, regions, and territories”. The notion of spatial analysis in French covers a perspective centered on human geography and a broader and less strictly technical theoretical content than in the practices of British or North American geographers. For example, British geographers Paul Longley and Michael Batty closely associate the spatial analysis with specialized GIS software in their 1996 and 2003 books, and the preface to their 2003 book defines it as “a kind of data mining technology”. More broadly, the definitions given by French-speaking geographers for spatial analysis readily incorporate the statements of theories and models, and some specialists in “social geography” have sometimes also claimed this expression as a means of designating their activity. 1.1.3. The discussed status of modeling Since the 1970s, attempts at modeling in geography have been subject to heavy criticism. To mention just one example, let us recall one of the most eminent geographers of his generation, Pierre George, a member of the

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Institute, who denounced both a “scientific adventurism”, “quantitative illusion”, and a “new determinism” (1972). For this Marxist geographer, criticism focuses above all on the idea that quantified formalizations can only use biased data, as they depend on the policies that build them. More surprisingly, by placing himself in the field of philosophy, Pierre George also denounces a “much more serious mystification” brought by the “formalization applied to geographical data”. According to him, it “presupposes, indeed, the acceptance of the idea that men and their initiatives are integrated into concentration camp categories from which they can only escape by a statistically negligible, politically and socially reprehensible marginalism, the marginalism of the anomaly, compared to an institutionalized system and disseminated by all modern means of imposing information and official culture” (1976, p. 54). Many other authors have denounced the models as too general and simplistic. The use of mathematical models, often quite simple, was denounced as unsuitable for accurately representing individual and social processes, e.g. in terms of location or displacement choices. The main argument against any modeling was the respect for human freedom, which was not to be represented as “obeying” the constraints of distance or natural conditions. The modeling was also denounced for political reasons such as an attempt to “naturalize” social processes, which would have been tantamount to accepting the established order and would not have allowed it to be called into question. This tension is also well expressed by the Anglo-American geographer David Harvey, who accepts Popperian models and logic in a first book on explanation in geography (Harvey 1969), then in a second book on the relations of domination in the urban space (Harvey 1973), and finally proposes a Marxian critique of capitalism and imperialism (Harvey 1982) – without, however, going so far as to accept post-modern criticism or to deny modeling. The dissociation between Marxist interpretations and the use of quantitative models has often been more pronounced in English-speaking countries4 than in continental Europe, where the “theoretical and quantitative revolution” was more opposed to conservative geographers, both politically                                         4 There are exceptions, including the work of William Bunge, who in 1962 proposed a “Theoretical Geography” based on axioms and which was rather geometrical, and who also analyzed social inequalities in the suburbs of Chicago with quantified indices (Fitzgerald: Geography of a Revolution, Schenkman Publishing Cy, Cambridge, 1971, p. 1071) where he denounced the capture of land rents by the richest and the poor living conditions imposed on black people.

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and methodologically. The successive waves of radical geography, phenomenology, and then post-modern geography that have emerged in the United States since the 1980s have spread to Europe with unequal intensities while making many criticisms of modeling (under the pretexts of “fetishization of space”, voluntarily forgetting actors, conflicts, social, or colonial, then forgetting representations, sensations, or, even more recently, emotions). An integrative definition of spatial analysis as “the formalized study of the configuration and properties of space produced and experienced by human societies” (Pumain and Saint-Julien 1997) proposed in a handbook signified a willingness to calm these controversies, which have aroused animated debate among all social sciences. In the 1990s and the decades that followed, there was a very large development of models, a widening of their practical uses, and a progressive enrichment of their content, largely supported by the generalization of geographical information systems and the integration of geolocation into all kinds of technical devices (see Chapter 6). Finally, the dizzying increase in computing capacity was expected to free up modeling from some of the qualitative limitations that could hinder the consideration of hazards and individual specificities in models (see Chapters 3–5). According to our constructive perspective for modeling, proposals contrary to modeling, which are still used in some publications today, are based on misunderstandings that are deliberately not well clarified. They are likely to maintain controversies, not very valuable for the image of geography, and can be classified under three main types: those that reject any kind of regularity in the organization of the space of societies and deny the usefulness of a geographical discipline; those that treat geographical space as an inert container of physical objects and social relationships; and those that place any explanation within the exclusive framework of a theory of mono-disciplinary inspiration, such as certain geo-economic models or even certain narratives of post-modern inspiration or certain militant texts. However, we believe that geographical modeling can integrate a very wide variety of social processes, both individual and collective, and can be based on knowledge established by several disciplines, at different levels of resolution and granularity of its objects, from the individual to the world. Like a more discursive geography, strengthening existing powers is not the primary function of modeling; it can also be used to promote sustainable development and help the poorest populations and territories.

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1.2. Modeled regularities With their theories of complex systems, physicists who enter the social sciences to propose models are often tempted to project some of the constraints they have built to analyze the forces at work in the physical world. Although energy, in the various forms of solar radiation, gravity or animal, human, and mechanical work, is always taken into account in technical artifacts or human organizations, it is not very effective to consider that this is the main constraint (or last resort) that would govern the construction of human activity on the Earth’s surface and from which the form of the socio-spatial organizations studied in geography would have been identified (West 2017). The configurations of cities and territories that can be modeled by geographers are built by accumulated human work, carried out under material constraints, but also with some well-identified anthropological and social determinants, e.g. the relatively universal principle of the “law of least effort” as enunciated by G. K. Zipf (1949), or the frequent effects of political, cultural, or economic domination were observed in social relations and interactions. The history, the forms of political and economic organization of societies, and their cultural creations are always part of the explanations proposed in “general geography” or in local or regional monographs. However, geography itself provides a modelable dimension to these constructions, to which the other disciplines of the natural and social sciences are articulated as in any explanation of complex social systems. Modeling takes into account major regularities, which are accepted, often implicitly, by most geographers. These regularities include the constraint of proximity, which brings into play various expressions of distance in all gradient models of the center-periphery type, or the organization of geographical space in levels, leading to great attention being paid to the scale of structures and processes or the reduction of interactions by territorial boundaries or barriers (physical or socio-cultural) that create discontinuities. Models of spatial change integrate the other regularity of temporal persistence of geographical objects, which is certainly shorter than those of geological periods or ecosystems, but so much longer than that of daily movements or human lives or even sometimes than the passage of generations, which leads to many reflections on the resilience of cities and territories and justifies their modeling. These major regularities of spatial organization and evolution of space and geographical objects are presented in the following, which necessarily

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introduces some repetitions, as the processes that generate them are complex according to the meaning of this term in the social sciences. These processes are difficult to separate from each other because they often interfere together during the genesis of cities and territories. 1.2.1. Proximity and distances The concept of distance encompasses a range of indicators and measures of separation, adapted to the different types of relationships considered to signify distance, spacing, or remoteness, which have greatly broadened the scope of the concept of distance in the geographical explanation. To conceive a distance is indeed to give oneself a relational representation of space, whose properties then depend on the nature of the chosen distance and, therefore, on the form of the possible relations (offered or revealed) between the parts of space. To do this, we must no longer see space as a simple container, an empty room furnished by human activities, but as a construction, a representation of the relationships (virtual or realized) between different places, variable according to the traffic facilities, or the intensity of the exchanges that we consider. Broadly speaking, two complementary insights are used to define distance as a structuring factor of geographical space, in this relational and also “relativistic” conception of the distance between places. The notion of geographical location (situation géographique in French) belongs to “classical” geography, appearing very early in the history of the discipline as a major way of explaining inequalities in the concentration of populations, wealth, or certain activities. It defines, to a certain extent, the added value of a location by its position, relative to other locations, therefore by its greater or lesser distance from other locations. The situational advantage is often a better accessibility, i.e. a shorter distance from a number of other places where wealth is produced or circulates. Geographical location is advantageous when the topography improves the accessibility of the place by reducing its access distances: this is how the development of cities located at the crossroads of large valleys or at the maritime outlet of a major land route, such as that of estuary cities, was explained in the 19th Century. Geographical location is also considered more favorable when traffic conditions are easy, relatively reducing distances, e.g. in lowland areas as opposed to mountainous regions. The so-called “contact” situation is the one that makes additional resources close to the sites. The time and cost savings associated with distance travel, when they persist long enough, thus become

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important components in explaining concentrations and accumulations of population and activities in the territories. Distance is a decisive factor in many location models, which represent the effects of “location rents”, which complement those of fertility rents or resource sites. Weber’s optimal industrial location model, developed around 1900, combines distances to sites (raw materials, markets, and labor) to estimate the best possible position for a production plant, minimizing transport costs; the von Thünen agricultural specialization zone model, developed in 1826, uses distance to the urban market and the differential rent it generates as the main explanation for land-use choices. Some effects of distance are so systematic that they result in repeated configurations, which arise in the spatial organization of most societies at different times, and which are broadly identified as “center-periphery structures”. These are forms of geographical space without precise but highly organized boundaries, a bit like a magnetic field, with a gradient of decreasing intensity as a function of the distance around a pole. The measurement of the relationship between places that define these spaces in the form of fields is then a flow, a quantity of exchanges, a frequency or intensity of relationships (number of commuters between places of residence and work, number of customers between a service provision center and the places surrounding it, number of telephone calls, origins of migrants and goods or investments attracted by a center). These configurations could admittedly be explained as society taking into account the laws of physics because it is a question of saving energy, thus minimizing an expense that then weighs as a constraint on the dynamics of social activities in space. By playing on the similarity between physical and anthropological expressions, the statistician G. K. Zipf (1949) also proposed calling this universal propensity to cut as short as possible and to go as close as possible, “the law of the least effort”, which amounts to organizing activities and movements according to distance. However, the origin of these almost geometric configurations, generally circular, can also be found elsewhere. Distance explains the shape they take: it does not explain why and how they are formed. The geographical space produced by the societies is oriented (anisotropic). Some places, selected as centers, acquire a social, symbolic, and economic value, which makes them centers where flows of people, energy, materials, and information from the periphery converge. More often than not, this attraction is explained by the fact that the center exercises domination, which may be political, military,

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religious, commercial, administrative, or symbolic (emotional and cognitive), over its periphery in various ways, which results in an unequal exchange, an asymmetry in the balance of interactions between the center and periphery to the benefit of the center. This process tends to reinforce the accumulation of supply in the center, which also increases the degree of complexity of its activities. The center redistributes some of the amenities, central functions, or innovations toward the periphery, but without totally reducing inequalities. However, maintaining the attractiveness of the center presupposes that it improves its accessibility and attractiveness for its periphery over time, according to a positive feedback loop between centrality and accessibility (Bretagnolle 1999). The value of geographical locations is not immutable over time. It is, therefore, not the physical analogy5 but rather the relevance of its mathematical formula to summarize the form taken by observations of spatial interactions that made the success of the gravitational principle to describe space organizations very strongly structured by distance from a center. The potential models, or the so-called “Reilly’s law” model (presented in section 1.1.2), indicate that the attraction force is proportional to the mass of the center and inversely proportional to the distance between it and the other places considered. It is used to delimit market areas, around shopping centers, or zones of influence around urban centers. Geomarketing techniques have a large intake of gravity models, in which factors of attraction, as well as distance measurements, are obviously modulated according to the cases analyzed. The spatial interaction model derived from the gravitational principle, which represents the volume of exchanges between two places as being proportional to the product of the masses present and inversely proportional to the distance between them, is also universally used to summarize, analyze, or predict the geography of flows, whether they are transport- or migrationrelated. Migratory fields (studied since 1970 in France by Daniel Courgeau), as well as urban fields (analyzed on a European scale by Marianne Guérois (2003)), are described by decreasing power or exponential functions of distance, which demonstrate its prevalence and universality in the social and geographical construction of interactions.                                         5 The physicist and geographer Alan Wilson, who considerably improved the estimation technique of the spatial interaction model, interpreted it in terms of “entropy maximization” and then linked it to the statistical theory of information.

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Whether the centers are spread out as stages on a route or tend to cover a territory according to a grid, they emerge at a distance characteristic of other centers, called spacing. Spacing is on average twice the range, i.e. the maximum length of travel by customers to obtain the service in question. The regularity of spacing is explained by the amount of population or activities that the centers serve, not simply by physical distance. The average spacing between centers increases with their level of complexity. The result is a hierarchical organization of the spatial structure of the centers, which is clearly demonstrated in the models of Walter Christaller’s central places theory, for example. The differentiation of space into centers and peripheries can be seen at different geographical scales. The multi-scale organization characteristic of the exercise of centrality and polarization encourages us to explore the fractal nature of the evolutionary processes that generate the hierarchical configurations of central places and their peripheries (see Chapter 3). The centers compete for the resources on their periphery and develop innovations during this interactive process. The development of innovations depends on the action of the actors located in the center. This consists either in a creation, anticipation, and attempt to exploit a profit, or in an imitation of an innovation that has succeeded elsewhere, and these two attitudes constitute an adaptation strategy. The innovations thus imposed or imitated are disseminated among the centers, by proximity or hierarchical dissemination (see sections 1.2.2–1.2.4). A center only acquires a higher level of centrality by accumulating and complexifying its activities if it succeeds in competing with other centers by capturing the initial advantage of a sufficient number of innovations. It is because this process has been carried out under the constraint of distance, wherever interactions have occurred over a fairly long period of time in contiguity, according to the proximity rule, that so many regularities have been introduced into the spacing of urban centers, at least in the very ancient regions of the world. Proximity explains why interdependencies are often detected in “statistical landscapes”, representing the values of all kinds of indicators through maps. These interdependencies are measured by autocorrelation indices of spatialized variables in a given neighborhood (Anselin 1995; Cliff and Ord 1973). Autocorrelation is positive when the effects of spatial diffusion have produced similarities as a function of proximity; it is negative when territorial competition has selected locations that have benefited over the long term from asymmetries in territorial exchanges. These correlations have long been thought of as troublesome in the application of statistical regression models (often referred to as “econometric models”) to geographical data, but geographers have developed spatialized regression

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models that, on the contrary, allow the analysis of the heterogeneity of variable associations in the geographical space to be specified and strengthened (Brundson et al. 1996). Finally, in the era of globalization, which is manifested in particular by the deployment of multinational companies opening subsidiaries in all parts of the world, or by the trend toward the universal use of global communication tools such as the Internet, the so-called “social” networks or smartphones, one could imagine that “the Earth is flat” and that distance would no longer be a major constraint in the organization of geographical space. Yet, it should be noted that proximity continues to play an important role in the creation of new international institutions, whether political, such as the European Union, or economic in nature, such as trade agreement areas negotiated between countries around the world, such as ASEAN, NAFTA, or Mercosur (Mareï and Richard 2018). 1.2.2. The scale Geographers have a constrained vocabulary when they produce a discourse on scales. They are major map producers and consumers whose scale is the measurement of the ratio between a distance measured on the map and the distance in the field. They therefore spontaneously speak of (cartographic) large scale for cadastres or urban plans at 1/10,000e for example, of medium scale for a road map at 1/200,000e, and of small scale for a representation of the world at 1/1,000,000e. However, the common language, and often that of decision makers, is that regional planning or global problems are on a “large scale” compared to the local scale, which concerns smaller areas. It is, therefore, better to find other adjectives to avoid these unfortunate ambiguities. Scale is thus associated with the orders of magnitude of geographical objects, which can be measured, for example, in terms of area, population, or wealth. Scale is called “resolution” when it indicates a degree of precision in cartographic representations or satellite images or even qualitative descriptions, which include more or less detail or generalization depending on whether one is at a large, medium, or small geographical scale. Increasingly, geographical information is presented with reference to the coordinates of the Earth’s surface in a form known as “geolocalized”, which makes it possible to form analytical filters by aggregation in grids (or rasters) of different dimensions that more or less smooth out the heterogeneities in the geographical space. Discourses produced from information thus aggregated at different scales can vary

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significantly, according to the principle of the MAUP (Modifiable Areal Unit Problem), well studied by Stan Openshaw (1983a). This also does not prevent us from considering that scale in geography represents a conception of the organization of space in more or less distinct levels of organization, which differ not only in their dimensions but also in the emerging properties that characterize them, due to the complexity of the spatial interactions that generate them. These spatial organizations can be “spontaneous”, self-organized, for example, in the case of cities or diaspora networks of linguistic or cultural groups, and they can also be led by institutions, for example in the case of political or administrative territories or economic regions or contractual networks. These levels, which are easily identifiable in the geographical space, are taken into account by the models. A very good example of “spontaneous” organization in levels is given by the distinction that geographers make between the city, the level of the organization of daily life, and urban networks or systems of cities, which regulate longer-range exchange networks in regional and national, even continental or global territories. At the city level, several types of regularities can be noted as “stylized facts”, characterizing the organization of urban space, regardless of periods and political regimes or forms of economic relations. Spatial interactions are intense because residents visit an average of three to four different places per person per day. These interactions have always been constrained by the length of the 24-h day, which has not changed over the course of history. The total daily time spent on these trips averages 1 h (i.e. distances of 3–4 km whilst walking and 30–40 km in motorized cities). Traveling is done at relatively slow speeds (from 4 to –25 km/h). The high densities of cities and the difficulties of organizing traffic explain why a large number of models have been built for urban transport. The geography of urban flows has thus been modeled by gravity models, derived from statistical mechanics, information theory or fluid dynamics, and percolation, before more sophisticated models integrate more social processes into them (see Chapters 2 and 3). However, it is not these interactions of everyday life which really produce urban forms, with their emerging properties characteristic of the spatial organization of centrality, contrary to what a simplistic application of complexity theories might suggest. Even if the demand for transport over time produces a tension for the construction of new networks, the emergence of urban forms results from determinations of another kind, both in terms of time and space scales and in terms of social processes. Indeed, the forms of

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cities are generated over much longer periods of time than in everyday life (from a few decades to a few centuries), by processes that are often incremental, more rarely organized as large-scale urban planning schemes, in the construction of buildings and transport infrastructure. The main constraint here is that of the social value attributed to more or less central locations, which is expressed by competition for space and the demand for accessibility, and therefore by more or less strong inequalities in the capacity of occupation by activities and populations that are endowed with different degrees of power and wealth. It is these processes of competition and social distinction in geographical space, which lead to often highly structured configurations of urban space, generally arranged according to a decreasing gradient of prices and densities from the center to the periphery of cities (according to a configuration called urban field, which can be mono or polycentric). This constraint on urban forms due to the unequal social value of space also explains other emerging forms of spatial distribution, according to fractal geometries of buildings, the street network, open spaces or different urban services, and highly variable forms, more or less marked but still present, of the spatial separation of social categories of populations or zoning of activities. At the level of systems of cities, other emerging properties characterize the organization of well-connected cities over the long term within the same territorial unit: the urban hierarchy expresses the very large inequality in city sizes, in terms of population concentrations (from a few thousand to a few tens of millions of inhabitants in the largest territories such as China or India today) or the number of urban activities and the value of their production. Functional diversity reflects the presence in the same region of cities with different and complementary functions that result from a geographically differentiated process of economic and social specialization. The interactions that make it possible to define a set of cities organized in a system are carried out with lower frequencies than those that take place in a city on a daily basis. With a lot of variation, it is estimated that about a day’s travel is possible for interactions to be strong enough to lead to interdependence in the demographic and socio-economic evolution of cities. Of course, national, linguistic, or cultural boundaries are involved in these very approximate boundaries; they can slow down or reduce interactions without, nonetheless, ever completely nullifying them. An important feature of these interurban interactions is that they now operate at much higher speeds (a few hundred km/h) than those of internal city interactions (between 20 and 30 km/h). Rapid transport, rail, then air and high-speed trains have,

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over the past two centuries, brought cities much closer together than other parts of the territories. However, here again, it is not these incremental interactions, represented by the physical movement of people, the exchange of goods, or even the very rapid exchange of information between cities, that explain the formation of urban hierarchies. The explanation lies at another temporal level, through the accumulation of these slightly asymmetric or partly qualitatively different incremental changes, which we summarize as the social processes of innovation creation and adoption. These particular modalities of urban growth and transformation through innovation are both what results and what generates them. Innovations are socially accepted inventions of all kinds: technical, cultural, political, organizational... Torsten Hägerstrand’s (1952) theory of innovation diffusion shows how larger cities are more likely to have rapid access to innovations due to their greater social and economic diversity and due to their more central positions in physical and social communication networks. Hägerstrand, therefore, created a hierarchical diffusion model that shows how innovations, especially those he calls “entrepreneurial innovations”, sometimes at very long distances, spread, according to the urban hierarchy, following roughly a downward progression in the size of cities, while the innovations he observed in agriculture spread in the geographical space from one place to another, according to an oil spill model. Detailed empirical observations of urban change over periods of a few decades have confirmed these modalities of innovation diffusion (Pumain and Saint-Julien 1978) on urban transformations (see section 1.2.4). Thus, in these two examples of the shaping of geographical objects, at two distinct levels, it is understood that the historical duration that allows these objects to adapt to changes in the forms of social and economic organization is a very important ingredient in their genesis. In other words, reasoning that would imply an “instant” emergence of a balance or structure with synchronous mathematical or computer processes is not really adapted to the study of the dynamics of geographical objects. Cities, territories, or landscapes are in fact, according to Philippe Pinchemel’s pretty formula, “interterrested duration”.

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1.2.3. Concentration and inequalities and scaling laws

accumulation:

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Two main processes are involved in geography to qualitatively and quantitatively differentiate noticeable and identifiable entities at a particular scale or rather at a particular level of observation. The first process, which can be called “territorialization”, produces mainly qualitative differences. It induces differentiations, within relatively tight borders, by a kind of “genetic drift”, which constructs attributes specific to localized entities from the most frequent interactions within the territory. This process can lead to significant differences with neighboring territories, for example, in terms of culture, language, landscape, social practices, and collective rules, at least as long as borders remain stable or as long as crossing distances only allow sporadic exchanges with other territories. The second process covers all interactions of the center-periphery type and the associated network asymmetries (including possible predations and conquests) and results in quantitative inequalities between geographical entities. In a given territory or between connected territories, this process induces inequalities in accumulation or in concentrations, which generate geographical entities of varying sizes. The geographical space is, therefore, neither homogeneous nor isotropic. The objects constructed by social interactions are characterized by strong asymmetries and hierarchies: thus, the dimensions of cities and territories, whether measured in terms of population, surface area, wealth, number of enterprises, or various indicators of notoriety, are always characterized by very asymmetric statistical distributions, comprising many small units, a little less medium and very few large ones. The Pareto or Zipf distributions, or the lognormal law, are the statistical models that best fit these very high inequalities. Systems of cities thus gather objects that, although bearing the same name, differ by four orders of magnitude (or powers of 10), grouping from a few thousand to a few tens of millions of inhabitants. In a highly connected geographical space subject to the same types of rules of interaction, the explanation of inequalities between these geographical objects is given by exponential growth models, according to the “law of proportional effect” (Gibrat 1931), or by logistic growth models, when the dimensions of the entities are limited by a certain threshold, for example, a quantity of available resources. This growth model is sufficient as a first approximation to characterize the evolution of inequalities in city size over short time intervals in the medium term. However, in the long term, inequalities often increase further

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due to the qualitative differences associated with size inequalities (Cura et al. 2017a). Large cities thus generally grow faster than those of the other cities in the system for which they are the political or economic capital. This is due not only to the control they can exercise over their system but also to the hubs or relays they play to connect their territorial unit with other territorial units (Bretagnolle and Pumain 2010). The trend toward increasing inequalities and qualitative differentiation of city attributes does not only concern a few cities at the top of urban hierarchies but also subtly affect the distribution as a whole. Thus, the larger the cities, the higher the proportion of innovative activities or skilled jobs in their population. This observation can be summarized by applying the scaling law model, which is also used for other complex systems. These statistical models describe, in a formalized way (by variable exponent power functions), the often non-proportional relationships that are established over time between the size of an object and that of one of its parts or certain measures of its activity (the “allometric growth” studied in the early 20th Century by D’Arcy Thompson). In biology, among living species, the metabolic rates (energy consumption per mass unit) of large species are systematically lower than those of small species, and the relationship between metabolism and size is, therefore, sublinear, with exponents of less than 1. These laws are explained by the fractal structure of the networks that distribute energy in living entities (West et al. 1997). In geography, the scaling laws have exponents greater than 1 for some urban attributes, such as those that characterize the innovative functions of cities or the value they produce, while declining or obsolete activities have lower exponents. A geohistorical interpretation of these scaling laws links urban concentrations to the ways in which major waves of innovation are adopted in urban hierarchies (Pumain et al. 2006). The role of interurban spatial interactions in the evolutionary trajectories of city populations was confirmed by an experiment with a simulation model on the subject of Soviet cities (Cottineau 2014 and see Chapter 4). The mathematical theory of scaling laws, applied to urban systems by Bettencourt et al. (2007), shows that activities that benefit from the social incubator role of cities are necessarily hierarchized. According to J. Raimbault (2019c), hierarchies, whether in the sense of the interweaving of multiple levels or scales, or of statistical distributions with large tails, would be endogenous to complex territorial systems (many examples of this type of socio-spatial organization are presented in Chapter 3). Contrary to traditional economic theories that predict convergence (equalization) of satisfaction or productivity levels between regions, geographical diffusion theory predicts both the maintenance as well as the

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catching-up or accentuation of previous inequalities. The ability to exploit the benefits of an early adoption of innovation often depends on the previous accumulation (capital) and social complexity (human capital) of the collective geographical entity, but it can also arise in some places as a result of the intervention of “individual” actors. Whether it is carried out by contagion or hierarchically, diffusion does not produce the same effects on localizations, depending on when it occurs in the trajectory of places, and also according to the differences in the condition between places thus connected. The colonization by European countries of many territories in all parts of the world, which brought together and then interacted strongly with countries that had very unequal levels of resources and power, has increased the lasting inequalities between Third World or developing countries. The complexity of these co-evolutions is expressed, however, by the fact that these inequalities and the changes that generate them are susceptible to reversals or bifurcations in their dynamics. The case of China is representative of this non-stationarity of relative geographical situations: its technological level was the most advanced at the time of the European Renaissance, and then its relative position declined until the end of the 20th Century before rising to the level of second major world power. It would be interesting to be able to model the evolution of inequalities between the world’s territories over time as it has resulted in many inversions in the positions of the main concentrations of wealth and power. For the oldest periods, the unequal allocations of resources available for the Neolithic agricultural revolution seem to give an ecological explanation for the formation of ancient territorial inequalities (Diamond 1997) but the rest of history shows that the interference between the processes of territorialization and accumulation–concentration has become much more complex, involving spatial interactions at a longer distance, up to contemporary globalization. Social and political domination, coupled with inequalities in economic wealth, has produced and reproduced center-periphery patterns that have been exchanged or redistributed differently across the globe throughout the history of societies. 1.2.4. Spatial change and trajectory dependence The longevity of geographical constructions is often a surprise to observers. The persistence of urban hierarchies can be measured over centuries, while the persistence of functional specializations of cities, especially the social characteristics associated with them, often exceeds a few decades. Since the end of the Second World War, the United Nations’

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decision not to allow territorial conquests and redrawing of States has also contributed to the persistence of the division of territorial entities at this level, which has not totally avoided conflicts, redrawing, and annexation. However, a change in political regime may be accompanied by territorial changes for finer constituencies: for example, at the sub-national level, reorganizations of administrative boundaries took place in Eastern European countries after the fall of the Berlin Wall (Maurel 2004). Sometimes it is the evolution of geographical entities themselves, such as cities in demographic and spatial expansion, which determines a reorganization of boundaries for the political management of territories (such as the organization of urban areas in France into “communities of communes” or “communities of agglomerations”). However, in general, the traced borders move little, or very slowly, and are sometimes found long after their official disappearance in the form of “ghost borders” (von Hirchausen 2017). These continuations are often interpreted as an “inertia” of geographical space, whose forms indurated physically in the habitat, in the networks, but also culturally by institutions, in the sometimes long duration of territorial planning and development procedures, which would show “inertia” and would oppose the fluidity of social change. On the contrary, careful observation of cities and territories demonstrates their formidable adaptability. Despite the apparently fixed nature of buildings, infrastructures, borders, and nomenclatures, the people who live in these cities and territories are rapidly renewing themselves (migration and the passing of generations), and their uses and practices are changing even more quickly. The social matter of territories and the individual and collective representations associated with them (“the hearts of Men”) are changing faster than their form, quoting the beautiful expression of the geographer and writer Julien Gracq about the city of Nantes. Figure 1.1 shows a simple representation, both of the persistence of the spatial organization of the territorial forms of systems of cities and of the coherence of these forms across the scales of geographical space. Céline Rozenblat (1995) had the idea of linking European cities (delimited according to a harmonized definition of morphological agglomerations) of more than 10,000 inhabitants by a segment of varying length, less than 25 km on a first map (Figure 1.1A), then 25–50 km (Figure 1.1B), and finally between 150 and 200 km for the cities that are 10 times larger (more than 100,000 inhabitants) (Figure 1.1C). The result, which is spectacular, shows on each of the maps the same large territorial areas. To the West, the urbanization of France and Spain, territories where early centralization in

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large kingdoms created high concentrations, shows very contrasting spatial distributions. In the center, a dense wrap of closer cities characterizes the states (Germany and Italy) whose national unity, which occurred later, allowed rival cities, capitals of principalities, or bishoprics, to develop in competition for a long time (Great Britain, although centralized early on, belongs to this diagonal because of the intensity of its industrial revolution, which in the 19th Century filled the urban void in the center of the country by creating fairly large cities). In the East, cities are spaced much more evenly, because these regions were urbanized later and were quite systematically colonized between the 13th and 17th Centuries, often by religious congregations. This simple representation is testimony to the strength and durability of the spatial integration of the socio-political structures established in urban interactions and the solid coherence of the resulting multi-scalar spatial organizations6. A fairly general property observed in complex systems, fractality, characterizes the hierarchical and spatial organization of cities and systems of cities (Tannier 2009 and see also Chapter 3). However, the particular conditions of the evolution of political and territorial social systems are manifested in a strong path dependence (which I also propose calling historical chaining) and decline this fractality into three styles of settlement configuration, in Western, Central, and Eastern Europe, which persist over time, well beyond the conditions that have prevailed in their settlement. These regularities of city dynamics and their socio-economic transformations mentioned above are integrated into an “evolutionary theory of cities” (Pumain 1997). The theory has been used as a basis for an important collective modeling work in the form of multi-agent simulation models that are presented in several chapters of this book (notably Chapters 4 and 5).

                                        6 In a similar approach, by systematically varying distance thresholds within a country and by percolation on the road network, E. Arcaute et al. (2016) identify the regional, urban, and local structures of Britain’s spatial organization, as well as their successive interlocking.

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Figure 1.1. Three settlement styles in Europe (source: Rozenblat (1995)). For a color version of this figure, see www.iste.co.uk/pumain/geographical.zip

The process of change in the geographical space is closely linked to its functioning. This is the result of a continuous effort of mutual adaptation by the many actors involved in the social space. The change produces a very large number of small local movements and transformations, most of which cancel each other out statistically and have virtually no apparent effect on spatial patterns. One example is the very small effect of residential migration on the transformation of territorial inequalities in terms of population concentrations. Unlike a simplistic representation that would see migration

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as a one-way movement, we know at least since Ravenstein (1885) that trade is always done in both directions, with an almost equal volume. As a result, the net balance of these movements – the net migration balance – often represents less than 1% or 2% of the volume of populations that have moved (Baccaïni 2007). Media representations that anticipate “invasions” by international migrants are part of the ideological myth. Moreover, the social compositions of observed movements between regions or departments are very similar between entry and exit flows. Foreign investment flows into industrial establishments reinforce existing specialities much more than they modify them (Finance 2016). In fact, the understanding of this contrast between extremely volatile micro-geographical processes and seemingly much more stable spatial structures is now understood as the result of complex system dynamics. This fluctuating nature of geographical change usually only produces incremental effects. When coupled with a strong effect of proximity and translated by spatial autocorrelations, it can explain the great success in geography of modeling using cellular automata. Relatively, simple local transition rules between the states of the cells of a grid representing land use are thus implemented to represent the transformations and to possibly anticipate them (Engelen et al. 1995; White et al. 2015). However, when it is useful to take into consideration spatial forms of interaction, which are not only related to proximity effects and are more diverse, in the design and scope of their networks, multi-agent systems are increasingly used as instruments, for example, to simulate innovation diffusion (Daudé 2004) or the trajectories of cities in systems of cities and territories (Sanders et al. 2007). 1.2.5. Territorial globalization

drifts,

space-time

compression,

and

In the long history of the human species, the prolonged effects of distance between isolated groups have paradoxically resulted in territorial “drifts”. This is a process that geneticists observe in terms of progressive changes in genetic heritage, and which socially creates significant differences between languages, cultures, names, and even the visible signs on which concepts of race and ethnicity were later based7. While the “genetic distance” between                                         7 F. Cavalli-Sforza’s (1984) book, The Neolithic Transition and the Genetics of Population in Europe, provides fascinating images of the effect of ancient migrations, greatly constrained by distance, on the current differentiation of secondary genetic signs between European regions.

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human groups remains relatively small, due to their common origin and the time involved in biological evolution, these social characteristics that evolve much more rapidly may have diverged very considerably, to the point that they have sometimes been erected as cultural barriers and conflicts between nations. In this respect, the transport revolution of the mid-19th Century really represents a bifurcation in the world’s history, from the point of view of the spatiality of societies, insofar as its consequences have not only been a shift in the center of the world (as has been the case many times since the Neolithic era, for example, when the center of Europe shifted from the Mediterranean to the North Sea in the 16th Century, so well described by Fernand Braudel). The changes we are thinking about are much more general; they have affected to varying degrees in all parts of the world and all relationships in the world, as well as the representations we have of them. We must be aware of the extraordinary distortion that has occurred between the “physical” distance, measured in kilometers on topographic maps, and the distance measured by the time required to travel due to the increase in transport speed as a result of mechanization. The transport revolution has literally created types of geographical entities and levels of scale that did not exist before. The American geographer Donald Janelle (1969) proposed the terms time-space compression and spatial reorganization to categorize these processes. This is an example of a quantitative change that leads to very significant qualitative changes. More recently, the considerable acceleration in the speed of financial transactions, which has taken international regulators by surprise, has led to economic crises of global proportions, the effects of which are still difficult to measure in the longer term. It may also be the case that the acceleration of economic development during the 20th Century (even more so than population growth, which tends to self-regulate), by inducing climate change and biodiversity loss, can lead to other major shifts. Many people consider it necessary to take corrective action to these human-induced upheavals (which led to the naming of a new geological era known as the “Anthropocene”) by advocating an “ecological transition”. The 19 sustainable development objectives and 169 targets advocated by the United Nations are an important first step in this attempt at regulation. It is likely that the acceleration of social communications via Internet-based networks will also lead to profound changes in practices and representations. It is still difficult to determine whether all these upheavals will bring about new transformations in territorial configurations and in the way we inhabit Earth. Simulation models of various scenarios can help us think about the modalities of these possible futures.

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For centuries, even millennia, the entire organization of human activities on the Earth’s surface has been carried out in a space-time system regulated by low traffic speeds. In this spatial system subject to the “tyranny of distance”, we, therefore, had geographical entities of daily life, which were defined as small contiguous regions, which included places connected by strong but short-range interactions. However, the role of these slow speed relationships in the construction of interactions with much longer spans should not be overlooked. Geographical entities may have formed at higher levels of scale (e.g. the empires of Central Asia, well studied by P. Frankopan (2017)), due to the slow spread of information and innovations (e.g. the spread of Buddhism, Christianity, or Islam, technological innovations, or even political forms in the pre-industrial world). Exchange networks have sometimes been established over very long periods of time (consider the ancient Silk Road, the role of Venice in the integration of Mediterranean trade from the 13th to the 15th Century, or the cities of Hanseatic League in northern Europe) as well as in warlike undertakings and matrimonial and diplomatic strategies of conquest, domination, or integration. These slow but far-reaching relationships have produced political entities and economic networks of much larger dimensions than the territories of daily life, defined at a more elementary level of scale, and punctuated by the life of the fields or the formation of agricultural markets. However, from the beginning of the 19th Century, very suddenly on the historical scale of time, the obstacle created by distance was considerably reduced. We see here the interest in considering socially significant distance, which regulates the intensity and frequency of social interactions, and which is expressed in units of transport cost, or time sacrificed to travel, or possibilities of access to information. Only this distance makes it possible to understand the structures of the geographical space envisaged as a space of social relations, or produced by social interactions. The effects of space-time compression on the spatial organization of systems of cities are not well-known to the general public. As a result of the repeated adjustments of all movements, the increase in speeds widens the scope and spatial influence of the centers, which can now attract a more distant clientele. The latter also finds it advantageous to visit a larger, betterequipped center. Thus, in the second half of the 20th Century, motorized French populations became accustomed to frequenting regional capitals for their use of services much more than the departmental capitals, planned at the time of the French Revolution to be located within reach of the inhabitants. As a result, there is a tendency to increase inequalities between

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centers, a “simplification from the bottom” of urban hierarchies. When this simplification from below occurs in a period of urbanization of populations, population growth, and living standards (which leads to the creation of new functions and jobs everywhere, even in the smallest centers), this decrease in the weight of small centers is only perceptible in relative terms (in that they grow less quickly than large ones). However, this is no longer the case when there is no longer a reserve of rural population to feed them or when the slower enrichment no longer makes it possible to equip them again. As a result, small and medium-sized cities are threatened, and their probability of development weakens on average even if local elected officials refuse to accept this fate (Baron et al. 2010). Many questions about shrinking cities have sometimes neglected this heavy spatial trend in their explanatory diagrams. Of course, the trend is still not very noticeable in emerging countries due to the high population growth and the rural exodus that continue there, but it is likely that the processes outlined earlier, reinforced by the financialization of urban development, will eventually produce similar effects there. The resumption of the growth of small and medium-sized cities becomes more likely again if they are “brought closer”, also by the contraction of space-time, to a still-expanding center. The geographical concept of the contraction of space-time invites us to do another reading of urban development and of the recurrent “theories” of a “counter-urbanization” (Berry 1976; Champion and Hugo 2004; Van den Berg et al. 1982). Is there a contemporary decline in city centers, to the benefit of the urban periphery? Is the “renewal of rural municipalities” on the agenda? Does the emergence of satellite cities, the edge cities, go against the theory of the tendency to strengthen centers? In fact, in an unchanging support space, which would be represented, for example, by a circle 30 km in radius, the growth of an isolated medium-sized city seems to propagate in a wave-like manner from the center to the rural periphery. However, if we imagine a space-time, represented by a circle or a dendritic figure of about 45 min around the center (i.e. with an expanding surface in the support space), then it is likely that we will observe a more permanent dichotomy between a center, a growing urban space, and a declining rural periphery – with, of course, the short-term fluctuations that characterize the processes of territorial growth and adaptation. More generally, the replacement of the concept of topographic space, where distances are measured in terms of physical distance, by a concept of geographical space that is relative in evolution as it is constructed by the

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relationships between places, measured in social terms of cost (especially for long distances) and time (for shorter distances), is a necessary change from dominant representations, which can lead to a better appreciation of the permanence and transformations of geographical entities. For example, the contemporary process of the re-emergence of “countries” is most often interpreted as expressing a retreat into smaller local areas than the regional framework, which would be considered too vast for development leadership. In the light of the increasing spatial scope of interactions, this process could just as easily be interpreted as an extension: in terms of possibilities for social interactions, today’s “country” would be the equivalent of the village or commune of the past. Similarly, the “fragmentations” into smaller states observed in some regions of the world could also be read as the formation of new interactions, at geographical levels hitherto ignored by the spatial integration processes acting within the framework of the large dismembered states (Pumain 1997). 1.3. Conclusion These geographically specific conceptions of complexity induce modeling practices that are partly discipline-specific. They are detailed in the following chapters of this book. Geographic modeling is quite often multiscale in principle, giving itself the freedom to define its “agents”, not always as individuals or actors but also as collectives, geographical entities of variable importance. These representations by computer science or mathematical formalization are thus carried out at several levels: micro-, meso-, or macro-geographic. The choice of their attributes is closely linked to the scale of the entities, the epistemological choices, and the questions asked (see Chapter 2). Geographical modeling uses stylized facts from empirical observations more often than fully logic-deductive models. Due to the “geolocation” of the data used, specific methods are implemented in the coupling of models with geographic information systems and by the deployment of appropriate spatial analysis methods. Among the many definitions of complexity, “the number of nonequivalent interpretations that an observer can make of a system” (Livet 1983) seems to us to be appropriate for the systems that the humanities and social sciences study. Indeed, each discipline: psychology, sociology, economics, and so on, produces its own representations and interpretations of complex processes, and it is these interpretations that must be articulated in an attempt to account for social objects and processes. The contribution of

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geography to the construction of this knowledge mainly concerns the spatial dimension. It proposes an interpretation of planetary and world diversity, based on its “natural” and socially constructed origins, by specifying the processes of resource exploitation and inequalities in geolocalized interactions at several levels of observation. The resulting geodiversity is perhaps the most historically secure engine of social change, first by encouraging people to look elsewhere, and then to network, always encouraging emulation, even if predation often prevails. Current dynamic models now make it possible to explain the diversity of geographical objects (territories, cities, regions, networks, and systems of cities) no longer through the completion of a biographical narrative but as one of the possible outcomes of a set of complex interactive processes. The aim is not to replace geographical processes (ecological and socio-spatial) with explanatory processes that would be relevant for other systems, but rather to propose an explanation of the observed evolutions that is part (to be determined) of more general evolutionary dynamics common to a number of systems and that can be abstracted in models, mathematics, or computer science. In the other chapters of this book, we will see how the difficulties inherent in introducing more than two levels of the time and space scale in the models are overcome, taking into account the heterogeneity of agents and the variability of behaviors in models, and in representing time compression in emergence processes.

2 Choosing Models to Explain the Dynamics of Cities and Territories

2.1. Introduction As the title of the chapter suggests, this contribution focuses on the choices made throughout a modeling process. The subject is vast and here it is delimited, on the one hand, by a thematic field, which is that of geography, and, on the other hand, by an objective that is to explain a phenomenon. The path between formulating a set of questions to explain a phenomenon linked to the dynamics of cities or territories and developing a model designed to respond to them, or at least to open up avenues for reflection, is indeed punctuated by a whole series of choices. The methodological approach that a researcher chooses to adopt depends both on his objective and on his disciplinary habits and know-how. His choices are not always made in a linear manner and are often based on implicit positions. For example, in response to the same thematic question on the evolution of socio-spatial inequalities in a given territory, one will adopt a qualitative approach based on semi-directive interviews, the other a quantitative approach based on statistical analyses of census data, while a third will turn to agent simulation models. The scope of possibilities thus remains very wide and it will be impossible to be exhaustive in this chapter. The objective is to show a set of nodes within a wide network of approaches, methods, and models that the researcher investigates on the dynamics of cities and the uses of territories. The first step is to specify the object of interest, particularly the phenomenon that we are trying to explain. Empirical examples will be used to establish the reasoning behind concrete cases of                                         Chapter written by Lena SANDERS.

Geographical Modeling: Cities and Territories, First Edition. Edited by Denise Pumain. © ISTE Ltd 2019. Published by ISTE Ltd and John Wiley & Sons, Inc.

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questioning about cities and territories, e.g. the emergence of spatial and social configurations, the evolution of urban forms, and the rates of transformation of activities. These cases will thus be mobilized to shed light on the nature of the choices to be made rather than to develop the thematic knowledge associated with them. In the rest of the text, the different choices punctuating a piece of research will be discussed, from the more general to the more specific, some assumed, others more implicit. The first choice concerns that of an epistemological framework of explanation (section 2.2). This choice, which is made before the model is developed, is linked to the researcher’s expectations and their epistemological positioning. The diversity of models available to the researcher is then discussed in order to review the polysemy of the term “model” (section 2.3). The intersection of these two discussions then leads to present, in a comparative way, two families of explanatory models, statistical models, and agent-based models, implementing an explanation by mechanisms (section 2.4). This last family of models is then further developed. First, the level of abstraction of the phenomenon is explained and the different forms that the individual and the general can take in the empirical field are analyzed and illustrated (section 2.5). Finally, the parsimonious (KISS) or realistic (KIDS) nature of the model is discussed with respect to the representation of space and spatial mechanisms formalized in the model. 2.2. Explaining by reasons or laws: choosing an epistemological framework The first choice is of an epistemological nature and the title of this paragraph refers to a series of debates about scientific explanation in the social sciences. These debates on the nature of the explanation emanate mainly from philosophers and were initially developed for the field of history. A few major points will be considered to illustrate those with questions rooted in geography. The term explanandum is used in this context to refer to the phenomenon to be explained and explanans to refer to what provides the explanation. The debate between the views of Hempel (1963) and Dray (1966, 2000) dates back to the 1960s, but the comments remain relevant and are often repeated and discussed (Lenclud 2011; Nadeau 2007), even if the title “The (hopefully) last stand of the coveringlaw theory: A reply to Opp”, given by Ylikoski to an article in 2013, suggests that the debate should be closed. Ylikoski is an advocate of an

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explanation by mechanisms and we will come back to this later on. The heart of the debate is the historical explanation. For Hempel, explanandum is derived from the combination of a set of initial conditions and laws (called “covering laws”), and this combination constitutes the explanans. These laws can be universal, which makes the approach deductive, or statistical, which makes the approach inductive. This explanatory model of a nomological nature that Hempel proposed as an explanatory approach in history is close to the so-called scientific explanation, traditionally used in the natural sciences. To this approach, Dray (2000) contrasts an explanatory approach based on reasons. To answer a specific question about a given historical fact or event, it is necessary to identify which actors were involved, what their actions were, and in particular what led these actors, in the context in which they found themselves, to act as they did. For him, rather than laws, it is a matter of identifying a logical sequence of behaviors based on a form of rationality. While the explanation refers quite directly to a law in Hempel’s approach, which consequently makes explanation and prediction synonyms of one another, the two notions are clearly separated in Dray’s approach. In a discussion on the difference between explanatory approaches in humanities and natural sciences (Martin 2011), Lenclud (2011) points out that the answer depends on the point of view adopted, be it ontological (“the way things are”), or gnoseological (“the way things are known”) (Veyne 1971). In the first case, it is the very nature of the entities being questioned that will determine the model of explanation. In the second case, there is a possible choice between different modes of explanation. Lenclud proposes distinguishing between the explanation, which would be in the natural sciences, and the understanding that would be appropriate in the case of the historical sciences: “Hunger is explained, fasting is understood; a fall on the knees is explained, genuflection is understood; aphasia is explained, neurosis is understood; aggressiveness is explained, revenge is understood; the phenomenon of crying is explained, Ulysses’ tears are understood; Etna’s anger is explained, Achilles’ is understood” (Veyne 1971, p. 111). How should we position this debate when attempting to explain a phenomenon in geography, particularly when we are interested in the dynamics of cities and territories? In this field, examples of explanandum are: How were cities formed? Why do cities bear a regular or irregular pattern in a given territory? What are the causes of growth differentials between territories? What factors underlie electoral geography (e.g. the overrepresentation of populist parties in some territories and underrepresentation in others)? Let us examine the respective contributions of

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these two schools of thought on the basis of a simple and very empirical example: what factors explain the very existence of the city of Montpellier? A historical explanation based on the reasons and intentions will highlight that Montpellier exists because it was founded on the initiative of an aristocratic family, the Guilhem, which decided in the 10th Century to move its heritage and activity, previously located in the upper Hérault valley, to the hill of Monte Pestelario (Favory et al. 1998, p. 233). This starting point is undeniably rooted in the decisions of actors who had reasons for leaving their previous location and reasons to choose this new site, for its assets in terms of physical potential, for its accessibility, or for other more personal reasons. An explanation based on laws can be based on classical spatial analysis models: Reilly’s law (1931) and Christaller’s model (1933). Reilly’s law, based on gravitational principles, makes it possible to estimate the respective areas of influence of different urban centers. It reflects the principle of spacing between cities. Christaller’s model (1933) describes “the hierarchical organization of a network of cities according to the level of services they offer, and their regular spatial arrangement at the tops of equilateral triangles or in the center of hexagons” (Hypergéo). The rules underlying such a regularity of the distribution of cities in a territory are based on the assumption of rationality of individuals traveling to the nearest city with the level of function corresponding to the objective of their travel (acquiring a good or using a service). These very classic models reflect the principles underlying the location of cities. Applied to the empirical field, these principles are such that the appearance (creation) of a new city “should” be done in a location sufficiently far from the other poles and thus completing the urban structure of the territory concerned. Multiple factors, at various levels of decisionmaking, are involved in the establishment of a city. The principle of regular localization requires a global vision, at the macro-geographical level, which can rarely be taken into account by the actors. These latter have very different profiles and levels (inhabitants, urban planners, entrepreneurs, and political actors), and they interact with various intentions that do not equate to creating a system of cities with a regular spatial pattern. These interactions give rise, according to a principle of self-organization, to a structure that can be maintained over time or evolve towards another organization. Montpellier, which has developed rapidly and became one of the main urban areas around the Mediterranean, illustrates a case whereby

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these interactions have reinforced Guilhem’s initial decision. Their choice was in a way “in line” with Christaller’s model: the creation of the city fills a gap in the local urban pattern and makes the regional urban network more regular. The city of Aigues-Mortes, created on the initiative of Louis IX in the 13th Century, offers a counterexample in the same region (Favory et al. 1998). This city never reached the expected level of development. The problems generated by the lagoon environment have certainly played a role, but it is very likely that the main cause of this relative failure is to be found in the competition posed by Montpellier and Nîmes. At the time of the creation of Aigues-Mortes, these were in full expansion and the city of Aigues-Mortes did not fill a void in the regional urban pattern as Montpellier had previously done. Another emblematic case of this type of failure is the city of Richelieu, created in 1631 by Cardinal Richelieu, Minister of Louis XIII. The reason for this choice of location was the desire to establish a city as an extension of its own castle. The creation of this city was thus very planned and led by a higher power. However, the choice of location did not correspond to a spatial law. The cardinal’s reasons did not correspond to the principles of urban location models and the city did not survive the disappearance of its initiator. While the buildings, now maintained by the Regional council, are still imposing, Richelieu is now a small town of 2,000 inhabitants. These examples show the extent to which reasons and laws are intertwined to explain a specific empirical fact such as the existence of a particular city. Rather than an opposition, it can also be seen as complementary (Sanders 2018). The reasons of the actors explain why the city was created: the reasons of the Guilhem family which led them to choose this hill rather than another place and those of the cardinal who wanted a real city near his castle. On the other hand, to explain why a city has or has not lasted over time, spatial models can provide possible explanations. The “laws” reflect very stylized facts that are what would happen if spaces were homogeneous and isotropic and if the behaviors were all rational. Such models can be used as filters to detect specificities in space or time, facts that are outside the law, to find reasons other than the most mundane (Durand-Dastès 1992). This first discussion focuses on the nature of the explanation. This is an epistemological choice made before the modeling process. Another trend that has developed in opposition to Hempel’s approach is mechanism-based explanation. This has the advantage of being close, in its construction mode, to the functioning of agent-based simulation models. Before approaching it, it is advisable to enter the network of choices through another entry point – one that relates to modeling.

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2.3. The modeling approach: diversity of models To introduce the notion of a model, Phan (2014) uses a linguistic analogy: “a model is a system of signs that refers to ‘something’ concrete in the real world that will be designated as the referent of the model” (p. 55). This “referent” refers to the phenomenon, which we are studying, observing, and questioning. However, the very term model is polysemous – refer to Phan (2014) and Tannier et al. (2017) for a complete presentation of all the theoretical and empirical aspects related to a modeling approach. To discuss the meaning that will be used in this chapter, two definitions are presented, which have often been used in the literature: one from geography, and the other from computer science: – “A model is a schematic representation of reality, developed to understand and make it understood” (Durand-Dastès 2001 after Haggett 1965). – “To observer B, object A* is a model of object A to the extent that B can use A* to answer questions that interest him about A” (Minsky 1965). In the first case, the “referent” refers to the “reality” (or an aspect of this reality) and the anchoring in an empirical fact is marked. It should also be noted that the verb “understand” is used rather than “explain” in this definition. In the second case, the referent is more generic, it refers to “object A”, the term object being taken in its broadest sense and it is neither a question of understanding nor explaining but more generally of answering questions. An experiment conducted within the interdisciplinary framework of a GDR MAGIS1 working group, bringing together geographers, historians, archeologists, and information science specialists (computer scientists and geomaticians), makes it possible to understand how the term “model” is polysemic and potentially a source of misunderstanding between researchers (Ruas and Sanders 2015). The reflection was on the “modeling of spatial dynamics”, a unifying expression behind which the participants actually represented very different things. However, the researchers did not follow the definitions of Durand-Dastès and Minsky according to their respective disciplinary origins. In fact, all participants agreed with both definitions and their complementarity, rather than opposition, was highlighted by all. The roots of the different interpretations of “spatial dynamics modeling” were not to be sought at this level of generality,                                         1 MAGIS (Méthodes et Applications pour la Géomatique et l’Information Spatiale): http://gdr-magis.imag.fr/.

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whereas, a priori, one might have thought that the strong empirical anchoring that emerges from the first definition would be more appropriate for “thematicians” (whether archeologists or geographers) and that the second, more generic, would satisfy computer scientists more. On the other hand, it appeared that these definitions were interpreted according to each person’s specific field of competence, ultimately leading to different representations of what it meant to “model spatial dynamics”. In this context, it appeared that the polysemy associated with the term model resulted from the lack of specification of the objective pursued, which was often implicit. While the search for an explanation of a given phenomenon was the primary objective of a modeling approach for some participants, such an objective was invisible for others for whom modeling is used to construct the phenomenon of interest in order to make it observable and readable. The three fundamental questions of geographic information at the basis of Peuquet’s triad (1994), what? when? where? (the three Ws), are then preferred. In this triad, the “what” is obviously central and the primary objective of a model can be to build or reconstitute what is or has been in a past era. A model is thus necessary to identify land use on a fine scale from a satellite image, to identify trajectories of ships or cyclists from GPS surveys, or to reconstruct elements of the past from archeological evidence in order to determine, for example, the evolution of a city’s functions over time. In each of these cases, a model is required to characterize a phenomenon based on indirect observables. It is a question of making the traces speak in order to identify what happened in “reality”. “Modeling spatial dynamics” can thus refer to data modeling work that makes it possible to consistently gather diverse and partial information on objects with changing definitions and, using geo-visualization or classification methods, to represent the phenomenon of interest, i.e. to represent the spatial dynamics in which we are interested (e.g. evolution of the built area or activities over time and reconstruction of the trajectories of international freight flows). This representation is the objective of the modeling and, in some cases, extensive work has been necessary to achieve it. In other cases, such a representation is the starting point of the modeling: the representation of the phenomenon leads to questions such as “how?” and “why?”. For example, why do cities experience differentiated economic growth? What factors explain why a territory is fragmented and recomposed? How does a new behavior spread among farmers in a region?

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A data model makes it possible to explore a rich and complex database, to make queries, and through them highlight regularities or breaks. An explanation model allows hypotheses to be tested on the factors that produce the spatial configuration and the evolution over time of the phenomenon studied. The use of the single term “model” without specification easily leads to misunderstandings in interdisciplinary contexts. However, some researchers propose more specific definitions. We can mention, for example, those of Alain Pavé, biologist, and Denis Phan, economist, both of whom are open to interdisciplinarity. Describing the modeling process, Pavé (1994, p. 29) thus highlights four points to be specified when developing a model: “the object and/or phenomenon to be represented; the formal system chosen; the objectives, i.e. the use that one wishes to make of the model; and the data (relating to the variables) and knowledge (relationships between variables) available or accessible through experience or observation” (words in bold are from the original text). After a development specifying each of its parts, Phan (2014, p. 60) comes up with the following proposal: “a model is a representation expressed in a formal language, which concerns a specific referent, in relation to a finalized and contextualized point of view in relation to a framework of thought that gives it meaning”. It is interesting to note the similarity between these proposals, beyond the choice of words and the 20 years separating the two pieces of writing. The only difference lies in Pavé’s choice to highlight the data, distinguishing between descriptors and knowledge about them, whereas these aspects are included in the “referent” of Phan’s definition. On the other hand, the latter insists on the framework of thought that gives meaning to the elements of the model. 2.4. Explaining through statistical relationships or mechanisms Once the problem has been formulated in the form of a search for explanation and understanding articulated around a “how” and/or a “why”, the same question can be studied using modeling approaches with very different philosophies. Two approaches of those are mentioned here: statistical models and computer simulation models. Manzo (2005) compares the operating modes of these two families of models by contrasting the “language of variables” associated with the statistical domain and the “language of mechanisms” specific to simulation methods.

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In the statistical model, the explanandum is materialized by the distribution of a variable and corresponds to the differences in the values taken by this variable over the different entities analyzed. In this context, explaining means reporting on the differentiations between statistical individuals (whether they are human individuals surveyed or spatial entities such as municipalities or cities) based on the distribution of other variables among these same individuals. The variable that describes the distribution of the phenomenon of interest is referred to as the variable “to be explained”, and the variables whose combination makes it possible to reproduce this distribution are referred to as “explanatory” variables. Data (census, surveys, genetic analyses, fossils, GPS data, etc.) are the driving force behind such an approach, which is often referred to as data driven. The challenge is to analyze what exists (has existed) “in reality” and the ability to reproduce what is observed is the key to a good model. Such a statistical model makes it possible to test hypotheses on the interrelationships between variables from a series of empirical data and it is a question of identifying the configuration of variables that best reproduces the observed phenomenon (calibration logic and search for the best fit with the observed distribution). When statistical individuals are spatial entities, this type of model highlights spatial co-variations that allow, to some extent, predictions (or estimates) of the variable to be explained (e.g. cities’ growth rates) based, for example, on cities’ economic or social attributes. The explanans thus refers to a system of correlations and not to causal links. Bulle (2005) uses the expression “realism of effects” to characterize this approach, which she contrasts with the “realism of causes” associated with agent models. In an agent model, the explanandum corresponds to the phenomenon that is produced at the macroscopic level (spatial segregation in the Schelling model), while the explanans corresponds to the mechanisms operating between the entities formalized in the model. An agent model makes it possible to build an artificial world in which agents (e.g. representing human individuals or groups such as companies or cities) are conceptualized and associated with rules of behavior concerning the interactions they maintain between themselves or with their environment. These models can be described as concept-driven and their driving force is the mechanisms that govern the relationships between the entities in the model and drive the dynamics of the system under study. Simulations then allow scenarios to be tested and alternative stories to be explored. Premo (2007), for example, points out that the classic question: “What happened in region X during period Y?”. The question, which may be replaced by a more exploratory question such as: “How likely is it that behavior Q or trait Z would evolve in

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the population in region X during period Y given a wide range of plausible environmental conditions and alternative histories?”. Such a model makes it possible to simulate a “thought experience”, to construct alternative stories, to answer questions such as what if, and to explore through simulation the spatiotemporal processes associated with the phenomenon of interest. Such models are fruitful in that they make it possible to reflect, even when the data is poor, on the functioning of different processes and the plausibility of different changes. This type of formalism is close to the spirit of explanation by the mechanisms. Hedström and Ylikoski (2010) stress the importance, in this mode of explanation, of making a very clear explanation of the phenomenon: “What are the participating entities, and what are their relevant properties? How are the interactions of these entities organized (both spatially and temporally)? What factors could prevent or modify the outcome? And so on”. These authors also point out that a mechanism, to be explanatory, must reflect how it works at a given level of study. If this explanation involves entities, properties, and activities, these must exist but not necessarily be explained: “their explanation is a separate question” (Hedström and Ylikoski 2010). Thus, if a mechanism deals with interactions between a set of cities, it is not necessary, from an epistemological point of view, to explain how these cities were created in order to claim to provide an explanation by the mechanisms on the emergence of a hierarchical structure in the city system, for example. According to Marchionni et al. (2013), agent-based models can provide explanations for a phenomenon of interest by combining two operations. The first refers to the generative component of the simulation: if the mechanisms introduced into the model, through a set of rules on how agents interact, bring out the phenomenon we are trying to explain (e.g. a segregated spatial configuration), then we have “proof of possibility”. For Epstein (1999), this is the fundamental component of explanation in an agent model: “If you didn’t grow it, you didn’t explain it” he wrote in a text on “generative social sciences”. For him, the explanation lies in the process that generates the phenomenon of interest, to account for its origin. However, the ability to generate does not mean that the causes of the phenomenon studied have been identified, and Macy and Flache (2009), in particular, point out that “if you don’t know how you grew it, you didn’t explain it”. Moreover, the proof of possibility does not mean that the explanation is the “right” one. It is sufficient to generate the phenomenon of interest, but there is no evidence to suggest that there are no other hypotheses that would have led to the same

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result. Thus, this generation capacity, if necessary and providing a “candidate for explanation”, does not make it possible to understand how and under what conditions the mechanism operates. To remedy this, it is necessary to add a second operation that Marchionni and Ylikoski (2013) call the “experimental component”. This involves systematically varying the assumptions of the model and studying the consequences for its results. To understand the “how”, it is necessary to study counterfactual dependencies (if A is the cause of B, this implies that if A has not occurred, then B does not occur). Such experiments make it possible to identify which hypotheses play a central or, on the contrary, indiscriminate role in the generation of results. In the next two points, the focus is particularly on agent models. There is still a variety of possibilities and it is a question of choosing the level of abstraction of the phenomenon to be explained, on the one hand, and the degree of parsimony of the model to be developed, on the other. 2.5. Choosing the level of abstraction for the phenomenon to be explained: general versus particular In an earlier work of Arnaud Banos (Banos and Sanders 2013), we had located a set of works on an axis ranging from general to specific. It emerged “that there is thus a whole continuum of empirical facts, from the most specific (why is there such a high concentration of privileged populations in the 16th arrondissement of Paris?) to the most stylized (why are metropolitan areas segregated?)”. This distinction between models whose objective is to explain a particular phenomenon (a specific spatial organization, observed in a given place at a given time) or a general one (a stylized organization-type, observed repeatedly in time and/or space) makes it possible to account for the positioning of the modeler relative to the observed phenomenon in which he is interested. This can be formulated in the form of a stylized fact (why growth differentials between cities?) or concern a particular empirical fact anchored in a given territory (for example, what explains the spatial configuration of these differentials in France? And in Europe?). The specific versus general distinction of a phenomenon is a relative notion that is dependent on the disciplinary background. While the question “why is the metropolitan area segregated?” is very general from the point of view of the geographer or sociologist, it refers already to the register of the particular for the physicist. A segregation process is indeed a particular case

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of a phenomenon of concentration in a given space of elements, whether they are particles, cells, or living beings. Such concentrations observable at a collective level are often the result of local interactions between elements that tend to attract and/or avoid each other based on their similarities or differences (whether they are attractions in a magnetic field or tend to cluster in urban space according to social profile). While keeping in mind this discrepancy in the grading from the particular to the general according to disciplines, we will adopt here a point of view rooted in the social sciences. Segregation is then understood as a “general” phenomenon defined by the existence of concentrations in certain places in the urban space of populations with similar profiles and the absence in these same places of other categories of population. One way of moving from the general to the particular is to characterize the populations studied. Some authors use very neutral terminology to describe the different populations present (e.g. blue and red tokens) in order to focus reflection on the general processes leading to such concentrations by abstracting from the exact nature of these populations. Others operate in the same spirit (by abstracting from social realities) by adopting a humorous method, such as Batty et al. (2004), which refers to supporters of different football teams. The choice of adopting terminology based on tokens or football team supporters illustrates a position based on the assumption that the nature of the differences between the two populations has no importance on the processes at stake and, therefore, on the functioning of the model we are trying to build. The challenge then consists of identifying the generic mechanisms underlying the processes of concentration of different populations in different places in space, by making hypotheses about the propensity of individuals to prefer or not to prefer locations within neighborhoods composed of individuals similar to themselves, without taking into account the character of this similarity. While establishing very generic rules, Schelling (1971) has in mind a particular observed fact: that of a concentration of black populations in some parts of the city and white populations in others. The generic model he develops allows him to reflect on this particular issue (Phan 2010; Sudgen 2000). Others are interested from the outset in the segregation of specific populations, according to their ethnic group, income level, cultural profile or voting inclination, and so on. Such a position leads them to reflect on the sociocultural mechanisms behind location choices, which may depend on the nature of the segregation studied (given that individuals’ behaviors are not necessarily the same according to different incomes or ethnicities).

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A second way of moving from the general to the particular is to specify the scale (that of the building and the neighborhood) and/or the type of space considered. This may be the place of residence (the most classic case), the place of work, or the school (e.g. when studying the segregation of school space). Schelling (1971), for his part, takes an approach based on a recurrence of the phenomenon of segregation between white and black populations from city to city in the United States. Its position is thus intermediate between the particular (the geographical context is specified: it concerns the United States and cities) and the general (all cities are concerned). A further step toward the “particular” is to focus on the phenomenon of segregation in a specific geographical location, e.g. a given city. This is the case of the work of Alivon and Guillain (2018) who studied social segregation in Marseille and showed the effect of a segregated structure on the increase in the risk of unemployment. Some issues on segregation are part of a combination of these different types of particularities: this is the case of the work of Poupeau and François (2008) examining the spatial and social logics at stake in the segregation of the Parisian school space. This is a particular type of space, the school space (composed of schools with students attending them), and a specific geographical area, Paris. Although related to specific cases, this work is based on generic conceptual frameworks and is, therefore, transferable to other cases. The cases developed earlier for illustrative purposes concern a phenomenon of spatial segregation, but many problems can give rise to formulations that place them on either side of this axis, ranging from the general to the particular. Another example that will be used later in this chapter concerns the settlement of new areas. In its most generic version, the question concerns a phenomenon of spatial colonization: what factors lead individuals or groups to migrate? What is the resulting configuration of the settlement? This distinction between the general or particular nature of the phenomenon that we are trying to describe and understand gives rise to a primary axis of categorization of the models. This axis is defined by the way in which the researcher formulates the question he seeks to solve by developing a model, i.e. by the precise specification or not of the populations involved as well as the geographical framework concerned. A second axis of categorization is provided by the very characteristics of the model that will be built.

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2.6. Choosing the level of abstraction for the model: stylized or realistic, KISS or KIDS While the previous paragraph was intended to specify the level of abstraction of the observation of the phenomenon studied, the aim here is to discuss the level of parsimony of the model. Literature on this subject is abundant in the field of agent models. The term KISS (for Keep it Simple, Stupid!) was proposed by Axelrod (1997) to recommend building the simplest possible model, with complexity to be reflected in the simulation results. Others replied that overly simplistic models did not really explain the phenomenon of interest but simply reproduced it. Edmonds and Moss (2004) thus contrasted the previous models with the KIDS (Keep It Descriptive, Stupid!) models built to account for all the factors involved in the dynamics of the phenomenon studied and to give more scope for empirical data. Different factors are involved in the grading of models on an axis ranging from “simple” (KISS) to “realistic” (KIDS). By focusing on the spatial domain alone, we can thus distinguish two gradations: the first relates to the representation of space (section 2.6.1) and the second concerns the formalization of the mechanisms governing interactions between the modeled agents and between them and their environment (section 2.6.2). The field is vast and we have chosen, in order to illustrate our purpose, to focus on a set of simulation models related to the territory and the city in which spatial and temporal dimensions are central. These are models in which spatial mobility plays a key role, whether the model formalizes the very modalities of an agent’s movements, or, more indirectly, the effects of their movements. It focuses on spatial patterns that emerge in the long term from interactions that have occurred at a local level and over a short period of time. These models were chosen for these common features to facilitate their comparison and exemplify a categorization of the models according to their “simple” (KISS) or “realistic” (KIDS) character. The themes addressed in these models, on the other hand, correspond to very diverse spatial and temporal scales: – models of large population migrations on the spatial scale of continents and the time scale of thousands of years (Paleolithic and Neolithic): Young (2002); Parisi et al. (2008); HU.M.E. (human migration and environment) (Coupé et al. 2017a); and Barton and Riel-Salvatore (2012);

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– models on the emergence of villages and a hierarchical organization of settlement: VILLAGE model (Kohler and Crabtree 2017) and MayaSim model (Heckbert 2013), on a regional scale and for hundreds of years; – intra-urban segregation models, e.g. Schelling’s (1971) model, on the scale of intra-urban space and over a temporality of the order of decades. 2.6.1. Modes of representation of space: from a stylized space to a realistic space The simplest and most stylized representation of space consists of a twodimensional, homogeneous, and isotropic mathematical space, either in the form of a continuous space or a grid composed of cells. This is the case, for example, with Young’s (2002) model, that models the expansion of a settlement in a rectangular space from an initial situation where an agent (representing a household or group) is positioned in one of the corners of a rectangle (Figure 2.1(a)). This is also the case in Schelling’s (1971) model where space is formalized from a grid in which two populations are randomly distributed during the initial situation. In both cases, the space is homogeneous and plays a simple supporting role. In the first case, the simulation represents a spatial progression corresponding to a process of expansion (colonization) of a settlement, and in the second case, the redistribution in space of the two populations considered is simulated (Figure 2.1(b)). One way of introducing a more realistic vision into the model is to consider a non-homogeneous space and introduce rules conditioning interactions between agents on their relative locations in space. An example is shown in Figure 2.1(c). The HU.M.E. model, whose objective is close to that of Young’s model (to simulate the spatial expansion of a settlement), differs from it in the specification of space: on the one hand, cells unsuitable for the establishment of a settlement (e.g. the sea) are introduced, and, on the other hand, if the environmental potential of the cells is homogeneous in the initial situation, it will differentiate over time as the space is exploited by the human groups that establish themselves there. After a number of iterations, the space is thus heterogeneous. It is a highly stylized representation of space but reflects the existence of ruptures (between cells suitable or unsuitable for human settlement) as well as a heterogeneity of environmental conditions, resulting in a spatial variation of available resources, which influences interactions between agents and their environment.

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Another way of moving more towards realism is to simulate the process of interest, not in a rectangle, but in a geographical space with realistic outlines. This is the case with the work of Barton et al. (2012) who model the way in which Sapiens came to dominate Europe at the expense of Neanderthal (Figure 2.1(d)). This case differs from the previous one, in which the contours separating the sea from the living spaces correspond to empirical observation. In this sense, the representation of space is more “realistic”. On the other hand, in this example, space is considered homogeneous and isotropic, acting as a simple support, whereas in the previous case, it has the potential to give access to resources that evolve over time as well as barrier effects that influence the movements of agents. The cases represented in Figures 2.1(c) and 2.1(d) thus correspond to two different ways of introducing “realism” into the representation of space, and the mere consideration of this representation is insufficient to determine which of these two modes is more stylized (KISS) or realistic (KIDS). A more precise examination of the formalized mechanisms will then be necessary to place them on an axis ranging from the most stylized to the most realistic representation of space. A complementary step toward a more realistic representation of space is to combine these two dimensions, i.e. a realism of contours combined with realistic distributions of resources at the local level. This is the case of the model by Parisi et al. (2007) on the expansion of agriculture in Europe during the Neolithic period (9,000-year simulations). The authors use a cellular automaton model, in which the European space, captured in its realistic outlines (Figure 2.1(e)), is divided into cells of 70 km2. Each cell is characterized by its physical properties at each date considered (altitude, rivers, precipitation, and soil characteristics). These properties make it possible to calculate the agricultural potential of each cell that plays a role in their attractiveness during the migration process. The model by Kohler et al. (2012) of the formation and increase in the size of Pueblo villages in the Mesa Verde (southwest Colorado region) is based on a similar degree of realism but corresponding to a finer spatial and temporal scale (Figure 2.1(f)). The cells are of the order of km2 and the duration considered is 700 years. Each of these cells is characterized by physical data (climatic and hydric) that make it possible to evaluate, on the 1-year-long scale, the corn productivity.

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(a) Source: Young, (2002) 

(b) Source: Batty et al. (2004) 

(c) Source: Coupé et al. (2017a) 

(d) Source: Barton et al. (2012) 

(e) Source: Parisi et al. (2008)

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(f) Source: Kohler et al. (2017) Figure 2.1. From a stylized to a realistic representation of space. For a color version of this figure, see www.iste.co.uk/pumain/geographical.zip

2.6.2. Formalizing spatial mechanisms: from stylized to realistic All the models mentioned above are simulation models and are based on the formulation of a set of rules. In the following section, we will focus on specific spatial mechanisms in order to illustrate the different degrees of stylization versus realism mobilized in the practices of modelers. Among the models discussed for illustration in this chapter, Young’s (2002) model is based on the simplest mechanisms: during a given iteration, it is a simple random draw that determines whether or not an agent moves, and if the draw results in a form of movement, it is done on a randomly chosen neighboring location. Schelling’s (1971) model is based on a more sophisticated rule since the movement of an agent is subject to a satisfactory condition that depends on the number of agents of the same type in his neighborhood (composed of the eight neighboring cells). The model is based on a simple rule that gives a “reason” for the movement: the agent who leaves his cell and settles in an empty cell (chosen at random) is an unsatisfied agent in his neighborhood. Moreover, Young’s model introduces several mechanisms in parallel since it does not only formalize the agent’s movement but also its survival and reproduction, always on the basis of random draws. These two models are thus very stylized, representative of the KISS family of models, and it is difficult to distinguish their respective positions on the “stylized versus realistic” axis, one having a more “realistic” formalization of moves but taking into account only this one dimension and the other integrating several dimensions of the life course.

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In the HU.M.E. model, the movement of an agent is basically governed by a mechanism of the same level of abstraction as the previous one: the agent moves if the resources available in the cell where he is located are insufficient. However, this mechanism incorporates two complementary elements that lead the model to be placed in an intermediate position between “stylized” and “realistic.” On the one hand, agents have different abilities, depending on their technological level, to exploit existing resources. On the other hand, they have different mobility capacities, depending on the energy that the agent was able to store during the previous steps. In the model of Barton et al. (2012), the movements of agents (representing hunter-gatherer groups) are formalized in a more abstract and detailed way. The potential mobility of agents is actually understood on two scales: (1) the scale of daily movements that take place in the area in which they obtain their natural resources, and (2) the scale of the so-called “residential” movements that correspond to a change of base camp. The core of the model is to determine which encounters with other agents (of the same or different type) result in the design of a descendant. The move itself is thus not reproduced by the model: it is the position in space of the descendant that is simulated. Level of abstraction of spatial mechanisms Level of abstraction of space Stylized and homogeneous space

Simple

Realistic

Young Schelling HU.M.E. SimPop

Differentiated stylized space Space: empirical contours Empirical space (contours and content)

Intermediary

Barton et al. VILLAGE

Parisi et al.

MayaSim VILLAGE

Table 2.1. Crossing of abstraction levels of representation of space and spatial mechanisms. Placement of some illustrative models

The illustrative models are presented in Table 2.1 according to the level of abstraction associated with the two aforementioned spatial dimensions, the first relating to the representation of space and the second to the spatial

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mechanisms introduced as rules in the models. Unsurprisingly, there is some correspondence between these two dimensions. Very realistic models generally require the mobilization of varied empirical data and reference to realistic geography, while the most stylized models are applied to neutral, homogeneous, and isotropic spaces. Intermediate situations are less obvious because they can be based on different combinations of the degrees of abstraction of the spatial support and the modeled mechanisms. 2.7. Conclusion In the work of Banos and Sanders (2013), we proposed crossing the two axes relating to the degree of abstraction of the phenomenon studied (from general to particular) and the degree of parsimony of the model developed (from stylized to realistic), respectively, in order to locate the models in this two-dimensional plane. Rather than making a typology of models, this plan makes it possible to identify and discuss different types of combinations (Figure 2.2). To use the models mentioned in this contribution, the models of Young and Schelling are clearly located in quadrant A, corresponding to a KISS model of a general phenomenon, while the VILLAGE model is located in the opposite quadrant, noted C, corresponding to a KIDS model of a particular phenomenon. This axis plane is particularly interesting for following model trajectories, i.e. to identify links between parent models, resulting from a similar problem, but developed according to an approach corresponding to different quadrants.

Figure 2.2. Crossing of the degree of abstraction of the studied phenomenon and the degree of parsimony of the developed model (source: according to Banos and Sanders (2013)). For a color version of this figure, see www.iste.co.uk/pumain/geographical.zip

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The work of the interdisciplinary SCID (Social Complexity of Immigration and Diversity) team led by Bruce Edmonds is a good example of a chosen methodological path from B to A quadrant. This is a model for the rate of citizen participation in voting based on the influential relationships in which they are engaged. A first multi-agent model formalizing a set of policy hypotheses has been developed (Fieldhouse et al. 2016). The central assumption is that the civic engagement of an agent is a function of the influence that other agents exert on him. This model integrates several mechanisms (demographic and behavioral) and formalizes in a precise way the forms of exchange networks. This model thus addresses a general question (place and time are not specified) using a KIDS approach and falls into quadrant B. This first model, which is quite realistic in terms of its functioning, is then simplified and several explicit mechanisms (e.g. the constitution of networks of exchanges between individuals through the workplace, school, etc.) are simply replaced by random draws. The simplified model (Lafuerza et al. 2016) is more efficient in terms of computing and many experiments have been carried out, showing the existence of a regime corresponding to a high participation rate and another corresponding to a low participation rate, depending on the values of the parameters. Further simplification through work with physicists leads to an analytical approach (Lafuerza et al. 2015) with a model clearly located in quadrant A. This example illustrates a progressive trajectory from B to A as part of a progressive simplification work carried out by an interdisciplinary team within the same research institute. The analytical version of a model makes it possible to understand its properties and functioning from a formal point of view. On the other hand, this understanding of formal properties is not necessarily accompanied by a better understanding of the social mechanisms at play. In the case of Schelling’s model, Clark and Fossett (2007) point out that the formal work conducted on this model in the literature did not allow us to answer how individuals’ movement choices are made nor the choices that lead or do not lead to different forms of segregation of residential space. These authors propose using empirical surveys to determine the rules of agent movement and to assess the effects of the local context on agent behavior. In doing so, they move the initial model from quadrant A to quadrant D. A third case of trajectory is illustrated by the HU.M.E. model, mentioned above, whose initial version is a priori included in quadrant B. It effectively includes several mechanisms: demographics (appearance, disappearance, and splitting of groups); exploitation of resources according to the

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technological level of the group, with the possibility of acquiring a higher level by imitating other agents; movement to another cell when the one in which the agent is located no longer has sufficient resources to feed the group; and ability to move according to an energy level acquired during sedentary periods. The mechanisms are thus numerous and intertwined, generating a certain level of complexity in the results (Coupé et al. 2017a). The adaptation of this model to the migration of Bantu from the Cameroon Highlands to the south 2,500 years ago leads to specifications such as the introduction of a new mechanism related to interactions between Bantu and Pygmies. The HU.M.E. Bantu model (Coupé et al. 2017b), which explores the effects of these interactions on migration rates and the ability of Bantu groups to reach the southern equatorial forest, is in quadrant C. With an initial position similar to the model for electoral engagement, this example illustrates, in contrast to the other, a trajectory toward greater complexity. The combination of the two axes in Figure 2.2 thus makes it possible to visualize different types of links between models, whether they are inheritance or skimming links. The choices made at this level, concerning the combination between the level of abstraction at which observation and questioning on the phenomenon of interest are formulated and the degree of realism introduced into the model’s mechanisms, are parallel to the discussion mentioned above on the choice of an epistemological framework for explanation. Explaining the inheritance links between the models should make it possible to better understand the form of the complementarities between the approaches and facilitate the cluster of choices to be made during a modeling process.

3 Effects of Distance and Scale Dependence in Geographical Models of Cities and Territories

This chapter questions the essential role of distance and scale dependence in models for analyzing the spatial configuration of human settlements and activities, as well as the processes that lead to their evolution, with reference to urban or regional study areas. The subject of study, therefore, concerns both the form of human settlements and the actions of people (individuals and groups) in their territory (or territories). A human settlement consists of the materialization in space – the physical inscription – of one or more human activities. It is characterized by a certain degree of sustainability. It can be a group of a few buildings or a larger group of thousands of buildings, parks, car parks, orchards, fields, and so on. Each element is connected to others, whether close or far away, with the same or different functions, by means of transport and communication networks. All this – buildings, unbuilt environment, and networks – is the container of human activities. Different models are available to study the spatial configurations, or shapes, of this container. The contents associated with this container are individuals and groups that perform activities and have spatial practices and social relationships. The spatial configurations of this content are studied in terms of locations, flows, and paths.

                                        Chapter written by Cécile TANNIER.

Geographical Modeling: Cities and Territories, First Edition. Edited by Denise Pumain. © ISTE Ltd 2019. Published by ISTE Ltd and John Wiley & Sons, Inc.

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Geographers tackle three main questions, each of which is equally important, about the cities and territories that they study. 1) Is the space differentiated? To answer this question, they focus on identifying and characterizing spatial differentiations. 2) Why is it differentiated? They are looking for explanations for the observed differentiations. 3) Why is this differentiation observed and not another one? They then try to distinguish the extent to which the explanations for these differentiations are general, valid for different places and/or different periods in time, or singular and related to local characteristics. Thus, (...) geography places the organization of space and its function in the foreground; it seeks to explain its diversity or rather its diversification, on different scales; it raises as its primary concern the question of location (why is it there and not elsewhere?); it uses space as a starting point to question reality, particularly society, in relation to its material support, inherited both from the action of past generations and from the forces of nature (Durand-Dastès 1989) (Figure 3.1).

Figure 3.1. Geographic questioning. According to F. Durand-Dastès (2001)

Geographical models are designed to answer one and/or more of the three questions mentioned above. These models make it possible to study spatial differentiations either in terms of locations (positions and situations) or in terms of movements and flows (changes in location). Modeled entities can

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be places or sets of places or individuals or groups of individuals. The differentiated characteristics of places create and are created by the movements of the individuals or groups of individuals. The resulting spatial configurations consist of spatial distributions (concerning places or individuals) as well as flows, trajectories, or travel routes (migrations, daily mobility, etc.). In the case of city and territory modeling, the differentiations identified are socio-spatial and not exclusively spatial (or exclusively social). Social and spatial are fundamentally linked in the sense that socio-spatial differentiations of places (differences in terms of social and/or spatial positions) create and are created by the movements of individuals in physical and social spaces (changes in social and/or spatial positions) (Grasland 2009; Tannier 2017). The rules (processes) that determine the location (position and situation) of the modeled entities are not distinguished a priori from those that determine their location changes. Indeed, the interactions between places are determined by the interest of each place for each type of settlement or activity and determine the interest of changes in locations or activities of individuals or groups of individuals. C. Grasland (2009) expresses it as follows: The crucial discovery of Tobler is the fact that positions and interactions can be analyzed in a symmetrical way through the concepts of movements and accessibility. (...) the division of spatial analysis between analysis of location and analysis of interaction is certainly useful for pedagogical reasons (...) but it can also be an obstacle for deep understanding of linkage between positions, distances and interactions. This is in line with the idea of Galton and Mizoguchi (2009) of mutual interdependence between matter and objects, on the one hand, and events and processes, on the other hand. 3.1. Three fundamental principles for modeling cities and territories The fundamental principles underlying the models for spatial analysis, the objective of which is the characterization of spatial configurations of cities and territories, are the same for the spatial simulation of processes (mechanisms) that generate spatial configurations. The first principle underlying these models is the minimization of energy used for trade and travel, studied by G. Zipf (1949) under the heading of the principle of least

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effort. The second principle is that of competition (or contest) to which places in the earth’s space are subjected. It is a competition between individuals or groups of individuals for land use, access to resources, access to customers, and so on. The intensity of this process varies according to the geographical location of the sites and their other characteristics. Depending on the case, this results in a dispersion or concentration of human settlements or individuals of the same or different types. The third principle is that of complementarity (or cooperation, congruence) between places, between activities, between social groups, and so on. This may result in both a concentration of entities of the same or different types, for example, the matching of supply and demand, or a dispersion, to offer a product or carry out an activity in one place and, at the same time, to offer another product or carry out another activity in another place. Geographical phenomena often involve a combination of these three fundamental principles, particularly in the form of competition– complementarity or attraction–repulsion. Thus, E. L. Ullman (1954) identifies three reasons why people, goods, or information move between a point of origin O and a point of destination D, i.e. three drivers of spatial interactions: complementarity between O and D (place D offers or allows a desired thing (e.g. a good, information, service, social relationship, etc.) that is unavailable or not possible at location O); transferability (the cost of travel between O and D is surmountable or, more fundamentally, travel is possible), and intervening opportunities (there are other possibilities to obtain or achieve the desired thing at other locations on the route from location O to location D). T. Hägerstrand (1952, 1967 [1953]) also uses these three principles to describe the spread of an innovation (it can also be the spread of a disease, a sport, etc.): the diffusion process involves the displacement of hosts and/or adopters (intervention of the principle of minimizing the energy used for travel), the fact that host and adopter must be in the same place or share a common interest for a given broadcasting medium (newspapers, television, Internet, etc.) (intervention of the principle of complementarity or congruence), and the fact that innovation must be able to impose itself as such (intervention of the competition or contest principle). A third example of a combination of the three principles is found in H. Hotelling’s (1929) model, which shows that two ice merchants on a beach have an interest both in locating next to each other in order to maximize the number of potential customers and in moving as far away from each other as possible to avoid mutual competition.

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From these three fundamental principles stems the fact that distance and scale dependence each play a very important role in the geographical modeling of cities and territories. 3.1.1. Effects of distance The effects of distance in geographical models correspond to the fact that elements close to each other are more likely to be related or similar than elements far away. This is the first law of geography according to W. Tobler (1970): Everything is related to everything else, but near things are more related than distant things. According to M. Goodchild (2001), the identification of spatial configurations is possible because spatial differentiations over short distances are assumed to be minimal and can be ignored1. In terms of process, M. Goodchild (2016) expresses it as follows: smoothing processes dominate sharpening processes and processes that differentiate the landscape are weaker than processes that smoothen the landscape. The effect of distance is manifested in the form of friction that reduces the mutual influence of phenomena as they move away. The distance can then be as much a kilometer distance as a cost distance or a time distance. Another effect of distance is that of belonging or not belonging to the same territory: the same community, the same nation, the same climatic conditions, the same language, the same social group, and so on. This second effect of distance partly explains the existence of spatial discontinuities and boundary effects. C. Grasland (2009) thus distinguishes spatial interactions, where the distance involved is measured in a continuous mathematical form (friction effect of distance), from territorial interactions, where the distance is represented by means of a spatial partition by discontinuous nature (effect of belonging to the same territory)2. However, the idea of associating the friction effect of distance with the measurement of a “continuous” distance is questionable. On the one hand, the distances measured over a metric space (most often Euclidean distances or Manhattan distances) concern a set of points that are by definition discrete. On the other hand, the friction of the                                         1 Spatial dependence provides the key to effective description, because it allows us to ignore differences over short distances, since they are likely to be small. 2 We propose to use the term “spatial interaction” for general effects of distance measured in a mathematical continuous form and to specify “territorial interaction” when we want to measure the discontinuous effect of a partition of space (Grasland 2009).

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distance can also be evaluated from discrete distance measurements: topological distances on a graph or neighborhood matrices (i.e. adjacency) of different orders. A. Páez et al. (2008), based on the reflections of P. Marsden and N. Friedkin (1994), pointed out the similarity of the methodological tools used to analyze social dependencies (e.g. autocorrelation measures in social networks) and spatial dependencies (spatial autocorrelation measures and, more generally, geostatistics and spatial statistics). The principle behind all these tools is that proximity in space (whether geographical or social) increases the probability that two phenomena are related, at least from a statistical point of view. Following the same logic, C. Grasland (2009) established a link between the distinction made by the sociologist P. M. Blau (1977a, 1977b) between “nominal parameters” and “graduate parameters” for the study of social positions, on the one hand, and the distinction that he himself proposes between “territorial parameters” and “spatial parameters” for the study of geographical positions, on the other hand. According to C. Grasland, “territorial characteristics” (the effect of belonging to the same territory) include the “nominal characteristics” defined by P. M. Blau as qualitative attributes of individuals defining social categories: ethnic group, religious affiliation, professional activity, and so on. At the same time, the “spatial characteristics” (friction effect of distance) cover the “gradual characteristics” of P. M. Blau, which are quantitative attributes used to define social strata: income, salary, age, and so on. The evidence of a correlation between the behavior of individuals sharing social or spatial proximity leads us to seek an explanation for this correlation. The question is whether this correlation stems from the fact that individuals share the same source of information or the same individual characteristic (correlated effect), whether individuals possess the same individual characteristic resulting from self-selection (contextual effect or exogenous social effect), or whether individuals actually exchange with each other (endogenous social effect) (Manski 2000). The second and third cases are two possible variations of the effect of distance in the form of belonging to the same territory. 3.1.2. Effects of scale dependence Socio-spatial differentiations are observed at a level that is necessarily aggregated with regard to the elementary entities modeled. However, more

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often than not, the measured geographical phenomena (concentrations and dispersions, correlations, etc.) vary according to the level of aggregation of the entities considered (Fotheringham and Wong 1991; Madelin et al. 2009; Openshaw 1983a) or the spatial resolution adopted (Goodchild 1980; Muller 1978). The spatial resolution corresponds to the fineness of the grain with which the elements of the container of a place are represented. For example, the built fabric of an urban agglomeration can be mapped building by building, each building having its own spatial footprint, delineated with great precision (metric or even infra-metric). In this case, the spatial resolution is fine. The same built fabric can be mapped as urban patches that roughly delimit the envelope of different groups of buildings. In this case, the spatial resolution is coarser. A built fabric can also be mapped as a regular grid of square or hexagonal cells with a side length of 20 m (fine spatial resolution) or 200 m (coarser spatial resolution). The level of aggregation of the entities under consideration is different from the spatial resolution. For example, a neighborhood can be studied as a whole, without breaking it up, or it can be considered as an aggregate of blocks or buildings. Similarly, residential mobility in an urban area can be considered at the household level (disaggregated analysis), at the neighborhood level (corresponding to an aggregate of households), or at the municipal level (higher level of aggregation). The fineness of the spatial resolution of the container of a place partly determines the level of aggregation of the entities considered and vice versa. Let us imagine, for example, that we want to study the relationship between the built form (height of buildings, type of buildings, local built density, etc.) and household residential satisfaction. If we have a fine-grained spatial resolution map of the building and individual data on household residential satisfaction, we can study the relationship at the level of the building– household duo. If, on the other hand, the frame map has a coarser spatial resolution, the relationship between the types of built aggregates and the groups of households residing there should be investigated. If the frame map is now fine-grained spatial resolution but household data are aggregated at the neighborhood level, the relationship between the type of buildings in each neighborhood and household residential satisfaction at the neighborhood level should be investigated.

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Scale dependence means that, with regard to settlements or human activities, the existence of a concentration process considering a certain neighborhood implies a dispersion process considering a wider or narrower neighborhood (Tannier 2017). In fact, in the absence of heterogeneities or inequalities and, therefore, of socio-spatial differentiations, there is no dependence on scales. One possible consequence of scale dependence is that concentration states observed at a certain scale (a certain level of aggregation or spatial resolution) imply dispersion states at another scale and vice versa. Another possible consequence of scale dependence is that a correlation between two phenomena can be negative when it is calculated on some spatial entities and positive when it is calculated on others (Openshaw 1981). This responds to the Modifiable Areal Unit Problem described by S. Openshaw (1983a): the states measured depend on the size of the elementary spatial units considered (scaling problem), the shape and positioning of the elementary spatial units (zoning problem), and the delimitation of the study area (“results depend explicitly on the bounds of the study” (Goodchild 2016)). In particular, the level of detail of the representation of space (level of aggregation or spatial resolution) influences the measurement of geographical shapes and structures. Therefore, (...) it is impossible to define a true population density at a point, since any estimate depends explicitly on the scale at which density is measured. (...) remarkably few geographical variables are scale-less (Goodchild 2001). W. Tobler (2004) makes the following observation on this subject: Arbia’s second law of geography reads ‘Everything is related to everything else, but things observed at a coarse spatial resolution are more related than things observed at a finer resolution’. This suggests that aggregation has a smoothing effect, as is well known (see Tobler 1969, 1990). This is very clear for recursively constructed fractal objects: the density of the number of occupied elements decreases as the spatial resolution becomes finer (Figure 3.2). This decrease in density is all the more marked when the fractal dimension is small (Tannier et al. 2012). The ratio between the density i measured at a spatial resolution i and the density i+1 at a finer spatial resolution i+1 is related to the fractal dimension D according to the relationship: i+

-2-D

[3.1]

where r is the size reduction factor of an element from a given spatial resolution to a finer spatial resolution. This relationship is reminiscent of

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another relationship that links the decrease in built density from the center to the periphery of cities to their radial fractal dimension (Batty and Kim 1992; Chen 2009; Fotheringham et al. 1989; Thomas et al. 2007).

Figure 3.2. Decrease in built density as a function of fractal dimension D when the size of each element is reduced by a factor r equal to 1/3 between a given spatial resolution i and a finer resolution i+1

3.2. Role of distance in spatial simulation models In order to describe the different ways in which distance can play a role in the modeling of cities and territories, we can start by studying four spatial simulation models. The first model is called SimFeodal (Cura et al. 2017b). It makes it possible to simulate, for a given region of Northwestern Europe between 800 CE and 1200 CE, the levying of taxes by the lords on peasant households, the construction of churches and castles, as well as the successive changes in the location of the agricultural holdings of peasant households. The simulation results show the concentration and fixation of the agricultural holdings around churches and castles. The intensity of polarization and hierarchy of the settlement system achieved in 1200 CE varies according to the simulated scenarios. The second model, MobiSim-MR (Tannier et al. 2016b), allows the prospective simulation, for a time horizon around 2030–2040, of residential household migrations in an urban region. The simulation results show the changes in the concentration of different types of households in different places of the urban region (neighborhoods, municipalities, sectors, etc.), as well as the evolution of the intensity of migration flow between these places. These two models were developed in a multi-agent formalism. They are, therefore, dynamic by successive iterations. The simulated dynamics concern different temporal ranges: the dynamics of SimFeodal is anchored

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over a period of 400 years, while that of Mobisim-MR is anchored over a period of 20–30 years depending on the scenarios. The temporal resolution (duration of a simulation step) of the first is 20 years while it is 1 year for the second. The notion of environment is at the heart of the dynamics of multi-agent models (agents react to and/or interact with their environment), and the spatial dimension plays a fundamental role (Mathian and Tannier 2015). In both models studied here, the environment is composed of spatial or socio-spatial entities represented explicitly and absolutely by means of geometry and geographical coordinates. These entities can be isolated points (e.g. shops and services in Mobisim-MR or castles in SimFeodal) or areas (e.g. taxing areas in SimFeodal or parks and wooded areas in MobiSim-MR). They can be both passive and active (agents). Entities that make up an agent’s environment are identified through explicit spatial relationships. When the relationship between an agent and an entity of its environment is in the form of proximity (geometric, temporal, or other), the role of distance is that of a friction force (Table 3.1). The intensity of the relationship between the agent and the entity concerned decreases more or less rapidly as the distance between them increases. Above a certain threshold, the relationship no longer exists, and the entity is no longer part of the agent’s environment. Another form of relationship is a joint membership of the agent and the entity in a single, more encompassing, whole (i.e. a territory) (Table 3.1). In this case, the relationship is dichotomous in nature: it is at work or it is not. The core of the SimFeodal and MobiSim-MR models is the simulation of individual residential migration (peasant households within a rural region or households within an urban region) and not the simulation of individuals’ daily mobility. However, in both models, agent migration depends to a large extent on the daily mobility (or travel) allowed by their environment. In SimFeodal, distances to the nearest castle and church are important determinants of the probability that a peasant household will undertake migration, the destination of which may be local or distant. If the probability of migration occurs, a random draw weighted by the respective attractiveness of the attraction centers (local or distant depending on the case) determines where the peasant household will settle. The attractiveness of the attraction centers consists of a measure of the possibility of benefiting, in a given place, from the joint presence of a castle, one or more parish churches, and a villager community.

Distance and Scale Dependence in Geographical Models of Cities and Territories

Entity considered SimFeodal

Head of agricultural holding

Friction

63

Belonging to the same territory

Distance to the nearest parish church and castle.

Belonging to a more or less attractive population center. Belonging to different taxing areas of seigniorial rights.

MobiSim-MR Household

Distance to the nearest park or square. Distance to the urban boundary. Number of shops and services with daily and weekly frequency of use and number of public transport stations in the neighborhood. Generalized accessibility to employment. Time and cost of access to the city center

Residential environment: number of high-income households; landscape characteristics; and type of residential environment (urban or rural).

MUP-City

Cell potentially worth urbanizing

Proximity to the existing road network. Proximity to public transport stations. Access to shops and services with daily, weekly, monthly, and rarer frequency of use. Access to natural and recreational areas with daily, weekly, monthly, and rarer frequency of use.

Fractalopolis

Center that could be the subject of residential development

Number and diversity of shops and services in the vicinity of each center. Number and diversity of green and recreational infrastructures in the vicinity of each center.

Table 3.1. Roles of distance in four spatial simulation models

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The modeling of the potential for daily mobility is more detailed in MobiSim-MR than in SimFeodal. Twelve variables describe a different potential for mobility in the residential environment of households (Figures 3.3 and 3.4): number of shops and services used daily (bakeries, schools, mini-markets, etc.) within 400 m of the dwelling (Edf); number of shops and services used weekly (butchers, supermarkets, general practitioners, etc.) within 2,000 m (Ewf); number of public transport stops within 400 m (Etc); distance to the nearest square or park (in m) (Egs); distance to the urban boundary (in m) (Eub); proportion of high-income households within a 200 m radius (Ehi); proportion of forest land use within a radius of 1,700 m (Efl); proportion of built land use within a radius of 100 m (Ebl); cost of access to the city center by car (Eccar) and public transport (Ectc); and general accessibility to jobs by private car (Ewcar) and public transport (Ewpt). This level of detail is explained, in particular, by the fact that MobiSim-MR was designed to work in conjunction with a simulation model of daily mobility (MobiSim-MQ – (Antoni et al. 2016a)) within an LUTI (Land-Use and Transport Integrated) platform and thus take into account the interactions between residential and daily mobility. We have seen earlier that the neighborhood of an entity can correspond either to the boundaries of a territory or to the limit beyond which the friction of distance is such that a point of interest can no longer be considered as representing a possible destination. While the friction of distance implies a movement, a movement of individuals between two positions, the influence of the territory of belonging (social, cultural, landscape, etc.) is exercised without the need for a movement; the partition of space that defines the boundaries of a territory is not fundamentally linked to a mode, a possibility or a will of movement. It is sometimes difficult to distinguish between a neighborhood defined on the basis of distance friction and a neighborhood corresponding to the boundaries of a territory. Moreover, the two definitions can be formally identical in a model. In MobiSim-MR, for example, different distance radii are used to define different neighborhoods (Figure 3.3). In some cases, distance radii are used to count shops and services or public transport stations. It is then the friction of distance that is modeled according to the idea that beyond the fixed distance radii, shops and services or public transport stations are no longer frequented. On the other hand, with regard to the proportion of high-income households within a 200 m radius, the underlying idea is not that a given household’s objective is to attend as many (or as few) high-income households as possible. The proportion of

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high-income households within a certain radius does not correspond to potential attendance; it serves as a proxy to represent a certain “social atmosphere” that is more or less appreciated by each household according to its income. In this way, the effect of belonging to the same territory and not that of friction of distance is modeled. The same logic applies to the assessment of the proportion of wood and forest areas and built areas in a certain neighborhood.

Figure 3.3. Rules for assessing the elements composing the local residential environment of a household in MobiSim-MR – parameter setting of the rules for application to Besançon’s metropolitan area. The value of 1 on the y-axis corresponds to a maximum appreciation. Based on (Tannier et al. 2016b). Note: distances are calculated as the crow flies

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The other two models we are interested in are not multi-agent models. These are MUP-City, which makes it possible to simulate fractal residential development under accessibility constraints (Tannier et al. 2012), and Fractalopolis, dedicated to the interactive design of multi-fractal urban development plans (Frankhauser et al. 2018). The purpose of these two models is to simulate different possible urban development configurations based on an initial spatial configuration (buildings, road and path networks, public transport stations, shops and services, and green and recreational infrastructures). They do not integrate any temporal dynamics: not only is the configuration obtained by simulation not located in time but also the transition from the initial configuration to the simulated configuration is done in a single step (“one-shot”) and is not the result of a trajectory that would have passed successively through a series of intermediate states. The simulation results are potentially interesting cells to urbanize in the case of MUP-City, and urban or suburban centers in which new housings could be built in the case of Fractalopolis. The rules governing the two models are of a geometric nature. In the case of MUP-City, it is a fractal rule of urbanization that imposes particular spacing between built cells and a certain form of connectivity between undeveloped cells. In the case of Fractalopolis, it is a system of iterative functions (Barnsley 1988) that jointly define the spacing between the different centers (i.e. their relative position) and their surface, as well as a certain connectivity of the spaces located outside the centers. With these geometric rules, distances between spatial entities created by simulation (cells or centers) are imposed without modeling the effects of distance in terms of neither friction nor membership to the same territory. These effects are indirectly taken into account through a series of hypotheses whereby it is assumed that the spacing between spatial entities (cells or centers) imposed by geometric rules allows certain mobility behaviors that are desired for a given development scenario, while they prevent others that are avoided for that scenario. The mobility behaviors concerned are the movement of individuals to access shops and services, public transports, and green and leisure infrastructures, as well as the juvenile dispersion of animal populations between different ecological areas (Frankhauser et al. 2018; Tannier et al. 2016a). In addition to the geometric rules for locating entities created by simulation (cells or centers), the effects of distance in terms of friction and the role of belonging to the same territory are directly modeled as part of the assessment of the interest of cells or centers in residential development

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(Table 3.1). To this end, the MUP-City and Fractalopolis models incorporate spatial accessibility measures, just like the SimFeodal and MobiSim-MR models: distance to the nearest opportunity/opportunities (points of interest) and number of opportunities in a certain neighborhood. However, unlike SimFeodal and MobiSim-MR, effects other than those of distance are also modeled in MUP-City and Fractalopolis, in order to represent the mobility behaviors of individuals in more detail. In particular, the diversity of the supply of shops and services, green and leisure infrastructures, and public transport are taken into account (Figure 3.5 and Table 3.2). Appreciation value

Appreciation value

Cost of access to the urban center by public transport, cycling or walking

Cost of access to the urban center by car 1st quartile of the distribution of access costs considering all individuals of the urban region

3rd quartile of the distribution of access costs considering all individuals of the urban region

1st quartile of the distribution 3rd quartile of the distribution of access costs of access costs

Appreciation value

Appreciation value

General access to employment by road 1st quartile of the distribution of 3rd quartile of the distribution of access values to employment for access values to employment for all individuals of the urban region all individuals of the urban region

General access to employment by public transport, cycling or walking

1st quartile of the distribution of 3rd quartile of the distribution of access values to employment access values to employment

Figure 3.4. Rules for assessing the elements composing the overall residential environment of a household in MobiSim-MR. The value of 1 corresponds to a maximum appreciation (Tannier et al. 2016b)

In Fractalopolis, each planned development center has a neighborhood (i.e. a catchment area) of which the size varies according to the distance between the center concerned and neighboring centers of higher functional level. The size of the neighborhood (catchment area) of centers of the same hierarchical level may be different, while the size of the neighborhood (catchment area) of centers of different hierarchical levels may be identical.

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Commercial cluster frequented daily

d ij (in m)

Commercial cluster frequented weekly

d ij (in m) largest catchment area of an establishment in the study area (default value: 4000 m)

Commercial cluster frequented monthly or more rarely Evaluation of the distance to the m closest establishments of each type μ(Λi)

Λ i (in m)

Access to public transport Evaluation of the access to bus or tram stops μ(PT)

Nb of PT stops at less than dmax (default value: 600 m)

Evaluation of the access to train stations μ(train)

Distance to the closest train station

Figure 3.5. MUP-City 1.2: accessibility variables used in the model to evaluate the interest of cells to be urbanized (default setting values). The value of 1 on the y-axis corresponds to a maximum appreciation

Distance and Scale Dependence in Geographical Models of Cities and Territories

Number of opportunities from which residents’ satisfaction is highest Shops and services used daily Shops and services used weekly Shops and services used monthly Green and recreational infrastructures used daily Green and recreational infrastructures used weekly Green and leisure infrastructures used monthly

8

Number of different types of opportunities from which residents’ satisfaction is highest 5

10

7

Not considered

2

Not considered

2

Not considered

10

Not considered

8

69

Table 3.2. Fractalopolis 1.0: configuration of accessibility rules for the design of urban development scenarios for Besançon’s metropolitan area (France)

In MUP-City, neighborhoods are determined by distance measured on the road and path network or as the crow flies (at the choice of the model user) (Figure 3.5). In the case, for example, of shops and services with daily and weekly use, the nearest establishment must be located at a maximum distance max (default values: 600 m for daily use and 2,000 m for weekly use) from the residential cell to be assessed. Otherwise, the evaluation drops to 0. From the nearest establishment located at less than 600 m, all establishments located at a maximum distance of 200 m from each other are considered, within the limit of a distance maxmax between the most distant establishment and the cell to be evaluated (default values: 1,000 m for daily attendance and 3,000 m for weekly attendance). In doing so, each commercial cluster is specific to each residential cell. The interest of a cluster of shops and services considering a given cell corresponds to the evaluation of the number and diversity of establishments present in this cluster combined with the distance that separates this cluster from the evaluated cell. When this distance is large (close to max), a good assessment of the characteristics of the cluster (high number of establishments and wide diversity of types of establishments present) does not compensate for the

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poor assessment of the distance between the cell assessed and this cluster. On the contrary, when the distance between the cluster and the evaluated cell is close to 0, a poor evaluation of the characteristics of the cluster is compensated by the good evaluation of the distance from the cell to this cluster. Unlike daily and weekly shops and services, where it is interesting to have a substantial supply in a very close neighborhood, it can be considered that having a shop or service of each category in “reasonable” proximity to the cell is sufficient in the case of monthly or less frequent use. For example, it is not necessary to have two hospitals, two dentists, or two libraries near your home. On the other hand, it is of interest to be within a few tens of minutes of all these services. This hypothesis is also justified in terms of accessibility to public administrations: it is not necessary to be equidistant from two municipal administrations, since by definition, a dwelling is located in a single municipality. Finally, with regard to the evaluation of accessibility to green and leisure infrastructures, the hypothesis is that the diversity of infrastructures present in the vicinity of a cell is more important than the number of infrastructures. Thus, access to a single football field or tennis court is as interesting as access to two of these fields. On the other hand, access to a football field and a tennis court is more valued than access to only one type of field. If we now compare the parameter setting of the accessibility rules made for the application of Fractalopolis and MUP-City to the same study area, i.e. the Besançon metropolitan area, we also notice differences (see Figure 3.5 and Table 3.2). In particular, the number of shops and services used daily from which total resident satisfaction is the maximum is equal to 3 in the case of the MUP-City application and 8 in the case of the Fractalopolis application. For shops and services that are used weekly, the same numbers are 15 and 10, respectively. These differences in values are mainly due to the different definition of cell neighborhoods (MUP-City) and development centers (Fractalopolis), as well as the use of different data for the two applications. It should be noted that, for the application of Fractalopolis, only two types of shops and services with monthly attendance were distinguished (hospitals and large shopping centers). This explains why two different types of opportunities are sufficient for the maximum resident satisfaction.

Distance and Scale Dependence in Geographical Models of Cities and Territories

Grand Duchy of Luxembourg

Besançon’s metropolitan area (France)

The nearest business or service frequented daily

400 m

400 m

The furthest business or service frequented daily

600 m

600 m

The nearest business or service frequented weekly

2,000 m

2,000 m

The furthest business or service frequented weekly

3,000 m

3,000 m

Shops and services frequented monthly or less: distance to the nearest m shops and services of different types

15 min

30 min

Natural and leisure areas used daily

400 m

300 m

Natural and leisure areas used weekly

2,000 m

2,000 m

Natural and leisure areas used monthly or less

5,000 m

5,000 m

Public transport stations: bus or tramway

300 m

600 m

Public transport stations: train

500 m

3,000 m

71

Table 3.3. Maximum acceptable distances for the application of the MUP-City model to two different study areas. Source: PhD theses by Maxime Frémond (2015) and Maxime Colomb (2019). The squares in gray show different values between the two study areas

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An important point to note is that the friction effect of distance varies according to the context, which is explicitly reflected in the rules for assessing the elements composing the overall residential environment of a MobiSim-MR household (Figure 3.4) and in the rules for assessing the accessibility of shops and services with monthly or rarer use of MUP-City (Figure 3.5): accessibility thresholds are set with regard to all accessibility values in the study area. It can also be seen that some distance thresholds vary for the application of MUP-City to two very different study areas: the Grand Duchy of Luxembourg and the metropolitan area of Besançon (Table 3.3). Indeed, the spatial configuration of green and leisure infrastructures as well as shops and services differs between the two areas. Also, the distance thresholds to the nearest parish church change over time in the SimFeodal model (Table 3.4). Threshold Distance beyond which the peasant household is no longer completely satisfied Distance beyond which the peasant household is totally dissatisfied

5 km

Value From 960 to 1060 3 km

25 km

10 km

Before 960

After 1060 1.5 km

5 km

Table 3.4. SimFeodal (version 6.3) – default values of two thresholds for the distance between a peasant household and the nearest parish church

In MobiSim-MR, MUP-City, and Fractalopolis, the different variables characterizing the environment of a modeled entity (household, cell, or planned development center) are not all equally important. In MobiSim-MR, the variables characterizing the residential environment are of relative importance, in relation to a series of household characteristics (Table 3.5 – empty boxes indicate the absence of a relationship between the household characteristic and the attribute of the residential environment concerned). In Fractalopolis, the relative importance of the different types of opportunities as well as the relative importance of the opportunities of different frequencies of recourse vary according to the functional level of each center (Tables 3.6 and 3.7).

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Attributes Household characteristics

Age

< 30 years old

Edf

Ewf

Ets

Egs

Eub

Efl

Ebl

Ehi Eccar Ecpt Ewpt Ewcar I I

MI

30–44 years old MI 45–60 years old MI > 60 years old

I I I

Income

Low Average

Lifestyle

No. of children

High

MI

MI

I

I

I VI

I

I

None 1 or 2

I

3 or more

I

VI Preference for urban amenities I

VI I

Preference for rural amenities Preferential car use Preferential use of public transport and other alternatives

I NVI NVI MI

MI

MI

VI VI

VI VI

NVI NVI

NVI

VI I

I I

I I

VI VI

I

I I

VI VI

I

VI I

I

Table 3.5. MobiSim-MR: assessment of the importance of the attributes of the residential environment of the current dwelling (in italics) and a future dwelling (in bold) in relation to different household characteristics – NVI: not very important; I: important; MI: moderately important; and VI: very important (Tannier et al. 2016b)

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Functional level of each center

Frequency of use Daily

Weekly

Monthly

First

Second

Third

Fourth

Shops and services

0.6

0.6

0.5

0.5

Green and leisure infrastructures

0.4

0.4

0.5

0.5

Shops and services

0.7

0.6

0.5

0.4

Green and leisure infrastructures

0.3

0.4

0.5

0.6

Shops and services

0.6

0.5

0.4

0.3

Green and leisure infrastructures

0.4

0.5

0.6

0.7

Table 3.6. Relative importance of shops and services versus green and leisure infrastructures, considering each frequency of use independently of one other. Values chosen for the design of urban development scenarios for Besançon’s metropolitan area (France) using the Fractalopolis 1.0 model. The sum of the values of importance in each cell of the table is equal to 1. Source: Frankhauser et al. (2018)

Frequency Daily Weekly Monthly

Functional level of each center First

Second

Third

Fourth

0.33 0.33 0.34

0.40 0.40 0.20

0.45 0.45 0.10

0.50 0.40 0.10

Table 3.7. Relative importance of activities classified by frequency of use, according to the functional level of the planned development centers. Values chosen for the design of urban development scenarios for Besançon’s metropolitan area (France) using the Fractalopolis 1.0 model. The sum of the values of importance in each column is equal to 1. Source: Frankhauser et al. (2018)

Concerning Fractalopolis and MUP-City, the relative importance of the different types of opportunities represents levers that can be pulled to simulate different planning orientations. In the example presented in Table 3.8, for Scenario A, more importance is given to proximity to shops and services used daily as well as to public transport stations (tram and train). Less importance is given to proximity to the road network as well as  

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to shops and services that are used weekly. Proximity to open (undeveloped) spaces is of intermediate importance. In Scenario B, on the other hand, proximity to public transport stations is much more important than that of all other criteria. Opportunity concerned Proximity to public transport stations Proximity to shops and services with potential daily traffic Proximity to shops and services with potential weekly traffic Proximity to the road network Proximity to undeveloped spaces (open spaces)

Values of importance Scenario A Scenario B 1.05

2.876

2.406

1.053

0.507

0.460

0.233

0.201

0.749

0.411

Table 3.8. Relative importance of different types of opportunities for two different scenarios simulated with MUP-City. Source: Tannier et al. (2016a)

The method adopted to quantify the respective importance of the different types of opportunities is the same in MobiSim-MR and MUP-City. This is Saaty’s (1977, 1990) paired comparison method, considering a scale of importance from 1 to 7 (Table 3.9). The different types of opportunities are first compared two by two to identify which is the most important in each pair and determine whether it is slightly or significantly more important than the other (Table 3.10). Comparison A and B are equally important A is a little more important than B A is more important than B A is much more important than B Intermediate values

Weightings 1 3 5 7 2, 4, 6

AB

Table 3.9. Weightings associated with the importance of opportunity type A compared to opportunity type B

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Comparison of importance Y is a little more important than X Z is of equal or very slightly greater importance than X Y is a little more important than Z

Weighting of the first type compared to the second

Weighting of the second type compared to the first

YX = 3

XY = 1/3

ZX = 2

XZ = 1/2

YZ = 3

ZY = 1/3

Table 3.10. Example of determining the relative weight of three types of opportunities (X, Y, Z) using pairwise comparison

On this basis, a comparison matrix is created (with (X, Y, Z) in rows and columns and XX = YY = ZZ = 1).

The calculation of the eigenvector of this matrix provides the weight of each type of opportunity: X = 0.16, Y = 0.59, and Z = 0.25 in the example presented here. In addition to our four examples that account for the role of distance in spatial simulation models, there are other accessibility measures that consider more factors than distance and the potential frequency of use of different types of opportunities in choosing the places people frequently visit. These other measures explicitly integrate the mobility behaviors of individuals, including time constraints and individual activity chains (Neutens et al. 2010). 3.3. Modeling scale dependence Changes in the position of individuals (migration, other mobility, etc.) and the spatial configuration of human settlements (location of activities, transport infrastructures, etc.) result from many processes acting at different spatial and temporal scales. Each process operates at one or more

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characteristic scales (Quattrochi et al. 2001, p. 143). They are represented in the models by means of meshes (or zonings), which can be nested hierarchically and represent the membership of social entities in the same territory or different spatial ranges for each process, which represent the friction of distance. The superposition and entanglement of these different neighborhoods result in spatial configurations (spatial distributions and flows) whose characteristics (concentrations or dispersions, hierarchies, etc.) vary according to the scale of analysis. According to M. Goodchild (2001, pp. 7–8), modeling scale effects in geography meets two needs. The first is to take into account the fact that scale effects are inherent in modeled processes. In this case, we consider that the generative mechanisms, at the origin of scale dependence, are the superposition and interweaving of multiple spatial neighborhoods (belonging to the same territorial grid, or geometric or temporal proximity) or others (social, cultural, etc. neighborhood), each of which defines the envelope of a category of potential interactions. Scale dependence is then considered as the result of processes for which the effects of distance are very diverse (see section 3.3.1). The second need is to integrate scale effects into the description of phenomena. The hypothesis of invariance of scales or statistical self-similarity is then used to describe and characterize sociospatial configurations (see section 3.3.2). The third case, not mentioned by Goodchild (2001), is the introduction of scale dependence as a generative mechanism for simulated configurations. To this end, successive spatial disaggregations, respecting a principle of hierarchical nesting or geometric transformations applied iteratively, can be used (see section 3.3.3). 3.3.1. Scale dependence as a result of processes acting at different scales We use here the examples of SimFeodal and MobiSim-MR. In both models, peasant households or households can change their location during a simulation depending on the differentiated attractiveness of the location for each of them. This attractiveness changes over time due, in particular, to changes in the agents’ environment.                                         3 The hierarchical pattern and structure of many landscape processes [...] require knowledge of how processes [...] operate over distances and time periods relevant to the study.

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In SimFeodal, environment changes include the creation of parishes, the modification of the catchment areas of parish churches, the increase in the number of seigniorial taxing areas, the creation of castles, and the emergence of villager communities. Exogenous influences also modify the behavior of peasant households during the simulation: the emergence of a climate of violence within the modeled region, resulting from the growing conflict between lords during the 10th Century, is reflected in the model by the appearance of and then the increase in a need for protection for peasant households (they thus seek to locate themselves as close as possible to a castle to benefit from its protection); the increase in religious obligations, resulting in particular from the strengthening of ecclesiastical supervision, is reflected in a desire by peasant households to locate themselves increasingly closer to parish churches. In MobiSim-MR, changes in the household environment include the construction of new residential buildings, the arrival or departure of highincome households, the increase or decrease in the proportion of woodland and forests, and changes in accessibility (time and cost of access by car and public transport). In the MobiSim-MR and SimFeodal models, the differentiated attractiveness of locations and activities results from interactions between the agents and their environment, both near and far. Knowledge of the macro-geographic configuration of the attractiveness of the locations is a collective reference for the agents of the models, in the sense that it is shared by all households or peasant households in the study area. In turn, it influences their individual behaviors. This collective reference is fixed in MobiSim-MR, calculated once and for all when the model is initialized. This is the median value of the attractiveness of all dwellings for all households at the time of initialization of the model. In SimFeodal, it is the relative attractiveness of the attraction centers in relation to each other, at each simulation step. Thus, both MobiSim-MR and SimFeodal integrate interactions between micro-, meso-, and macro-geographic levels. In the case of models other than multi-agent models, the integration of several geographical levels occurs differently. To illustrate this, let us take the example of the MobiSim-DR (Tannier et al. 2016b) and ArtiScales (Colomb et al. 2017) models, which simulate the construction of new buildings and housing units within an urban region. In these two models, the rules for creating housing units and buildings are based on three levels of organization: macro-, meso-, and micro-geographic levels. The comparison

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of Figures 3.6 and 3.7 shows that the processes at the macro-, meso-, and micro-geographic levels differ between the two models. In particular, the location of cells of potential interest for urbanization is considered as a global configuration at the macro-geographic level in ArtiScales, while it is involved in micro-geographic level processes in MobiSim-DR. Another crucial difference between the two models concerns their dynamics. MobiSim-DR simulates the construction of new buildings and housing units year by year, considering a temporal influence of around 20–30 years. Each year of simulation, new constructions reduce the number of potentially urbanizable cells at the micro-geographic level and modify the spatial configuration at the meso-geographic level. This, in turn, forces the location of the new buildings created. The model, therefore, represents an interaction between geographical levels. In ArtiScales, on the other hand, no such interaction exists because the model does not integrate temporal dynamics. If we consider that modeling the scale dependence of geographical phenomena requires not only taking into account different levels of aggregation or spatial resolutions but also representing interactions between scales, i.e. what happens at a microscopic analysis level is influenced by what happens at a mesoscopic or macroscopic level and vice versa (Tannier 2017), then modeling in ArtiScales is not scale-dependent but simply multi-scale. Macro‐geographic level

Targeted housing construction set in planning documents

Metropolitan area

determine

Number of housing units of each category that must be constructed each year determine

Rule set to allocate the housing determine units that must be constructed to the appropriate class of built cluster

Meso‐geographic level Built clusters classified according to their size

Number of housing units of each category that must be constructed in each class of built cluster

determine

Cells of 20 m width being potentially worth urbanizing

Micro‐geographic level Non‐developable areas

determine

Selection of the appropriate number of cells having the highest interest to be urbanized

Fractal dimension of residential development Additional planning rules weighted by their relative importance

Figure 3.6. Multi-scale modeling in MobiSim-DR

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Figure 3.7. Multi-scale modeling in ArtiScales

Simulated spatial configurations can be observed at different levels of aggregation. As an illustration, we have shown simulation results obtained with MobiSim-DR at the micro-geographic (Figure 3.8), meso-geographic (Figure 3.9), and macro-geographic (Figure 3.10) levels. Figure 3.8 shows that the local forms of residential development simulated for the two selected scenarios are significantly different from one other. Figure 3.9 shows that, at the meso-geographic level, the simulated residential growth is also spatially very different. With the moderately compact residential development scenario, residential growth concerns all built clusters (with a variable intensity) except the smallest ones, while with the residential development scenario favoring the use of public transport, it is concentrated in only 12 clusters and follows a radial spatial logic around the main cluster. In this scenario, in the West Southwest sector of the urban region, residential developments result in an extension of the main built cluster. In doing so, a

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fairly large built cluster, present in 2010 and located west of Besançon (communes of Franois, Serre-les-Sapins, and Pouilley-les-Vignes), and some secondary clusters located southwest of Besançon disappear by merging with the main cluster. These mergers largely explain the sharp increase in the surface area of the main cluster, visible on the rank-size distribution in Figure 3.10. Figure 3.10 shows that the hierarchy of the settlement pattern at the macro-geographical level is almost unchanged from the initial situation in 2010 with the moderately compact residential development scenario. By contrast, the scenario favoring the use of public transport shows an increase in the size of the largest built cluster and a decrease in the size of the smallest ones. In other words, with this scenario, the rank-size distribution of the built clusters is closer to a straight line (regular hierarchy) than that of the configurations built in 2010.

Figure 3.8. Examples of local forms of residential developments simulated with MobiSim-DR for Besançon’s urban region (focus on a few municipalities in the northern sector of the urban area). Source: Tannier et al. (2016b)

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Figure 3.9. Number of buildings in each built cluster in 2010 and 2030, and rate of change 2010–2030 for two prospective scenarios simulated with the MobiSim-DR model for Besançon’s urban region. The delimitation of built clusters in 2030 is specific to each scenario. Source: Tannier (2017). For a color version of this figure, see www.iste.co.uk/pumain/geographical.zip

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2

Figure 3.10. Rank-size distributions of built clusters larger than 0.2 km for two scenarios simulated up to 2030 with the MobiSim-DR model for Besançon’s urban region (in black) compared to the initial situation in 2010 (in gray). On the x-axis: the rank of each cluster; on the y-axis: their area in km2. Source: Tannier (2017). For a color version of this figure, see www.iste.co.uk/pumain/geographical.zip

3.3.2. Scale invariance for the description of geographical phenomena Classically, to describe socio-spatial configurations across scales, the spatial resolution or level of aggregation of the entities considered is systematically varied (Tate and Atkinson 2001). In this context, the scale invariance property is often used to introduce a scale dependency into models. Scale invariance means that the shape of a distribution is not changed and nor are the properties that result from it, when the unit of measurement of the samples in the distribution is changed. In other words, the distribution has the property of invariance of scales by changing units4 (i.e. by translation) (Dubrulle et al. 1997). This property necessarily implies a power law (scaling law), as illustrated by the following mathematical formula: y=kx

[3.2]

                                        4 There are other cases of invariance of scales independent of the unit of measurement when the quantities considered are dimensionless (Dubrulle et al. 1997).

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where k is a proportionality constant and definition, we have: = dy / dx

is the scaling exponent. By [3.3]

A power law can be expressed in a linear form via the passage in double logarithmic coordinates: log(y) =

log(x) + log(k)

[3.4]

In the case of a linear distribution, the inequality between two values of a variable corresponds, in order of magnitude, to the difference between the two values. With a power law, the order of magnitude of the inequality between two values of a variable corresponds to the ratio between these two values. Different growth models can lead to scale-invariant distributions, the best known being R. Gibrat’s (1931) proportional growth model, which shows that each city in a city system sees its size change over time in proportion to that of the system as a whole (Pumain 2007); allometric growth models inspired by D’Arcy Thompson (1917) (some elements grow faster than others); and fractal growth models (Frankhauser 1990). An important point to note is that these growth models only produce scale-invariant distributions and do not explain the determinants of their existence. Yet the fact that a distribution is scale-invariant does not necessarily imply that the processes at the origin of this distribution are scale-dependent if we consider that scale dependence implies the existence of interactions between scales. Indeed, a distribution of elements by size can correspond to a power law and yet result from a single process acting on a single scale. Conversely, the existence of a dependency on scales does not necessarily imply that the ordered distribution of elements is scale-invariant. This is the case, for example, of the SimFeodal model, in which the mesoscopic scale (i.e. the relative attractiveness of population clusters) interacts with the microscopic scale (i.e. the individual migration of peasant households), and of which the ranksize distributions of the population clusters obtained by simulation do not follow a power law. Among the scale-invariant distributions, some are statistically selfsimilar, i.e. fractal, meaning that the numerical or statistical measurements characterizing their shapes are identical across scales. The statistically selfsimilar nature of a spatial configuration is the result of rules for distributing

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elements relative to each other, which are approximately repeated at different scales. In doing so, the shape of the distribution is approximately, but not exactly, the same on different scales. Self-similarity implies the property of scale invariance but not vice versa. Looking at a self-similar density with different magnifying glass or scale is not the same as changing the units of the measurement (A. Wierman, blog Rigor + Relevance, December 5, 20145). Fractal dimension measures are of interest when studying cities and regions because they allow us to characterize very heterogeneous spatial distributions (François et al. 1995). Fractal geometry has been advanced as providing not only a suitable model of the irregularity found in nature, but also a description of that irregularity which is scale independent (Tate and Wood 2001, p. 36). The adaptation of fractal dimension measures to the study of unevenly concentrated spatial distributions results from the fact that the support of the measure is the shape of the measured object itself: a fractal dimension measures the change of the object toward itself by changing scale (Tannier 2017). Conversely, when measuring a density, the support of the measure is the support space of the measured object, which is why density measures assume a homogeneous spatial distribution of the elements as well as a linear, proportional relationship between population and surface. When calculating concentration indices (Gini index, Hoover index, Duncan index, etc.), we measure a deviation with respect to a random distribution (Bretagnolle 1996). Fractal dimension measures vary in space. For example, the fractal dimension of the built area estimated for an entire city and that estimated for each of its neighborhoods are different. Thus, for about 40 large European cities, based on Corine Land Cover images of built areas, M. Guérois (2003) has established that two areas of fractality separate the zone of the agglomeration built in continuity and the suburban fringes. She has shown that the orders of magnitude of fractal dimensions are very different: close to 1.8 in the agglomerate zone, well below 1 in the suburban fringes. Within a city, each neighborhood also has its own fractal dimension. I. Thomas et al. (2012) have shown, for 97 neighborhoods in 18 European urban areas, that fractal dimensions can be closer between neighborhoods belonging to different cities and countries than between neighborhoods belonging to the                                         5 Scale Invariance, Power Laws, and Regular Variation (Part I). https:// rigorandrelevance.wordpress.com/2014/05/12/scale-invariance-power-laws-andregular-variation-part-i/. Accessed September 2, 2017.

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same city or country. According to this view, the morphology of neighborhoods is independent of that of the cities or the countries to which they belong. Considering even finer scales, P. Frankhauser (2017) has shown that the local radial fractal dimensions calculated for the municipality of Cergy-Pontoise (Île-de-France) vary significantly from one part of the municipality to another. Moreover, for a given built fabric, which may be that of an entire neighborhood or city, even if the fit to a power law is statistically correct, the change between two scales = dN( )/d of the number of elements counted N for each neighborhood size varies significantly across scales, while it is constant for a self-similar fractal. This is highlighted by means of scaling behavior curves that represent different cities or neighborhoods (Frankhauser 1997, 1998, 2004; Thomas et al. 2010). In fact, very early pioneering works in geography pointed out that the fractal dimension is not supposed to be constant in reality (Goodchild 1980); more often than not, it is constant for a certain range of scales but varies across successive ranges of scales (Lam 1990; Lam and Quattrochi 1992; White and Engelen 1994). [...] real-world phenomena are seldom pure fractals and self-similarity rarely exists at all scales. In such cases, specific fractal dimensions are defined only for specific scale ranges at which regression behaves linearly (Quattrochi et al. 2001, pp. 16–17). Whatever the method adopted to estimate a fractal dimension, the smallest (respectively, the largest) neighborhood size below (respectively, beyond) which the estimation of a fractal dimension loses all its meaning is the one from which the measured object is no longer self-similar (Baveye and Boast 1998). [...] Any empirical measurement of fractal dimension thus highlights a domain of validity of the identified structure, generally between a lower threshold and an upper threshold below or above which the fractal dimension changes or can no longer be established (Pumain 2010a). The level of resolution of data sources also interferes with the determination of the validity domain of structural fractality. Indeed, since measuring fractal dimension consists of counting the sites occupied by a given type of object in increasingly smaller boxes, this counting becomes impossible when the scale of the supporting cartographic document does not allow us to distinguish between full and empty [boxes] (Pumain 2010a). Although the statistical self-similarity of geographical shapes is spatially circumscribed and concerns a limited range of scales, measures of fractal

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dimensions and associated scaling indices make it possible to differentiate them from each other, with identified differences or similarities having visual coherence. In practice, it is possible to assume that a spatial distribution is scale-invariant (or statistically self-similar) and to study deviations from this model. Deviations from the scale invariance may occur for some scale ranges and not others. Deviations from the scale invariance can also vary in space: spatial differentiations are thus highlighted (Tannier 2018). The study conducted by F. Sémécurbe et al. (2019) on the spatial distribution of buildings in mainland France provides a good illustration. Mainland France was covered by a grid of 2,000 m of separate estimation points i (145,178 in number). Within a radius of 8,000 m around each point i, the spatial distribution of buildings was studied. Data used for this purpose were those of the Topo® IGN 2011 database and represent approximately 24 million buildings. For radii of the distance between 50 and 800 m, it has been shown that the spatial distribution of buildings is locally scale-invariant in eastern France as well as in large urban areas, but that it is not in central and western France. The characterization of how the spatial distribution of buildings deviates locally from a scale-invariant distribution made it possible to establish a typology of 145,178 built patterns in France (Figure 3.11).

Figure 3.11. Typology of 145,178 built patterns in mainland France based on the characterization of how the spatial distribution of buildings deviates locally from scale invariance. Source: Sémécurbe et al. (2019). For a color version of this figure, see www.iste.co.uk/pumain/geographical.zip

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3.3.3. Scale dependence as a simulated spatial configurations

generative

mechanism

for

Here we use examples from the Fractalopolis model, which is used to design multi-fractal urban and regional development plans, and the MUPCity model, which allows the simulation of fractal residential development scenarios. The new residential developments simulated with MUP-City and the urban development plans designed with Fractalopolis are the result of the application of recursive geometric rules, which results in the fact that the spatial configurations thus created are statistically self-similar. MUP-City and Fractalopolis integrate a scale dependence relative to the shape of urban developments: an undeveloped space at a macroscopic or mesoscopic level cannot be built at a microscopic level. MUP-City and Fractalopolis thus preserve, at a fine spatial resolution, the undeveloped spaces identified at a coarser spatial resolution. With MUP-City, the new simulated residential developments are in the form of square cells, the size of which can be chosen (20 m sides in most applications made so far). The location of cells worth urbanizing is determined by a fractal rule of urbanization, based on a multi-scale decomposition of the existing built pattern (Figure 3.12). In addition to choosing a fractal dimension for the simulated residential developments (corresponding to the variable Nmax in Figure 3.12), the fractal urbanization rule requires that cells not urbanized at decomposition level i1 cannot be urbanized at a finer decomposition level i2.

Figure 3.12. Example of application of the MUP-City fractal urbanization rule for Nmax equal to 5, i.e. a fractal dimension equal to 1.46. Source: Tannier et al. (2012)

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Figure 3.12 shows that some grid squares have more urbanized cells than should be present in a statistically self-similar object. This is due to the fact that the initial built pattern is not organized according to a simple fractal logic with a reduction factor r equal to 3. In order to bring simulated residential developments closer to statistical self-similarity, a “strict” variant of the fractal urbanization rule has been introduced in MUP-City (Figure 3.13).

Figure 3.13. Strict variant of the fractal urbanization rule for Nmax equal to 5, i.e. a fractal dimension equal to 1.46. Source: Tannier (2017)

MUP-City can be used to simulate very diverse forms of residential development (Figure 3.14). The simulated developments correspond to a densification of existing built patterns, by increasing their local fractal dimension and/or by creating new morphologically self-similar residential extensions. It should be noted that these extensions result in an increase in the length of the urbanized border. It is also noted that simulating a fractal residential development provides visually realistic forms of residential development at a local level. When the fractal dimension is close to 1.5, the built patterns are characterized by a great diversity of sizes of the built clusters and distances between these clusters. Conversely, with a fractal dimension close to 2, buildings are either uniformly concentrated or uniformly dispersed.

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Figure 3.14. Two examples of results obtained with MUP-City in Besançon’s urban region. Nmax is equal to 5, i.e. a fractal dimension equal to 1.46. Source: M. Colomb et al. (2017). For a color version of this figure, see www.iste.co.uk/pumain/geographical.zip

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In Fractalopolis, the creation of a multi-fractal development plan follows an iterative logic based on the definition and application of an iterated function system (IFS) (Barnsley 1988). Two types of areas are distinguished: those favorable to urban development (called “planned development centers”) and those in which only little or no development is envisaged. The initiator of a development plan designed with Fractalopolis is a square of size L positioned on the study area. The plan generator generally contains a central square of selected size S1 = r1 L, placed on the main urban center, and N squares of smaller size S0 = r0 L placed on the secondary development centers (Figure 3.15). The number of secondary centers, the value of parameters r0 and r1, and the number of functional levels (usually three or four, corresponding to the number of iterations for which IFS is applied) are specifically defined for each case study. Then, the IFS chosen to create a multi-fractal development plan is iteratively applied until the smallest squares have approximately the size of the neighborhoods. At this iteration stage, the length of their sides varies between approximately 500 and 300 m. A development plan built on this basis is called multi-fractal because the generator of the plan has several reduction factors r (Mandelbrot 1982).

Figure 3.15. IFS generator chosen for a multi-fractal development plan for Besançon’s metropolitan area (Eastern France). Grey: non-urbanizable areas. Red points: public transport stations. Source: Frankhauser et al. (2018). For a color version of this figure, see www.iste.co.uk/pumain/geographical.zip

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Figure 3.16. A multi-fractal development plan for Besançon’s metropolitan area (Eastern France). For a color version of this figure, see www.iste.co.uk/pumain/geographical.zip

At each iteration, the number of development centers increases according to a multiplicative factor determined by the generator. This recalls the logic of Christaller’s (1933) central place model. Due to the presence of two reduction factors in the generator, the surface area of each center depends on its relative position, i.e. its distance from the higher level centers. As a result, the area of centers of different hierarchical levels may be identical, while the area of centers of the same hierarchical level may be different (Figure 3.16). In this way, the model differs from the Christaller central place model but corresponds to the empirical observation that centers of the same functional level are larger when located near a major urban center and smaller when located in sparsely populated areas.

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3.4. Conclusion When, to model a given phenomenon, several levels of aggregation or a series of nested spatial resolutions are taken into account, the modeling is multi-scale. Scale dependence is then considered as an observable outcome. When representing variations in the phenomenon across aggregation levels or spatial resolutions, modeling is trans-scale and scale dependence is considered as a generative process of simulated socio-spatial configurations. Adopting a multi- or trans-scale approach makes it possible to explicitly account for spatial hierarchies (e.g. the fact that an urban region has a large number of small built clusters, a smaller number of medium-sized clusters, and an even smaller number of large clusters) and functional hierarchies (e.g. different levels of functional centrality). In geographical models of cities or regions, the effects of distance influence the location (position and situation) of entities and their changes in location (migration trajectories and flows). When the modeled entities are places, the interactions between these places determine both the interest of each place for each type of settlement or activity and the interest of changes in the location of settlements or activity. When the modeled entities are individuals or groups of individuals, they interact via spatial neighborhoods. In SimFeodal, for example, interactions between peasant households and lords are carried out via the taxing areas: for a lord, the arrival and departure of peasant households in the territory he controls modifies his power and, thus, the possibility that he can build a castle. In MobiSim-MR, the residential environment of each household includes other households, businesses, services, recreational facilities, and so on. This makes it possible to represent an interaction between households, via their environment. Different authors distinguish between weak emergence, where macroscopic structures can be observed from the outside as a result of microscopic processes, and strong emergence, where the dynamics of microscopic levels adapt in return to the macroscopic level structures they have generated and observe from the inside (Livet et al. 2010). Indeed, social systems are characterized by intense and constant interactions between the individual representations and behaviors of agents and the collective references of the group or groups to which they belong. Collective references refer to beliefs, convictions, or representations common to each member of a social group. They govern social play, help to guide individual behaviors, and ensure the compatibility of all individual behaviors in a given context. By belonging or not to a social group or place, each individual

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participates in the construction of collective references that refer to them (weak emergence). In return, the adoption or not of these collective references influences their behavior (strong emergence) (Tannier et al. 2017a). In the SimFeodal and MobiSim-MR models, the evolution of concentrations and dispersions of settlements over time create and are created by the movements of agents in physical and social spaces (changes in social and/or spatial position). In SimFeodal, peasant households that have been selected to change location “observe” the attractiveness of the different attraction centers (locally or throughout the modeled space depending on whether their movement is local or distant) to choose their new location. This “observation” is formally represented in the model by the introduction, in the random draw used to determine the new location of a peasant household, of a weighting of the probability of selecting each center by its relative attractiveness. Because peasant households “observe” the macroscopic configuration of the attractivenesses of the different centers, the SimFeodal model simulates a strong emergence. MobiSim-MR also simulates a strong emergence because each household “knows” the median value of the attractiveness of all dwellings for all households at the initialization of the model and, in relation to this, it positions its own median value of the attractiveness of known dwellings. The MobiSim-DR model does not include social entities. Housing units and buildings are purely spatial entities: they do not adapt their behavior according to the spatial or socio-spatial configurations observed at a macroor meso-geographic level because only social entities can “observe” emerging spatial or social configurations. However, the meso-geographic spatial configuration, i.e. the buildings present in each built cluster, constrains the location of the new buildings created. The MobiSim-DR model, therefore, simulates a weak emergence. The other three models discussed in this chapter are MUP-City and Fractalopolis, both based on an explicit spatial-scale dependence principle, and ArtiScales, the nature of which is multi-scale and not scale-dependent. As these three models do not integrate temporal dynamics, they do not possess the emergence property per se.

4 Incremental Territorial Modeling

Cities and territories are complex entities which geography approaches at a mesoscopic scale, between the levels of social individuals and regional or continental groups. Therefore, cities and territories are considered both as products emerging from local social interactions and as “collective agents” supporting higher-level interactions, such as interurban interactions. For instance, while such interactions originally stem from individual choices, they are organized according to the aggregated and emerging properties of cities. This duality (in the representation of territories and the representation of their interactions) matters in the dynamic modeling of cities1 and geographical territories. A central question is, therefore, how to represent cities and territories in the models. Symbolic representation options (e.g. distribution of densities, functions, size, and mesh size) are at the heart of the geographical discipline, yet there has been little thought given to this question in the history of modeling. The relative lack of discussion about the representation of territories in geographical models is likely due to the appropriation of theories, methods, and models from other disciplines whose focus was not the territory. In this chapter, we seek to illustrate the importance of territorial representation by referring to a substrate closer to the discipline: cartographic modeling. Indeed, the choices of representation in maps, familiar to geographers, can constitute a first guide for territorial modeling.                                         Chapter written by Clémentine COTTINEAU, Paul CHAPRON, Marion LE TEXIER and Sébastien REY-COYREHOURCQ. 1 Dynamic modeling refers here to all models that produce a temporal evolution, such as differential equations or dynamic simulation, as opposed to statistical and static models, for instance.

Geographical Modeling: Cities and Territories, First Edition. Edited by Denise Pumain. © ISTE Ltd 2019. Published by ISTE Ltd and John Wiley & Sons, Inc.

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A second challenge is to produce models that adequately represent the urban and territorial dynamics themselves: local evolutions or territorial stylized facts. For example, some models simulate the evolution of land use in specific cities (Chaudhuri and Clarke 2013), while others attempt to reproduce the emergence of segregation in general (Schelling 1969) or the hierarchical evolution of a generic city system (Reuillon et al. 2015; Sanders et al. 1997). These two modeling perspectives lead to important differences in the genericity of the resulting model, its explanatory power, its reapplicability, and its level of detail. In this sense, a reflection on the situated and partial status of the explanation in the field of geography can help modelers build models and evaluation protocols, which are adapted to the simulation objective and the target territory. The aim of this chapter is to present the main issues with embedding territorial representation and territorial dynamics in simulation models. First, we depict current scientific practices and illustrate them with select model examples. Second, we propose a singular and reproducible modeling strategy, which aims specifically at describing a territorial system and its evolution. This strategy relies on multi-modeling or incremental modeling. This chapter ends with a presentation of the limits and opportunities of this approach, with a discussion of its applicability and interest to different case studies. 4.1. The map and the territory “Models are, by definition, a simplification of some reality which involves distilling the essence of that reality to some lesser representation” (Batty and Torrens 2001, p. 28). 4.1.1. Modeling as one map: selection and schematization The geographer’s emblem – the map – being a “simplified and conventional representation of all or part of the earth’s surface” (Joly 1976), is already a model of territory and territorial organization. Cartographic theory and graphic modeling can, therefore, provide insights into the representation of cities and territories in dynamic models of geographical space. A map is a model because it is impossible to represent all the detailed elements of a territory on it unless the map is at the 1:1 scale. In every other

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case, the cartographer has to generalize the information by reducing the quantity of this information to be represented on the map (selection) and by simplifying the qualitative information with respect to the objective of the map (schematization). “Generalization [...] applies both to the creation of the base map and to the processing of information. Generalization simultaneously combines selection, schematization and harmonization, the respective roles of which vary according to the type of map (topographic map, thematic map), the purpose of the map (dissemination map, scientific map, didactic map) and the scale of publication (format) which conditions the entire process” (Béguin and Pumain 2017, p. 27). In practice, the cartographic selection process consists of choosing which elements to represent and which ones to omit. Taking a road map as an example, the layout of roads and the location of tolls and cities are generally sufficient, whereas geological, agronomic, or meteorological elements are not selected, as this information is not relevant in the usual context of road map use. In the context of the dynamic modeling of a territory or city, the selection operation corresponds to the identification by the modeler of the essential elements and agents involved in the phenomenon under study. The model can be made more complex during the research, but it always remains schematic compared to reality. It is, therefore, a matter of prioritizing the elements most relevant to the research question; if not, the model might not be able to provide adequate answers. To guide the selection operation, the literature distinguishes between two standard approaches. The first one is the well-known principle of parsimony (or Ockham’s razor principle): the simplest model that reproduces the target dynamics is always preferred. The opposite approach consists of representing in more realistic detail the territorial system studied and its hypothesized mechanisms. Depending on the modeling objectives (and the methodological bias of the modeler), the compromise can favor one approach or the other. The comparison between the SIR model2, in its most traditional version, and the MicMac model (Banos et al. 2017) illustrates this point. Each of these models aims to simulate the spread of an epidemic within a population. In the first case, this population is divided into                                         2 SIR is a classical epidemiological model of disease spreading, which considers three possible states for social agents: susceptible, infected, and recovered.

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compartments (Susceptible, Infected, and Recovered agents) linked by a series of differential equations describing the transition rates from one group to another. This mathematical model allows us to examine the effect of contamination and to predict the number of agents belonging to each of the three groups over time. It is an aggregated model (the general population is subdivided into three groups, whose characteristics are studied without explicitly describing the individuals who compose them) and an a-spatial model (the location of individuals and groups is not modeled). The analytical resolution of the classical SIR model based on differential equations requires a continuous representation of time. In the MicMac model, the rules of the general epidemiological model are still defined according to an aggregated SIR model, but MicMac additionally describes the mobility of some individuals responsible for the spread in a disaggregated way, i.e. by spatializing agents. Mobility is defined on a longdistance range between cities, whereas for each city, an SIR model simulates the number of individuals infected, susceptible to be infected or recovered from infection at a given time. The relative proximity between cities is represented by a graph (whose links are airways and nodes are cities), whose topology and size can be modified. The model is solved numerically by simulation, using discrete time steps, i.e. the state of the population is computed at each step (interval) of time. Other models go even further in the level of detail required for simulating the spreading of an epidemic. This is the case, for example, with the MOMA model (Model Of Mosquito Aedes aegypti, Maneerat and Daudé 2017), which represents the biological and behavioral characteristics of the vectors of dengue fever, yellow fever, chikungunya, and Zika virus: the Aedes aegypti mosquitoes. This agentbased model is defined at the micro-geographic level: that of the environment perceived by the mosquito in movement. The behavior of mosquito agents depends on their own attributes as well as on the attributes of the environment, whereby local geographical patterns (e.g. the presence of ponds) influence mosquito dispersal. It should be noted that despite a relatively high level of detail, this model remains generic since it is transferable from one geographical context to another. The cartographic simplification operation consists of schematizing the layout or symbolic representation of certain elements as one changes scale or adds more information to the map. On a map of Norway, for instance, at a large scale, the coastline will be complex and fjord outlines may appear. At the European scale, however, Norway is usually generalized and its boundaries are sketched with about a hundred more or less straight segments. In the same vein, territorial modeling schematizes and simplifies

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the dynamics and representation of these objects. For example, “as the crow flies” distance is often used in neighborhood perception and transport cost assessment operations, even though it is recognized that large-scale human travel rarely conforms to Euclidean distances. Similarly, “as the crow flies” distances are often calculated between centroids of geographical units rather than between barycenters of the population in spatial interaction models (Wilson 1971), which is considered a minor difference that simplifies modeling and computation. The main difficulty for the modeler is to know when this schematization can be considered neutral with regard to the functioning of the model and its objectives and when it does not, even though it simplifies the calculations and the time management of the simulation. This problem, called the “representativeness of hypotheses according to objectives”, is difficult to assess in general terms (ReyCoyrehourcq 2015; Varenne 2013), especially since there is a tendency toward pluriformization in current modeling practice, i.e. the hybridization of formalisms (differential equations and agent-based models, for example) within the same model. Dynamic territorial models developed in geography, therefore, often differ from visual and procedural modeling methods that aim, among other things, at reconstructing urban landscapes from laser imaging and scanning (Musialski et al. 2013) or generating urban spaces of realistic shape and appearance using generative grammar (Parish and Müller 2001). These approaches, mainly oriented toward applications in cinema or video games, could nevertheless constitute an important development in geography and planning. The UrbanSim model (Waddell 2002) is perhaps most illustrative of this trend. In its most recent version, UrbanSim offers a 3D visualization platform that has the stated objective of facilitating the understanding of territorial dynamics by policy makers and the public. More recently, C. Slager and B. de Vries (2013) proposed a tool for the automated generation of spatial configurations with a high level of detail and realism for the evaluation of urban development projects, while SimPLU3D (Brasebin 2014) is aimed at simulating realistic residential built forms through the formalization of local urban planning regulations. The latter models of territorial dynamics are based on intangible information (projections, planning, and regulations), which require ad hoc modeling, and cannot be carried out by simply selecting or mapping available data. More generally, for a territorial model to work, its spatial components must be modeled, formalized, and then used as inputs to the model before the model dynamic processes can be simulated.

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4.1.2. The representation of territory as an input of the model Geographical models feature elements to represent territories that are more or less numerous and more or less schematic. Historically, models in urban geography modeling took inspiration from other disciplines. This has affected the way cities and territories are represented in models ever since. In particular, urban models have benefited from many ramifications of the “systemic project” (Pouvreau 2013; Rey-Coyrehourcq 2015; Varenne 2017). For example, physics and chemistry from the 1970s had a particularly strong influence on French urban geography: “with, on the one hand, Allen’s work within the theoretical framework of Prigogine’s dissipative structures, and on the other hand, that of Weidlich and Haag (1983) within the framework of the synergetics developed by Haken (1983), and finally that of Wilson (2000) who offered a theoretical basis based on the concept of entropy to the classical models of spatial interactions” (Sanders 2013, p. 834). Because of this disciplinary legacy, “although the ‘cybernetic’ phase of the systemic project [has] made it possible to shift the focus from the entities to their interactions, and to clearly differentiate between the simple measurement of evolutions (a kinetics) and dynamics themselves (including an interpretation of the factors controlling this evolution)” (Pumain 2013, p. 13), early models of urban geography3 have tended to over-represent stock characteristics of territories (e.g. population and the numbers of jobs) in a fictional and abstract space. These early models also tended to underrepresent the strictly territorial characteristics, reducing cities to interconnected points and the space between them to a uniform Euclidean field. The points were generally connected by flows that depended on the geometric distance between the points, and it was often not even necessary to represent space at all in the model, the coordinates of city-points being sufficient to calculate the distances and, therefore, the flows. This legacy has fostered the development of geographical models in which geographical space is isotropic and uniform, unlike its empirical equivalent. As a matter of fact, most of the scientific corpus of human geography aims to highlight the heterogeneous distribution of human activities and the “roughness” of the space, which supports them.                                         3 In Lowry’s or Forrester’s models, for example.

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The reintroduction of explicit geographical structures into dynamic models is, therefore, an important issue for territorial modeling, both because it is part of the geographer–modeler’s job description and because, as a framework and support for agent interactions, such geographical structures and variations at the initialization of the model have an influence on the simulated outputs. For example, A. Banos (2012) reveals the effect of the shape and structure of the urban network on the extent of spatial segregation obtained in the Schelling model, at constant parameter values. J. Raimbault et al. (2019) reach similar conclusions when varying the initial distribution of residential density on which the Schelling model is simulated. The challenge of this geographical structure integration also extends to the way the phenomena at work on these structures is observed: I. Thomas et al. (2017) show, for example, how the choice of boundaries and scale of the system represented in LUTI models can affect the results obtained, while M. Le Texier and G. Caruso (2017) reveal the impact of aggregation levels on the dynamics of the diffusion of Euro coins. In addition to the model sensitivity to initial spatial conditions, i.e. to the representation of the territory supporting the modeled interactions as a fullyfledged input to the simulation process, the degree of abstraction of the empirical fact to represent also changes the requirements of territorial models. A. Banos and L. Sanders (2013) identify two main dimensions that differentiate a dynamic model: a dimension of abstraction and, orthogonally to it in a 2D plane, a dimension of parsimony. The parsimony dimension, generally reduced to the opposition between KISS4 and KIDS5 models introduced by B. Edmonds and S. Moss (2004), contrasts parsimonious models (such as Schelling’s model6) to more complicated and complete models (such as MATSIM7). One end of the spectrum aims at understanding and schematically explaining fundamental processes, while the other end tends to favor realistic representations of systems and the prediction of future or alternative outcomes given the variations of certain conditions (scenario                                         4 Keep it Simple, Stupid! 5 Keep it Descriptive, Stupid! 6 The Schelling model is a classic and very parsimonious multi-agent model of urban segregation. It has two mechanisms: 1) the agent assesses their satisfaction with the composition of their neighborhood and 2) they move to a new location if their minimum satisfaction rate is not reached where they currently reside. 7 In MATSIM, the city is represented with dwellings of different sizes and rents, commercial premises with variable lease levels, transport networks described by their geographical location, bus schedules, individuals with different time budgets, and many other attributes.

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approach). The orthogonal dimension of Banos and Sanders – see Chapter 2 – contrasts general and abstract models (e.g. models of segregation) to particular models (e.g. models of the distribution of social groups in the Paris area in the 2000s). As a matter of fact, the abstraction of processes does not necessarily imply the abstraction of territory, as shown by the application of the Schelling model to the city of Yaffo, whose digitized building footprints were characterized by a realistic distribution of the population by religion (Benenson et al. 2009). By contrast, complete models can be applied to stylized spaces. An example of this practice is the application of the new geographical economy to linear cities or two-region world models (Fujita et al. 1999). Finally, the representation of cities and territories as inputs of a model can be hybrid. Instead of representing all the elements of a given geographical level in the same way, the modeler can choose to vary the representation level according to the distance to the agent or object whose action is simulated. For example, in a model of trade between countries, the use of a “rest of the world” category along with single-country partners may correspond to this hybrid strategy. For computational reasons, A. Hagen-Zanker and Y. Jin (2012) have offered a similar strategy: their spatial interaction model implements adaptive zoning. The areas far away from the considered area are aggregated into groups that are larger the further away they are, in order to produce flows of comparable size to that of the flows between nearby areas. Such an adaptive zoning is probably more appropriate to represent human geographical perception than the uniform mesh sizes generally used in territorial models. It thus constitutes an interesting avenue for research from a conceptual as well as a computational point of view. 4.1.3. The representation of territory as an output of the model Although territorial modeling generally targets fidelity to the represented city or territory, the simulation of territorial dynamics can be based on objects and concepts which do not exist or cannot be assessed in reality, but which serve as “stepping stones” to explain observed processes. In other words, the model can be used to explore the possible dynamics leading to configurations empirically observed, using the register of explanation by way of analogy (Workman 1964). The objects and dynamics selected by the modeler to feature in a model must be integrated into the reflection as an attempt to reconstruct a complex reality whose entire functioning cannot be observed. This bias being acknowledged, it is more important to focus on the

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coherence of this selection and its possible effects on the model outcomes rather than on the realism of an element in itself. In other words, it should not be forgotten that we are operating on an electronic substrate (the simulator) where the meaning and dynamics of the selected elements have very little to do with the complexity of their functioning in reality (Bulle 2005). Such assessments must be tested (by sensitivity analysis) to be confirmed. However, whatever the realism of the dynamics modeled from the input territory, and whatever its status (empirical territory at a past date, abstract space, and originally undifferentiated territory), the output territory produced by the model is assessed with regard to its ability to satisfy some requirements defined as ex-ante (or by iteration) by the modeler. These requirements can be of two kinds. On the one hand, the objective of the model can be to reproduce a trajectory that has been observed empirically. In this case, it is necessary to define the selection of elements to be simulated and what a “good simulation” is in terms of deviation from this empirical situation. In the case of MATSIM transport models, for instance, the configuration to generate is the distribution of daily mobility flows, by means of the organization of their activity schedules and locations. The share of poorly estimated flows and maximum delays is used to distinguish between “good” and “bad” simulations. In the case of the Anasazi model, the configuration to generate is the extinction of the settlement (Dean et al. 2000). The generation of the observed trajectory is necessary although not sufficient to validate the model (Amblard et al. 2006; Hermann 1967; Rey-Coyrehourcq 2015). On the other hand, the objective of the model may be, rather than to simulate an empirical trajectory, to generate one or more “stylized fact(s)”. Since N. Khaldor (1961), the typical regularities of a domain have been referred to as stylized facts. Without being scientific laws, these stylized facts can be compared to the generalizations or empirical laws of the classical scientific approach (Harvey 1969). An example of a stylized fact in the geography of cities is the hierarchical distribution of their size, and more precisely according to a power function of exponent a ≈ 1 of their rank, the rank being the position of cities in the list of populations by decreasing order (Zipf 1949). The interpretation (Sanders 2012) and the expected value of the parameters of this power function vary according to disciplines, territories, time periods, and ways of estimating it (Rosen and Resnick 1980) but the general aspect of the distribution and the regularity of the hierarchy persist. This is why some models take the generation of this stylized fact as an indication of a successful simulation (Cottineau 2017). In this case, even if

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the modeled cities have some economic, social, and technical attributes that can be used to reflect the simulated configuration, the characteristic selected to qualify the model output is reduced to the distribution of their size (Sanders et al. 1997). It is in this sense that the territory represented as an output of the model can diverge from the territory represented as an input of the model, and from the territory used by the model and transformed by the modeled dynamics. The territory represented as an output is thus only a subset of this intermediate territory modified by the model (Figure 4.1).

Figure 4.1. Different representations of the territory during the modeling process

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The question of identifying stylized facts and their importance in the construction and evaluation of models is not limited to geography. Ecologists, for example, are among the pioneers in developing methods and tools to expose the process of model building and evaluation. On the descriptive level, the ODD formalism8 (Grimm et al. 2010) is now widely used to support models in interdisciplinary publications. Even more to the point of model validation, ecologists rely on the POM methodology9 (Grimm et al. 2005) and the notion of patterns (or stylized facts) to qualify “good” models according to their ability to exhibit several stylized facts simultaneously. This method suggests using observed patterns as filters to compare and evaluate different model structures. In this sense, V. Grimm and U. Berger (2016a) speak of a modeling logic aimed at structural realism10, which is different from a search for reality. Models that generate the greatest number of patterns simultaneously are considered better in this framework. The POM approach is intended for models that simulate stylized facts, and whose expectations are numerous and detailed. This specification of expectations through a patterns protocol allows us to both reintegrate and assess hypotheses in an incremental and nonlinear model-building process. The path dependency inherent to model building is thus questioned (Augusiak et al. 2014; Grimm and Berger 2016b), but the methodology allows us to filter the “good” models more efficiently. Indeed, if several relevant processes can generate a single given stylized fact, exhibiting simultaneously several distinct stylized facts is a criterion that greatly reduces the number of model candidates. The number of simple relevant processes that can generate such a configuration is probably finite and decreases with the number of independent stylized facts considered. Overall, we see that the formalism, structure, and explanatory dimension of a model depend on the modeled issue and the purpose of the research. However, the status of geography as a historical science brings additional aspects to the discussion of the general and the particular, which we now discuss in section 4.2. A model is not so much what is being sought as such, but what facilitates the search for information about a real or fictional system, as part of a process of representation, knowledge, conceptualization,                                         8 Overview, design concepts, and details. 9 Pattern-oriented modeling. 10 The aim is to try, through a set of good practices, to capture as best as possible the actual functioning of a system and to establish testable predictions, which also implies being able to measure the difference between this capture and reality. The term also refers to the previous discussion about internal coherence (Bulle 2005).

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design or transformation (Varenne 2008). This is an idea that has been around for a long time among modeling geographers (Sanders 2000), for whom the content of a model is what counts when it comes to explanation. 4.2. Generality and geographical models

specificity:

explaining

by

ways

of

Although there is a variety of reasons to model social systems, including learning, communicating, and formalizing hypotheses (Varenne 2013), the main reason is to explain the modeled phenomenon (Epstein 2008). “Literally, to explain (‘expliquer’ in French) is to get out (‘ex’) of your folds (‘plis’) and to formulate hypotheses is to propose “a way of unfolding” (‘déplier’ in French). But to propose a way of unfolding is to situate oneself within a constructed world, the geographical world, and to use a language as unambiguously as possible so that the unfolding process is coherent” (Raffestin 1976, pp. 85–86). C. Raffestin considers the quantitative revolution in geography as a way of specifying the chosen way of unfolding, thus making the geographical explanation falsifiable and predictive. Moreover, with the incorporation of the principles of cybernetics, and the theory of self-organization and complexity, the relationship to the diversity of territories, as well as its origin, changed (Pumain 2003). Explaining by ways of territorial modeling thus embeds the notions of historical contingency and non-ergodicity (section 4.2.1) and makes the distinction between general, specific, and singular trajectories (section 4.2.2). 4.2.1. Historical contingency and non-ergodicity Any scientific explanation should produce falsifiable statements and predictions. In social sciences, the generic and predictive nature of theories and explanations is sometimes challenged on the grounds that general laws cannot apply to human behavior nor to its collective expression in space and time. In geography, because of the multivariate nature of the disciplinary objects, explanation must account not only for the phenomena under study (urbanization, the demographic transition, etc.) but also for their variation of expression over time and space. Explanation is, therefore, often multifaceted,

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combining systemic, ecological, functional, and causal analysis (Harvey 1969). “Even if they result in distinct geographical configurations, spatial frames are organized by temporal processes which reproduce or maintain the stability of this structure in its various components. The explanation of the durability of a combination lies not so much in the strength of the associations which bind its components together, but in the subtlety of the evolving principles by which the structure, incrementally and continuously, and in all its components, adapts to change and sometimes also helps to bring it about. Therefore, very quickly, this theoretical quest implied knowing how to move from the observation of regularities to the analysis of processes, from the identification of ‘combinations’ or structures, to the study of the change likely to produce and transform them” (Pumain 2003, pp. 7–8). Assumptions about the irreversibility of time and the unpredictability of the future underlie the non-ergodic property of territorial models (Pumain 2010b). This property implies that all possible states for all cities [and all territories] are [not] accessible to each of them (Pumain 2010b, p. 60), due to the evolving processes of diffusion and specialization, which guide territories along “paths” of evolution rather than toward a predictable end state. For example, observing cities of different sizes at a given time is not equivalent to observing a typical city during its historical growth path. By adopting the paradigm of synergetics and complexity, i.e. a modeling universe where the same equations are capable of generating a very broad diversity of forms and evolutions (Pumain 2005, p. 15), the contingency of observed patterns corresponds no longer to the historical contingency that produces the complete trajectory of a territory through a succession of singular events, but rather to a contingency that directs the system toward one or another of its possible trajectories, at the whim of bifurcations, and that a complex model allows to explore. “The theory of self-organization makes us understand how identical general processes are likely to produce different effects and structures, depending on the initial conditions and values of the parameters which control interactions and their evolution” (Pumain 2003, pp. 16–17).

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The complexity paradigm, therefore, invites us to rethink the distinction between general, specific, and singular trajectories (Durand-Dastès 1991), as well as the situated or partial nature of models that apply only to a single case study or predict only one type of outcome. The diversity of the results produced by a territorial model when varying its initial conditions and parameter values slightly allows us to reinforce the extent of its applicability when the results correspond to known empirical situations and to provide information on possible futures not yet realized, as well as to identify situations of falsification of the theory. “It is of course important to ensure that a model is able to reproduce the patterns it is designed to explain. And it is equally important, following Popper’s argument, to look for simulations that may have the power to falsify the model, those which display an association of input values and output patterns which contradicts data” (Chérel et al. 2015, p. 1). Without rejecting Popper-Hempel’s Hypothetico-Deductive (HD) and Nomologico Deductive (ND) models as a whole, as Passeron (1991) did for sociology, geographers prefer to rely on a multiplicity of knowledge, building regimes to enhance the toolset and methods of the so-called “qualitative” and “quantitative” work (Pumain 2005; Rey-Coyrehourcq 2015; Sanders 2000; Varenne 2014). In other words, deductive reasoning would by no means be the only way to produce scientific reasoning. For example, J.-M. Besse (2000) proposes to value abductive logic11 allowing a “progression of meaning” and a “progression in elucidation,” which leaves room to interpret the cognitive aspects in the course of reasoning when it comes to keeping or rejecting a hypothesis: “As such, much of science’s task would not primarily consist of seeking deductive causes and sequences, but in organizing points of view and frames representing the situations it aims to                                         11 For S. Catellin (2004): The starting point of abduction is a fact perceived as surprising, which is therefore against expectations, against habit, or against what was previously taken for granted. Abduction consists in selecting a hypothesis A likely to explain fact C, so that if A is true, C is explained as a normal fact. In other words, abduction is a normalization procedure of a surprising fact. It is an effort of reasoning that is undertaken when there is a rupture in our system of expectations, an “imaginative” reasoning that uses our knowledge. Abduction is part of a process logic and not a calculation logic, it refers to a context and a culture, to a social habitus. Other definitions of abduction and their relationship to modeling are discussed by S. Rey-Coyrehourcq (2015).

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account for. In other words, before seeking to explain and demonstrate successions of causes and effects, science is concerned with illuminating situations by abductively making meaningful connections. Science does not only seek to demonstrate, but also to enlighten” (Besse 2000). This logic is explained and operationalized for the modeling practices of geographers (e.g. see Banos 2013). 4.2.2. General/specific/singular The opposition between general and particular features or trajectories is at the root of scientific theory building since theories aim to account for particular cases by linking them to a general “law” through the explanation process. However, in the field of social sciences, but also of “historical” sciences to which even geology could belong (Harvey 1969), the distinction made by A. Bouvier (2011) between the individual and the singular (or unique) is essential. Indeed, while the general case derives from the standard application of the model in the abstract case, it can only be compared to particular cases of empirical reality. These particular cases may exhibit characteristics deriving from the general model, i.e. shared characteristics based on the presence of common attributes (e.g. capital cities share a common particular attribute and tend to be larger than the average city in a given country). The singular case escapes generalization (Sanders 2013, p. 12) and requires the use of historical explanation to understand its evolution (for example, Vienna is bigger than other Austrian cities but we need some knowledge about the Austro-Hungarian Empire to understand why). This distinction between general, particular, and singular is interesting when approaching the modeling of cities and territories because it allows us to compare the results of a model with particular geographical configurations, observable and measurable on empirical data, but also to highlight the singularities of some trajectories at the end of an iterative process of model complexification. While the empirical analysis of particular cases aims to increase in generality by the identification or classification of common categories, the complexification approach reflects the opposite path: a “descent from generality”. At the end of this path, the residual trajectories, which the model cannot predict, are deemed singular. Hence, the model as well as the methodology of its construction can facilitate the explanation of a geographical phenomenon in general (for

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example, the differentiation of city sizes in a country), in particular (the evolution of city sizes in a socialist country, in a developing country, etc.) and in “singular” (the contemporary Chinese evolution). In section 4.3, we present an incremental and modular approach to model building, based on the MARIUS modeling experience. We detail the steps and issues involved in this construction. 4.3. Incremental territorial modeling “Traditional models get the present right and are then used to predict the future. In contrast, [...] simulation enables [complex systems models] to generate different outcomes, which under some circumstances might appear to be different futures but really define a space of different model outcomes. The way this space is generated is not simply through systematic variations in parameter values, which is the time honored methods of model calibration in the case of traditional models, but through varying the model structures within some limits, that is usually varying the rules that encode different processes into the model, thus simulating different experiments within a kind of virtual laboratory” (Batty and Torrens 2001, p. 32). In the spirit of this programmatic quotation, the method we present aims to separate the explanation of the geographical pattern under study into more or less independent mechanisms, which are more or less general or specific to the geographical object being modeled in order to combine them into a single, modular model. This model is evaluated both in terms of the empirical geographical configuration it has to simulate and in terms of how well it matches with more general stylized facts about the object under study. The methodological question raised by this incremental approach is the following: how can we build “realistic” models with regard to empirical data and stylized facts, which integrate successively (and simultaneously) a richer information on their processes and on the diversity of their geographical expression? We propose a six-step approach. First, we consider the identification of the scale of analysis, of the configuration to simulate, and of the stylized facts (section 4.3.1). Subsequently, we address the question of collecting and categorizing the various existing explanations (section 4.3.2) and then prioritizing them with respect to the generality of their explanatory power

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(sections 4.3.3 and 4.3.4). Finally, we describe how models are implemented in a modular manner (section 4.3.5), combined, simulated, and compared with the empirical data and stylized facts prepared for their evaluation (section 4.3.6). 4.3.1. Identifying the object, scale, configuration, and stylized facts The first step in incremental territorial modeling consists of defining the research question and identifying the objects, the geographical scale, and the target evolution to be depicted by the model. There are a multitude of territorial models because there are an infinite number of geographical questions. For example, there are pedestrian flow models, oriented toward emergency evacuation analysis (Zheng et al. 2009), which are different from the pedestrian models aimed toward the optimization of dense areas such as stations (Hoy et al. 2016). Other pedestrian models focus on the emergence of urban riots, with particular applications in London in the United Kingdom (Davies et al. 2013) or Kibera in Kenya (Pires and Crooks 2017). The resulting models are sometimes similar, often incompatible, and always contingent on the research team producing them. We therefore suggest, in addition to the documentation of ODD models (Grimm et al. 2010) allowing their communication, diffusion, and potential reuse by others, that modelers make an extensive modelography (Schmitt and Pumain 2013) of existing theoretical and applied models before they start building yet another model (O’Sullivan et al. 2016). The re-use of models cannot generally be direct, as each model answers a specific research question. The rather uncommon practice of model docking is interesting in this respect (Wilensky and Rand 2007) because it consists of realigning models developed with different objectives by showing that they can produce, and therefore partly explain, similar patterns. The practice of reuse with modifications, which is certainly demanding because of the reproducibility efforts it involves (Grimm et al. 2010, 2014; Rey-Coyrehourcq et al. 2017), should be much more frequent than it is now because it fosters the accumulation of knowledge (Pumain 2005, 2009; Rey-Coyrehourcq 2015). Once the object of the model has been identified, it is necessary to decide whether the model is expected to simulate a singular empirical configuration, a particularity of this configuration, or the general underlying process expressed through the geographical configuration. A two-fold ambition may be to build a model that is capable of reproducing both the particular

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configuration that motivated its development as well as the empirical variations of the phenomenon, thus demonstrating its general explanatory power. In this case, the objectives for evaluating the model have to identify both requirements and to characterize their level of generality/particularity, for example by distinguishing between general objectives (“obtaining a distribution of city sizes according to a power law”), particular objectives (“obtaining a concave distribution for socialist countries”), and singular objectives (“reproducing the distribution of the former USSR at a particular date”). This definition/explanation of patterns is essential in the search of the mechanisms to be modeled as well as for conducting a rigorous and reproducible evaluation, especially for a POM type of evaluation. 4.3.2. Gathering the different theoretical explanations In concrete terms, the search for explanations of the targeted phenomenon and their modeling can also start from the object studied and the existing models and theories reported in the literature (may it be about urban riots, the risk of marine flooding or social segregation, etc.) but also from the geographical scale of this object or from the type of evolution at stake. In the case of the approach that starts from scales, the review of existing models at a given scale (e.g. the city, the agricultural plot, or the globe) allows us to explore processes and themes that are not considered directly but which may have an effect on the pattern to be simulated and play a role in the explanation. In the case of the approach by types of evolution, a comparison between models from different disciplines can be fruitful. For example, the process of size hierarchization of interacting elements is generated by stochastic dynamics in mathematics, preferential attachment dynamics in network physics, or by increasing returns in economics. These different approaches can serve as competing and complementary model candidates to explain the demographic differentiation between cities, companies, or archeological settlements (Pumain 2006; Sanders 2012). The “cartography” of competing and complementary explanations is not new or necessarily related to territorial modeling: the pioneers of dynamic modeling in the 1960s (Hermann 1967; Levins 1996) already considered a diversity of mechanisms and the advantage of dynamic modeling to decide between them. For example, R. Levins (1966) listed and linked prey– predator models of the Lotka–Volterra type with theories postulating the effect of competition between species and food chain models to map a “cluster of models” able to exhibit the emergence of ecological communities.

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In general, the verification of theories by comparing alternative explanations is a common epistemological practice that, although different from the Popperian and Kuhnian approaches, applies to geography as well as to other sciences (Harvey 1969). For example, in urban geography, C. Cottineau et al. (2015a) identify five mechanisms that can explain the differentiation of city sizes over time: the effect of spatial interactions and the hierarchical innovation diffusion; self-reinforcing effects of city size differences; site effects and the presence of natural resource deposits; the effects of situations (on transport networks in particular); and territorial effects, i.e. linked to a political organization of solidarity on a defined space, such as a region or state. Once the mechanisms are listed, we claim it is important to hierarchize their supposed importance in order to organize the implementation of the model, especially to make testable assumptions about the explanatory power of the different mechanisms. One way of doing this may be to prioritize the mechanisms according to a subjective (although not arbitrary) assessment of their general or system-specific nature, as well as to separate interaction mechanisms between geographical agents from interaction mechanisms between agents and their geographical environment. 4.3.3. Hierarchizing the interaction processes between agents Hierarchizing interaction mechanisms between agents is an important step in most of the modeling approaches but is rarely mentioned in the published results of the model. A notable counterexample is the presentation of the Sugarscape model in the book by J. Epstein and R. Axtell (1996). Starting from a simple model, the authors describe, in successive chapters, the increasing complexity of behaviors available to the simulated agents, from static agents harvesting a local resource to mobile, gendered agents capable of building up food stocks and transmitting them, trading, reproducing, and polluting. In the example of the MARIUS model simulating the differentiated evolution of city populations in the former Soviet Union (Cottineau et al. 2015b), the interaction mechanisms between city–agents are hierarchized from the most general one (i.e. exchanging value according to a gravity model) to the one most particular to the study space (i.e. socialist economic planning and the exclusive specialization of cities in the production of goods for the entire country). In between, we find the mechanisms of territorial equalization, the memory of exchanges, or the diversification of urban functions (see axis 1 in Figure 4.2). This

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hierarchization has enabled us to choose which mechanisms to implement and evaluate first.

Figure 4.2. Hierarchy of mechanisms potentially explaining the urbanization dynamics of the former Soviet Union over the past 50 years. Source: Cottineau et al. (2015a), JASSS

4.3.4. Hierarchizing the interaction processes between agents and their environment The hierarchization of interaction processes between agents and their environment is a particularly important aspect for territorial modeling. Indeed, this dimension of differentiation relates to both the level of detail with which the model’s environment is represented (from a simple uniform grid to an empirical cadaster representing individual plots) and also to the

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richness of the agents’ geographical behavior. The detailed description of an urban environment makes it possible to model more realistic navigation behaviors (as in the policing model of Camden (Wise and Cheng 2016) or contagion (Perez and Dragicevic 2009)), whereas the addition of localized data on the agricultural potential of cultivated plots makes it possible to accurately reproduce the agricultural production dynamics of Amerindian societies (Dean et al. 2000). In the example of the MARIUS model, the interaction mechanisms between city agents and the Soviet environment are hierarchized from the most general one (the effect of distance on interactions) to the most specific to the study area (the modification of borders over time). In between lay intermediate mechanisms such as the local presence of raw materials, the macro-regional differentiation of demographic regimes, and the impact of transport infrastructure on the calculation of time-distances (cf. axis 2 in Figure 4.2). This hierarchy was produced on the basis of a prior statistical analysis of the evolution of these cities, observed over a long period of time. 4.3.5. Implementing mechanisms and their formal alternatives Figure 4.2 presents a third axis of organization of mechanisms, for a given level of representation of the agents, their interactions, and the environment: the dimension of formal alternatives for a given theoretical explanation. A pioneering example of exploring mathematical variants of the gravity model comes from S. Openshaw (1983b, 1988). During the 1980s, he has implemented an “automatic geographical machine” that automatically generated combinations of gravity models (e.g. using logarithmic, exponential, or power functions assigned to the population) to be estimated using empirical data on inter-zone flows. Since then, model docking movements have headed to a similar direction, although less systematically, by aligning models from different disciplines and issues, but producing equivalent results (Axtell et al. 1996). More recently, J. C. Thiele and V. Grimm (2015) suggested that ecologists should explore existing models more systematically, break them down, and explore their modifications in order to capitalize on previous efforts, and also to improve the robustness of models re-implemented and tested by several research teams. We could add a fourth dimension, the one that is often ignored: the technical implementation of mechanisms since the decomposition of

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mechanisms into computer algorithms naturally gives way to interpretative variations. When modeling the behavior of interacting social entities (actors or collective agents) in a territory, an additional dimension along which mechanisms can differ is the cognitive capacities of the agents. The hierarchy can be organized with respect to the amount of information they have (complete or limited) or to the complexity of their individual reasoning or behavior: from the purely reactive agent to an agent who, on the basis of perceptions that they confront with their beliefs, plans their actions according to their expected effects. Finally, for models based on “highly” social agents, we can consider an additional dimension according to the complexity of social organizations, from the colony of undifferentiated agents to organizations structured by roles, groups, and rules, which are themselves hierarchical (Bouquet et al. 2015). We assume that the evaluation of alternative formalisms of mechanisms can be done in parallel with the evaluation of models of different structures (with more or less mechanisms describing interactions between agents and with the environment). To do this, it is necessary to set up the most robust possible strategy for combining, simulating, and evaluating models. 4.3.6. Combining, simulating, and comparing The perk of subdividing the explanation into different mechanisms lies in the fact that we can implement basic “building blocks,” each of which represents a candidate mechanism (and its formalism), and combine them into a modular model. The modularity of the model must, therefore, be transcribed using a programming language, which allows the automated combination of bricks and conveys the information about the parameters required by each combination to execute the model. In this respect, during our experiment with the MARIUS model, we used the computer notions of “trait” and “dependency injection” (also known as Cake Pattern12) of the Scala programming language to generate all possible combinations of building blocks (64 combinations in this case), to which a structure identifier is assigned (Cottineau et al. 2015a). This identifier is                                         12 This is a way to extend the functionalities of the methods of an object class (here: the mechanisms) according to the context in which they are called (here: the particular combination of bricks forming a model). See also (Rey-Coyrehourcq 2015) for an example of the use of these technologies.

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used as a meta-parameter when assessing the performance of simulation results against empirical data. This assessment is done by measuring the distance between the simulated city populations and the (post-)Soviet cities population data, and relating this performance to the model structure, i.e. its content in terms of combined mechanisms, which this identifier condenses. This experiment allowed us to analyze which are the most probably needed mechanisms to simulate the evolution of the city populations in the former Soviet Union, according to their presence in the most efficient models at different levels of complexity (estimated, for example, by the number of blocks of mechanisms present in the model combination). In particular, it was shown that the mechanism reflecting the process of rural migration to urban centers (or urban transition) was the most important to account for the differentiation of Soviet city sizes between 1959 and 1989, whereas the mechanism of natural resources extraction appeared to be the most important after 1991, confirming in this case the previous insights regarding the postSoviet urbanization. We believe that this experimentation can be generalized to other territorial models and that it presents interesting opportunities in terms of robustness analysis (each combination of mechanisms being confronted with the others) and of formalized knowledge accumulation (using the qualification of the explanatory power of each mechanism). However, multi-modeling (i.e. the combination of different mechanisms and their competing evaluation) presents significant challenges. Section 4.4 offers a discussion of some of these challenges. 4.4. Challenges and limits of multi-modeling “The data requirements, problems associated with parameter estimation, and possible magnifications of parameter errors [make spatially explicit] models an onerous process” (Wiegand et al. 2004). Among the main challenges of multi-modeling are the human and computational costs, due in particular to the high number of possible combinations, which grows more than proportionately with the number of building blocks the choice, number, and order of these building blocks and the absence of standardized methods for comparing models of different structures.

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4.4.1. The combinatorial curse “Combinatorial explosion” is one of the challenges that modelers have faced for a long time. The high number of possible model combinations implies lengthy calculations to evaluate the model (calibration, sensitivity analysis, and robustness) and also to analyze and interpret these results. Indeed, the more descriptive and complete the modeling is, the more numerous the alternatives of formalization are, and the higher the number of building blocks to combine. The number of combinations increases geometrically. In the MARIUS case, with one base mechanism and five additional mechanisms, the multi-model resulted in 26 = 64 possible combinations13. Its calibration required more than 400,000 h of calculation14. If we were to implement C. Cottineau’s project (2018, p. 20) on urban inequalities based on the 12 mechanisms identified in the literature as candidates for explaining the dynamics of economic inequalities in cities, we would arrive at 212 = 4,096 possible model structures. The tools for analysis and interactive visualization of the results developed for MARIUS (Pumain and Reuillon 2017) would not be sufficient to manage such a level of complexity. The method is, therefore, envisaged as a prototype and a methodological approach rather than as a universal modeling standard. 4.4.2. Human and technical costs Since the pioneers of the 1980s, enormous progress has been made on the issue of computing infrastructure, both in terms of hardware and software. Despite this, the difficulty of accessing computational structures for social sciences studies (Banos 2013; Rey-Coyrehourcq 2015) and the constancy of the computational cost associated with model exploration are constraints that still need to be addressed. The design and implementation of a software chain, which supports (a) the automatic generation of a tree of possible combinations from a multitude of heterogeneous building blocks, (b) the evaluation of this tree on distributed computing platforms with adapted methodologies, and (c) an automatic re-composition of the bricks of the tree formulated in (a) on the basis of relevant evaluation criteria, remain to date the result of an ad hoc modeling process. To become affordable, this                                         13 Number 2 refers to the possible states of the mechanisms, i.e. active or passive in the model, while number 6 refers to the number of distinct mechanisms. 14 Distributed on a computing grid using the OpenMole platform (Reuillon et al. 2013).

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complex engineering will have to be integrated into the form of new construction primitives within modeling platforms (NetLogo, Gama, etc.). This also allows us to discuss the human cost of such an undertaking. Indeed, a project like MARIUS required about 2 years of work by three young researchers (doctoral and post-doctoral) funded on the ERC GeoDiverCity project. This experience of interdisciplinarity is described by Chapron et al. (2014); Pumain and Reuillon (2014); Rey-Coyrehourcq (2015); and Pumain (2019). 4.4.3. Subjectivity in the choice of building blocks Another weakness of multi-modeling is that it is based on a partially subjective choice of implemented increments (or building blocks). Indeed, although the hierarchy of processes follows scientific arguments, it is unlikely that the result will be unanimously accepted, which in itself is a weakness as much as a strength. Moreover, given the combinatorial explosion issue, it seems unwise to aim at exploring the exhaustive set of the possible mechanisms into a multi-model. Our recommendation to the novice multi-modeler would, therefore, be to favor parsimony in the selection of building blocks after having justified as far as possible the hierarchy of processes described in section 4.3, by referring to empirical regularities as well as strong theoretical arguments. It is also possible to hope that the reuse and re-evaluation of different blocks of mechanisms will make it possible to characterize their robustness and interest in modeling the geographical object in question, facilitating the choice of robust and efficient increments in the applications tested for subsequent models (Thiele and Grimm 2015). 4.4.4. Comparing models of different structures An additional problem of multi-modeling is to take into account the content of the building blocks in their comparative evaluation. Indeed, given the impossibility of defining the likelihood value of each model, traditional statistical analysis tools for model selection, such as Akaike or Bayes information criteria, no longer work in the case of complex territorial simulation. If we were to reason more simply, by trying to arbitrate between distance from simulation objectives and parsimony, let us imagine the comparison of three models. Model A contains only one mechanism, e.g. the random

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growth of economic firms. This mechanism has two parameters: the average growth of firms and the standard deviation of their distribution. Model B contains only one mechanism, namely, the growth of firms based on their interactions with other firms. This mechanism is based on three parameters: the range of interactions, the multiplier effect of size, and the average growth of firms. Model C contains the combined mechanisms of models A and B and, therefore, has four parameters in total. It is easy to consider model C as more complex than models A and B. However, are A and B equivalent (since they have the same number of mechanisms) or not (since B has more parameters and, probably, more lines of code15)? The MARIUS experiment (Cottineau et al. 2015a) considered them as equivalent, which is probably too simplistic. However, it is not clear how it would always be possible to order the degree of parsimony of different model structures when their number and complexity grow. The approach of C. Piou et al. (2009) is quite different: these authors use the POM method and define an information criterion called POMIC. This indicator is based on the estimation of a deviation measure between the entropy of the model outputs and that of the field data. This solution, applied to different mathematical forms, reflects differences in terms of a number of parameters, but no differences in content. It is, therefore, still difficult to compare the influence of a mechanism involving the consideration of data external to the model with a more parsimonious mechanism on this aspect. Although we wanted to highlight the limits of the multi-modeling approach in territorial applications, we still believe that this approach is the most consistent with the scientific approach of social sciences in general and geography in particular. Moreover, the advantage of such a method is that it encourages the accumulation of formalized and evaluated knowledge, making it possible to reproduce stylized facts in diverse configurations, reflecting the diversity of territories. This opportunity will necessarily require the sharing of models and their evaluation protocol, and a theorizing enterprise: a kind of overarching theory of complex models themselves.

                                        15 A tricky measurement, which only works if language, programming experience, and the programmer remain constant during the development of the model.

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4.4.5. Sharing and accumulation of knowledge This overarching theory of multi-agent models is the subject of a research group led by U. Berger, V. Grimm, I. Lorscheid, and M. Meyer16. The first path envisaged by this group is the documentation, evaluation, and sharing of “sub-models” within catalogs of mechanisms implemented in common computer languages. Like the package operation of the R software or the model libraries of the NetLogo software, one can imagine libraries of mechanisms (building blocks) relating to objects and scales of territorial modeling, from which modelers could choose the most interesting combinations for their research question. The challenge is then to standardize the conditions of experimentation: input and output data formats, methods, and tools and documentation of model source codes17, and also the acceptance of these standards in a community that has until now been characterized by a diversity of practices, languages, and investigation issues. 4.5. Conclusion This chapter has pointed out the importance of adequately representing cities and territories and also the dynamic interactions between simulated agents and simulated territories in complex simulation models. This territorial approach presents specific issues. Therefore, we have detailed the different states a territory can undertake during the modeling process. First, it is abstracted from reality as the modeler assesses, whose characteristics are the most relevant with respect to the research question – as in cartography. Second, the territorial setting is described using a formalized procedure, i.e. it is transposed into an algebraic system whose structure, scale, and level of details are at the heart of the modeling process. We have stressed that initial conditions of this first territorial representation have a huge technical and theoretical impact on the simulation process. As such, the territory is indeed both an input and an output of the simulation. It is first altered by the mechanisms of the model during simulation and then abstracted again at the end of the simulation when the modeler selects which territorial components will be used to qualify the simulation outputs and to measure the correspondence with empirical data and/or stylized facts.                                         16 http://abm-theory.org/. 17 Not to mention their openness and free accessibility, execution, and modification, as proposed in the GeOpenMod section of Cybergeo magazine https://journals.openedition.org/ cybergeo/26452.

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The chapter dealt further with the question of the nature of explanation in territorial simulation. Models of this type intend to explain a geographical phenomenon by combining parametric mechanisms, translated into mathematical structures or computer programs. This formalization ensures a precise analysis of their independent and combined effects. Such a monitoring allows modelers to assess the variety of potential territorial dynamics as well as to characterize a particular historical trajectory by comparing it to a set of alternative results arising from the same mechanisms. This approach leads us to distinguish, in the study of a territory and its models, between the general, the specific, and the singular conditions. Finally, we proposed a modeling strategy that goes beyond the classical definition of a model as a fixed set of mechanisms deriving directly from a research question. Instead, this strategy considers a model as a singular combination of mechanisms selected among a broad collection of potential ones. A classification is made according to its degree of generality (i.e. from the most general to the most specific) and complexity (i.e. from the simplest to the most complex). This allows us to better understand the effects of a variation in the model structure on its dynamics and outputs and, therefore, to better inform the wealth of information it provides. Other ordering criteria can be used depending on the research question. In this chapter, we have, for instance, chosen to arrange the incremental mechanisms according to two dimensions: the interactions between entities (cities here) and the spatial resolution of the environment in which interactions take place. However, this method implies significant costs, which we have detailed in the last part of the chapter. The analysis of existing modeling approaches and of the incremental modeling strategy sought to provide the reader–modeler–geographer with a guide to represent territorial complexity in a progressive and well-reasoned manner, in order to develop a reproducible territorial model and evaluation protocol. The incremental multi-modeling approach tackles the issue of model adequacy with regard to the geographical object under study and it clarifies the elements of the scientific debate in case of alternative explanations as it requires a fine specification of the simulation objectives, of the conditions under which the model operates, and of its implementation details. It lays down the foundations for testing and confronting empirical and theoretical hypotheses from simulation models. We believe that this incremental and multi-modeling strategy is very promising and in line with the more general concerns of the agent-based modeling community. However, this method implies high implementation costs as the automated

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combination of modular building blocks and their systematic calibration rely on an important technical and computer arsenal, which we have partly discussed in the last part of the chapter and which will be further detailed in the following chapter.  

 

5 Methods for Exploring Simulation Models

Simulation models are an absolute necessity in the human and social sciences, which can only very exceptionally use experimental science methods to construct their knowledge. Models enable the simulation of social processes by replacing the complex interplay of individual and collective actions and reactions with simpler mathematical or computer mechanisms, making it easier to understand the relationships between the causes and the consequences of these interactions and to make predictions. As the formalism of mathematical models offering analytical solutions is often not suitable for representing social complexity (Jensen 2018), more and more agent-based computer models are being used. For a long time, the limited computing capacities of computers have hampered programming models that would take into account the interactions between large numbers of geographically located entities (persons or territories). In principle, these models should inform the conditions for the emergence of certain patterns defined at a macro-geographic level from the interactions occurring at a micro-geographic level, in systems whose behaviors are too complex to be understood directly by a human brain. Moreover, it is also necessary to analyze the dynamic behavior of these models with nonlinear feedback effects and verify that they produce plausible results at all stages of their simulation. This essential work of exploring the dynamics of modeled systems remained in its infancy until the late 2010s. Since then, algorithms combining more sophisticated methods, including genetic algorithms and the use of distributed intensive computing, have made it possible to make a significant qualitative leap forward in the exploration and validation of models. The result is an epistemological turn for the human and social                                         Chapter written by Juste RAIMBAULT and Denise PUMAIN.

Geographical Modeling: Cities and Territories, First Edition. Edited by Denise Pumain. © ISTE Ltd 2019. Published by ISTE Ltd and John Wiley & Sons, Inc.

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sciences, as indicated by the latest applications realized with the help of the OpenMOLE platform presented here. 5.1. Social sciences and experimentation Experimentation has greatly helped build the natural sciences. Experimenting consists in reproducing material, physical, chemical, or biological processes, according to devices designed by researchers to select, often by isolating them, simpler sequences of facts than those operating in a complex reality. The comparison of the results of these manipulations with observed data, in whole or in part unrelated to those used to construct the experimental design, is considered to provide evidence of the veracity or accuracy of the explanatory reasoning underlying the construction of the model. The evidence is supposed to be more or less conclusive depending on the quality of the fit between the model predictions and the observations. However, it is well-known that the accuracy of a model’s predictions is not sufficient to fully validate the adequacy between the explanatory mechanism imagined by the manipulators of the experimental device and the processes at work in the system under study, even if it remains an important step in the construction of models and theories enriched by observations. In the human and social sciences, the development of experimental devices is very delicate because it faces many practical and ethical obstacles. Ethical and political criticism imposes limits on the manipulation of people and the control of their freedom. The scruples of scientific ontology and ethics (part of what is now called integrity) have certainly not prevented in practice the manipulations, benevolent or not, carried out in historical times by actors with political, cultural, or economic power from making decisions, more or less well informed “scientifically” (see the writings of the “prince’s advisors” across all eras, such as Bodin, Machiavelli, Botero, etc. to name a few of those who have dealt with spatial planning) and to carry out “experiments” in forms of governance or technological or cultural innovations whose results have been evaluated, sometimes as beneficial and sometimes as disastrous. Assessing the effectiveness of decisions is even more complicated since there is often no countertest, no alternative scenario, and the actors themselves do not deprive themselves of “biasing” the game with their “self-fulfiling prophecies”, ensuring in advance the result they expect (Rist 1970). The often deplored difficulty of evaluating public policies is thus exacerbated by the uncertainty of the boundaries between action and context, both in space and time.

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Driving change in social life, whatever the scale of the interventions, remains a costly and risky operation, ethically difficult for scientists to accept, and there are few who actually dare to embark on “research-action” projects. During the 1960s, there was a controversy in France between the advocates of “applied geography”, who were familiar with the “terrain” but were sometimes methodologically and politically conservative, and those of “active geography” who were more committed to transforming society. Sometimes, for example, to contribute to the definition of the policy of equilibrium metropolises in France (DATAR1 operation in 1964), the geographers participating in planning studies (including Michel Rochefort in this case) relied, without really daring to say it, on scientific models (in this case Walter Christaller’s central place theory). Today, geographers are more willing to want to assist in decision-making in the most informed way possible according to the state of their knowledge. They often choose to use in silico simulation models, implemented in computers. Computer simulation has thus become a substitute for experimentation. It is no coincidence that, among social scientists, geographers became pioneers in the field: the diversity of the multiple categories of data (landscapes, populations, habitats, etc.) that they manipulate to account for the transformations of the earth’s surface and land interfaces operated by societies, the often large extent of the territories they examine at regional, national, or global levels, explain their need to use computers to organize these masses of information, and understand the dynamics they represent. 5.2. Geographical data and computer skills We consider a simulation model as a computer program that produces outputs from input data and parameters. In an ideal case, all the following steps are necessary for a robust use of simulation models: 1. Identification of the main mechanisms and associated crucial parameters, as well as their range of variation, suggested by their thematic meaning if applicable; identification of indicators to assess the performance or behavior of the model. 2. Evaluation of stochastic variations: a large number of repetitions for a reasonable number of parameters; establishment of the number of                                         1 Délégation à l’Aménagement du Territoire et à l’Action Régionale – Inter ministerial delegation of land planning and regional attractiveness.

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repetitions necessary to achieve a certain level of statistical convergence. 3. Direct exploration for a first sensitivity analysis; if possible, statistical evaluation of the relationships between parameters and output indicators. 4. Calibration, algorithmic exploration targeted by the use of specific algorithms, such as Calibration Profile (Reuillon et al. 2015) and Pattern Space Exploration (Chérel et al. 2015). 5. Returns on the model, extension, and new multi-modeling bricks; returns on stylized facts and theory. 6. Extensive sensitivity analyses, corresponding to experimental methods (under development and integration in the OpenMOLE platform), such as the sensitivity to meta-parameters and initial spatial conditions proposed by Raimbault et al. (2018). Some steps do not necessarily need to be taken, such as stochasticity assessment in the case of a deterministic model. Similarly, the steps will become more or less important depending on the nature of the question asked: calibration will not be relevant in the case of completely synthetic models, while a systematic exploration of a large number of parameters will not always be necessary in the case of a model that is to be calibrated on data. The first geographical simulation models were first calculated “by hand” in the 1950s. It is no coincidence that these models all deal with stylized facts that reflect the most frequently observed regularities in the organization of social space and which are effects of the “first law of geography”, summarized as early as 1970 by the American cartographer Waldo Tobler: “everything interacts with everything, but two close things are more likely to come into contact than two distant things”. The attractive power of proximity appears in all social processes of spatial planning, which are constrained by the “obligation of spacing”. This expression was proposed by Henri Reymond in 1971 in a formalization of the problems of geography, which first stated that societies tend to transform the heterogeneous, rough, and discontinuous earth’s surface into an organized space with properties of greater homogeneity and continuity. Thus, regularities emerge because two objects cannot occupy the same place. The assertion that individuals and societies are most likely to choose to occupy and interact with the nearest locations, both because they are better known and because they save on the

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costs (physical, monetary, and cultural) of distance travel is certainly the strongest theoretical proposition in geography. It is found in all spatial configurations that lead to the distinction between a center and a periphery, which appears at all levels of geographical space, from local to global. The first simulation models in geography therefore first touched on processes for which the choice of the closest, among the places with which one wishes to establish an interaction, is a very dominant anthropological constant. Proximity is preferred in spatial interaction, whether to observe the effects of an innovation before imitating it, according to Torsten Hägerstrand’s spatial theory of innovation diffusion (1952) or for the choice of destination places by migrants (Hägerstrand 1957; Morrill 1962, 1963). Models based on the proposal, as early as 1954, of the American geographer Edward Ullman to construct geography as a “science of spatial interactions”, particularly in relation to trade relations, first gave rise mainly to experiments with statistical models, using various forms of “gravitation models”. These were then integrated into urban models, first static (Lowry 1964) and then dynamic (Allen 2012; Allen and Sanglier 1981; Clarke and Wilson 1983; Wilson 2014). A later generation of models, which played with the effects of proximity in a more complex way, made extensive use of cellular automata. Spatial autocorrelation measurements, which positively or negatively reflect the attraction or competition effects of proximity, are thus used to test the plausibility of simulated configurations for land-use change, particularly urban growth (White and Engelen 1993; White et al. 2015) or the spread of epidemics in the geographical area (Cliff et al. 2004). However, the development of these models was hindered at an early stage by the computational capabilities of the computers of the time, as the explicit representation of spatial interactions increases as the square of the number of geographical units considered. Thus, statistician Christophe Terrier had to segment his Mirabelle program (Méthode Informatisée de Recherche et d’Analyse des Bassins par l’Etude des Liaisons Logement-Emploi) processing data from the 1975 INSEE census before being able to simulate the division of resident populations into employment basins according to commuting between all 36,000 French municipalities (Terrier 1980). The first simulation model of interactions between cities, designed to reproduce their demographic and economic trajectories influenced by urban functions over a period of 2000 years on a laboratory computer, could only accept a maximum of 400 cities (Bura et al. 1996; Sanders et al. 1997). The increase in the

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power of computer calculations has been relatively slow, allowing only the consideration of about a thousand cities in 2007 with the Eurosim model (Sanders et al. 2007) or the Simpop2 models applied by Anne Bretagnolle to Europe and the United States (Bretagnolle and Pumain 2010). Above all, experimentation with these models has long remained at a low tech stage, requiring a high degree of application in the “manual” modification of parameter values, which were rarely directly observable, and which, therefore, had to be estimated on the basis of the plausibility of the model dynamics. However, the equations of urban dynamics models incorporate nonlinear relationships that produce many bifurcations, requiring a very large number of round trips in the procedure for estimating parameter values (Sanders et al. 2007). This long work limited the number of simulations from which the estimated parameters could be considered satisfactory, and above all, once the model had been calibrated in this way, there remained a fairly high degree of uncertainty as to the quality of the results obtained. 5.3. New generation simulations The 2000s and 2010s were to completely change the researchers’ working environment, because the spread of the Internet, then mobile phones, and finally massive data produced by all kinds of digital sensors had rapid and intense feedback effects on the rise in computing capacities, which in turn enabled these disruptive technological innovations. The simulation models were then able to integrate considerable amounts of interactions between localized entities characterized by a wide variety of attributes. Until 15 years ago, Gleyze (2005) was forced to conclude that network analyses for public transport in Paris were “limited by calculation”. To give just one example of the quantitative leap represented by the increase in computational capacity and its consequences on the increased confidence in models that results from it, we can cite the pioneering work in digital epidemiology carried out by Eubank et al. (2004) to simulate, using EpiSims and TRANSIMS models, the daily trajectories, on a transport network, of the movements of one and a half million people between some 180,000 places in the virtual city of Portland, in order to predict the propagation paths of an epidemic based on the probability of interpersonal encounters, in social networks organized in “small worlds”. The epidemic can spread rapidly in a city, while the number of contacts per person remains small (maximum 15, Eliot and Daudé 2006). Simulation platforms have been developed so that as many researchers as possible, even those not specialized in computers, can implement multi-

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agent models. NetLogo (Tisue and Wilensky 2004) is probably the best known; it is generalist, and allows access to multi-agent simulations without the need for in-depth computer knowledge, thanks to its simple programming language and integrated graphical interface builder. Other more specialized platforms, such as GAMA (Grignard et al. 2013), are immediately built to offer a coupling with geographic information systems. However, confidence in the results from simulation models goes hand in hand with an increase in the size and a number of simulations required, i.e. the scale of numerical experiments. Although platforms such as NetLogo and GAMA integrate basic tools that allow a first step toward such a “scaling up”, a need for a “meta-platform” dedicated to the exploration of simulation results has naturally emerged. 5.3.1. A virtual laboratory: the OpenMOLE platform Since 2008, the OpenMOLE platform has been designed to explore the dynamics of multi-agent models (Reuillon et al. 2010; Reuillon et al. 2013) and has rapidly extended to simulation models more generally. It is the result of the development of a previous software, SimExplorer (Amblard 2003; Deffuant et al. 2003), which already provided its users with an ergonomic interface for designing experimental plans and gave access to distributed computing. OpenMOLE generalized SimExplorer in its early days, in particular by making it possible to parallel tasks on a massive scale. OpenMOLE2 is a collaborative modeling tool in perpetual evolution: “A permanent effort of genericity has made it possible to create in a few years a generic, pragmatic, and proven platform for the exploration of complex system models in the form of a dedicated language, text, and graphics, exposing coherent blocks and at the right level of abstraction for the design of numerical experiments distributed on simulation models” (Schmitt 2014). Reuillon et al. (2013) describe the fundamental principles of the platform, while Pumain and Reuillon (2017) provide a context for the different uses in simulation models for systems of cities. The procedures (or workflows) proposed in OpenMOLE are described independently of the models and are, therefore, reproducible, reusable, and exchangeable between modelers. A market place is integrated into the software, such as the model library included in NetLogo, and allows users to benefit from exploration scripts that can be used as templates or examples, in                                         2 https://openmole.org/.

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a large variety of thematic fields and for all the methods and languages implemented in OpenMOLE (e.g. for calibrating geographical models, analyzing biological networks, and image processing for neuroscience). OpenMOLE uses a domain-specific language (DSL) (Van Deursen and Klint 2002) for writing exploration workflows. This practice consists of creating a rating and rules specific to the field of a given problem. It is a kind of programming language dedicated, in this case, to model exploration and associated methods. This one is, of course, not created from scratch but comes as an extension of the underlying language, i.e. Scala in the case of OpenMOLE. A reduced number of keywords and primitives make it easy to use even for a user who has no programming knowledge, and the DSL remains very flexible for the advanced user who can use Scala programming. According to Passerat-Palmbach et al. (2017), the OpenMOLE DSL is one of the key elements of its genericity and accessibility. One of the OpenMOLE’s main assets is its transparent access to highperformance computing (HPC) environments. The increase in computing resources mentioned above can be physically manifested in different aspects for the modeler: local server, local computing cluster, computing grid (networking of multiple clusters, such as the European EGI computing grid), and cloud computing services. In most cases, their use requires advanced computer skills, which are generally inaccessible to a standard geographer modeler. OpenMOLE includes a library allowing access to the majority of these computing resources, and their mobilization in the DSL is completely transparent to the user. The person can test their script on their own machine and scale it on HPC environments by modifying a single keyword in it. Since the presentation of the use of DSL and the implementation of scripts is not the objective of this chapter, we refer the reader to the OpenMOLE online documentation for examples of scripts and model exploration. We simply recall the fundamental components of an exploration script: (i) the definition of prototypes, which correspond to the parameters and outputs of the model, which will take different values during the experiment; (ii) the definition of tasks, including the execution of the model but which can also be, for example, pre- or post-processing tasks – tasks covering a very wide variety of languages (Scala, Java, NetLogo, R, Scilab, and native code such as python or C++); (iii) the description of the methods to apply (exploration by sampling, calibration, diversity search, etc.) that will affect the values of the prototypes and launch the evaluation task under consideration (most often the model); (iv) a specification of the data

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retrieved from the script execution (simulation data is often massive, so a selection of these is crucial); and (v) the definition of the calculation environment on which the method will be launched. The platform aims to considerably extend the practices of generative social science proposed by Epstein and Axtell (1996), who considered each multi-agent model as an artificial society, generating macroscopic behaviors based on hypotheses about microscopic behaviors. According to Clara Schmitt (2014), who used the OpenMOLE platform to develop with Sébastien Rey-Coyrehourcq (2019) the SimpopLocal model to simulate the emergence of a system of cities, the virtual laboratory that this platform represents “is no longer just the simulation model and the hypotheses it simulates (i.e. the artificial society). It also contains the modeling methods, tools, and procedures adapted to the design and exploration of the model and whose practice provides as much theoretical knowledge and feedback as the design of the model itself. This virtual laboratory is, therefore, all the more similar to a real research laboratory with a bench (the model to be designed and explored), a researcher’s hypotheses (the geographical processes transcribed into the model’s mechanisms), methods (the iterative and intensive computationassisted modeling method), tools (automated exploration procedures, and any other experimental design incorporated in OpenMOLE), all gathered in a room, the SimProcess modeling platform (an alternative name for the framework in which OpenMOLE is embedded)” (Rey-Coyrehourcq 2015). Compared to general protocols such as the one introduced by Grimm et al. (2005) to present all the modeling steps, the principles applied in OpenMOLE are novel in terms of their new capabilities to explore the dynamic behavior of simulation models. Two main innovations consist of the systematic use of optimization metaheuristics, mainly genetic algorithms, to quickly test as many combinations of model parameter values as possible, and in the simultaneous sending of simulations to multiple machines on a computing grid, which considerably reduces the duration of experiments, which would otherwise quickly become unacceptable. The choice of genetic algorithms as optimization heuristics is justified by their effectiveness in multi-objective optimization problems. In addition, the

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island distribution scheme (populations evolving independently for a certain period of time) is particularly well suited to the distribution of grid calculations, each of the nodes of the grid evolving a sub-population, which is regularly retrieved, merged into the overall population, from which a new sub-population is generated and sent to the node. This type of algorithm could be relatively applicable to stochastic model simulations although a number of problems remain for this type of application (Rakshit et al. 2017). According to Rey-Coyrehourcq (2015), these methods are part of the more global framework of Evolutionary Computation, and the Scala MGO library, developed simultaneously with the platform and which allows evolutionary algorithms to be implemented there, was designed to be easily extended to other heuristics in Evolutionary Computation, leaving completely open the possibility of including new methods in OpenMOLE. According to R. Reuillon cited by Raimbault (2017a), OpenMOLE’s philosophy revolves around three axes: the model as the “black box” to be explored (i.e. exploration methods “rotate the model” without interacting with its code, which is thus somehow “embedded” in the platform), the use of advanced exploration methods, and transparent access to intensive computing environments. These different components are strongly interdependent and allow a paradigmatic turn in the use of simulation models: the use of multi-modeling, i.e. a variable structure of the model, as presented in Chapter 4 (Cottineau et al. 2015a) and a change in the nature of the questions asked of the model, such as a complete determination of the space for possible model behaviors (Chérel et al. 2015), with all this being made possible by the use of intensive computing (Schmitt et al. 2015). The online documentation provides an overview of the methods available in the latest version of the software and their articulation in a standard framework. To illustrate this general presentation of the OpenMOLE platform and associated methods, we propose developing the example of the SimpopLocal model in the following section, whose genesis has been closely linked to that of the platform, and which has been a candidate for the development and application of various methods. 5.3.2. The SimpopLocal experiment: simulation of an emergence in geography The SimpopLocal model was designed to represent the emergence of systems of cities, as observed in five or six regions of the world, some

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3000 years after the emergence of agricultural practices in settled societies (Bairoch 1985; Marcus and Sablof 2008). It is indeed a question of explaining the emergence not only of “the” city but also of “systems of cities”, because we know that cities from that time were never isolated but already organized in networks in the territory of each of these ancient “civilizations”. The most recent publications by archeologists insist on a certain continuity of the processes that have led to the sedentarization of hunter-gatherer populations, grouped into hamlets and villages, and then to the emergence of cities in some of these regions. The development of agriculture has been accompanied by a considerable increase in population densities and the size of human groups in these regions (from 0.1 people per km2 to 10, a factor of 100 between the two orders of magnitude), as well as by a greater complexity of political organization and the social division of labor. This very slow process of resource accumulation and population concentration is carried out according to a series of processes involving substantial feedback, with many fluctuations in growth due to frequent adverse events such as natural disasters or predations from neighboring groups. Due to the slowness of the transformations and their frequent interruptions, archeologists sometimes now contest the name “Neolithic revolution”, which was proposed by Gordon Childe in 1942 (Demoule et al. 2018, p. 159). However, geographers continue to identify the emergence of cities as an emergence, a “bifurcation” for two main reasons: on the one hand, it has not occurred systematically in all regions where agriculture has been practiced, where two regimes for the evolution of settlement systems are possible and historically viable (purely agricultural and village regions have been able to function for several centuries and now remain residual in some forests or on Pacific islands, for example), and the territorial regime operating with cities is indeed a specific “attractor” in the dynamics of old settlement systems; on the other hand, the evolutionary trajectory that sees cities emerge reflects a significant qualitative change (an emergence) with a significant increase in the diversity of social functions associated with habitats and also a considerable expansion in the scale of spatial interactions: the trade that takes place over a longer distance thus allows cities to be less dependent on a “site” of local resources as it is the case for agricultural villages and to develop the assets of a geographical “situation” exploiting the wealth of a network of increasingly distant sites (Reymond 1971). The SimpopLocal model aims to reproduce this remarkable aspect of the dynamics of settlement systems, which invariably produces an amplification of the hierarchical differentiation between habitats, defined in the literature

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as a major stylized fact: already in any settlement system, in any place, and at any time in history or prehistory, the distribution of the sizes of inhabited places (measured by population or spatial extent, or even the diversity of functional artefacts) is statistically very asymmetric, comprising many very small agglomerations and only a few very large agglomerations with a fairly regular distribution of the Zipf’s law or lognormal type (Fletcher 1986; Liu 1996). This hierarchical distribution is a structural property (size order of entities) at the macroscopic level that is particularly persistent over time, regardless of local fluctuations at the entity level. The SimpopLocal model is designed to test the hypothesis set out in the evolutionary theory of urban systems (Pumain 1997), which explains this structural characteristic by a process of urban growth on average proportional to the size acquired, and its amplification by the creation of multiple technological and societal innovations producing the increase and diversification of wealth that spreads among places connected by all kinds of exchanges. The SimpopLocal model is first of all based on the statistical model, which is an excellent first approximation of the evolution of populations in a system of cities by simulating urban growth as a simple stochastic process that varies the size of each city in a manner proportional to its size and leads to a lognormal distribution of urban populations (Gibrat 1931). The high quality of this basic statistical model is that it uses the size already acquired, which expresses both the accumulated wealth and the attraction and resilience of the inhabited place, as an “explanation” for the growth. In a way, it is a model according to the concept of “endogenous growth” of economists (Aghion et al. 1998). However, SimpopLocal is designed, like the previous models of the “family” of Simpop multi-agent models (Bura et al. 1996; Sanders et al. 2007; Pumain 2008), to compensate for the insufficient capacity of Gibrat’s model to predict the everywhere observed trend of higher than expected growth in the largest cities at the top of networks (Moriconi-Ebrard 1993) and the exaggerated inequality between city sizes (Bretagnolle and Pumain 2010; Pumain 1997). These deviations from the Gibrat model are related to long-range correlations (Rozenfeld et al. 2008), caused by spatial interactions. The effect of these amplifies the hierarchical differentiation between the sizes of cities participating in exchanges in an urban system (Favaro and Pumain 2011). Simpop models reflect this effect by introducing, exogenously to the model and at different times during the simulation, new urban functions that select certain cities or are captured by them in a continuous process of adaptation to these innovations. Compared to the other Simpop models, SimpopLocal introduces two new features: it uses an abstract representation of successive

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waves of innovation and brings them all together in a single “innovation” object. A second originality consists of making endogenous the process of creating innovation by linking it to the size of the inhabited place, supposed to amplify in a nonlinear way the emergence of new technical, social, or cultural forms (with a probability of creation varying as the square of the populations in presence or in relation). This more parsimonious version of the model construction considerably reduces the number of parameters and, therefore, allows for more systematic exploration and evaluation. 5.3.3. Implementation OpenMOLE

of

SimpopLocal,

from

NetLogo

to

SimpopLocal was initially developed with the NetLogo language and then redeveloped with the Scala programming language. The simulation with NetLogo benefited from the facilities of the interface, which allows numerically and graphically following the modifications generated on the macroscopic variables that summarize the state of the system, but very quickly showed its limits in terms of experimentation. The manual method of adjusting parameter values made it difficult to avoid the “runaway” of urban growth leading to increases in city size that was far too huge for the historical period being simulated. The reprogramming in Scala and then the transfer to the OpenMOLE platform allowed a more precise and complete exploration of the model’s behaviors. The model represents the evolution of settlement units dispersed in an area large enough to accommodate a few thousand inhabitants but of a surface limited enough to ensure a possible connection between the inhabited places according to the transportation means available at the time (e.g. it could be former Mesopotamia or ancient Mesoamerica). The simulation space is composed of about a hundred inhabited places. Each site is considered a fixed agent and is described by three attributes: the location of its permanent habitat (x, y), the size of its population P, and the resources available in its local environment. The amount of available resources R is quantified in units of inhabitants and can be understood as the carrying capacity of the local environment to support a population, which varies according to the skills that the local population has acquired for using resources, through innovations they have created or received from other inhabited places. However, resource exploitation is done locally and the sharing or exchange of goods or people is not explicitly represented in the model. Each new innovation created or acquired by an inhabited place develops its operating skills. The innovation

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entity is understood here as a large socially accepted abstract invention, which could represent a technical invention, a discovery, a social organization, new habits, or practices, and so on. Each acquisition of innovation by an inhabited place brings the possibility of exceeding its capacity thresholds and, consequently, authorizes demographic growth. The model was designed to be as parsimonious as possible, minimizing the number of agent attributes (which are inhabited places) and the parameters that control their evolution. The average orders of magnitude indicated by the archeologists’ work were used directly to set the length of the transition period between an agrarian settlement system and an urban settlement system at about 4,000 years, to estimate an average annual population change rate of about 0.02% per year and to estimate that the size of the largest inhabited place in the system would increase from about 100 to about 10,000 inhabitants. However, the values of five other parameters could not be estimated from the literature and had to be deduced from the simulation experiments. These are the probability of creating an innovation by interaction between two people in the same place, the probability of spreading an innovation by interaction between two people in different places, the intensity of the dissuasive effect of distance on these interactions between places, and the impact of an innovation on population growth (through an increase in available resources) and the maximum possible size of an inhabited place (measured in terms of population or available resources) that is part of the logistics growth equation adopted as a generic model of a development that is still very strongly constrained by local resources. The equations that summarize the model and the tables that precisely define the parameters and their action are detailed by Schmitt (2014) and Schmitt et al. in Pumain and Reuillon (2017, pp. 21–34). An initial value is defined for the population and resources of the inhabited places, and then the network of interaction between them is created. Then, at each step of the simulation, the mechanisms of population growth and innovation diffusion are applied. The impact of innovations on the efficiency of resource extraction is calculated. This loop is iterated until the stop criterion is reached: in this case, after 4,000 steps or when an arbitrary maximum number of innovations have been reached. The evolution of the state of the settlement system at the macro-geographic level is observed by the distribution of the size of the inhabited places, summarized by the slope of the rank-size distribution. As the model includes certain parameters that are probabilities, it is stochastic; thus, the same set of parameter values can give significantly different results. An automated

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method for varying parameter values and interpreting the results obtained has been gradually developed through collaboration between computer scientists and geographers. 5.3.4. Calibration and validation The automation of the exploration of the dynamics generated by simulation models with the OpenMOLE platform uses genetic algorithms that systematically carry out variations in parameter values previously performed “manually” by the researcher. The distribution of calculations on a grid infrastructure (a network of computers) also makes it possible to carry out this very large number of combinatorial operations by considerably reducing computing time, thanks to the parallel processing of information. However, the implementation of this new form of model experimentation requires the intervention of the thematic researcher, who must select the precise objectives that their model must satisfy. In return for what could be considered as a reductionist operation, further refinement of the exploration method can lead to an increased confidence in the scientific assumptions of the model. 5.3.4.1. Calibration as optimization using genetic algorithms Calibration is a procedure that seeks to minimize the gap (called fitness) between the behavior simulated by the model and the empirically observed behavior, by incrementally varying unknown values of the model parameters. Stonedahl (2011) recalled the difficulties of this exploration, which quickly becomes tedious when conducted manually because of the multiple bifurcations occurring in models where most of the mechanisms linking the variables are nonlinear. An exhaustive exploration of the parameter space is not possible because it would require excessive computation times, which would increase exponentially with the number of parameters. As these procedures also produce large quantities of results, they also require the use of appropriate methods to process and visualize the information generated by the simulations. A whole set of software must, therefore, be implemented to enable the researcher to discover the main dynamic schemes associated with variations in the parameters of their model. This is where appropriate IT procedures can be used, relating the calibration issue to an optimization problem. Genetic algorithms have been used to calibrate multi-agent systems in several fields, including medicine (Castiglione et al. 2007), ecology (Duboz et al. 2010), economics (Espinosa 2012; Stonedahl and Wilensky 2010a), or hydrology (Solomatine et al.

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1999). Despite the wide use of multi-agent systems in the social sciences, this method has not been applied very often (Heppenstall et al. 2007; Stonedahl and Wilensky, 2010b). This type of numerical experiment requires the definition of quantitative objectives to assess whether the simulation results are compatible with the experts’ expectations. It is also necessary to know how to manage enormous computational load and how to optimize a fitness function that is susceptible to present very large stochastic variations (Pietro et al. 2004). In the case of SimpopLocal, which includes five parameters whose values are unknown (even their orders of magnitude cannot be estimated from empirical data), we had to identify three “objective functions”. These characterize a simulation result at the macro-geographic level and correspond to stylized facts whose orders of magnitude could be established on the basis of archeological and historical knowledge: the final distribution of city sizes must be lognormal (similar to a Zipf’s law), the maximum size reached by the largest city must be about 10,000 inhabitants, and the simulation duration must be equivalent to 4,000 years. This obligation to define objective functions could be considered as a strong constraint on the epistemological validity of the model. It seems to contradict the hypothesis of an open evolution for systems of cities. In fact, this intermediate step of calculation represents a compression of knowledge, our minimum requirement on the representativeness, and plausibility of the model’s behavior in relation to the possible set of dynamics of cities in a system (at the historical time of the emergence of cities). The result in terms of evaluation of the simulations must make it possible to progress in the knowledge of the intra- and inter-urban interaction processes likely to generate this general dynamics at the macroscopic level of the system, this theoretical reconstitution thus being similar to what physicists call the “opposite problem”. A rather wide range of numerical variation is established a priori for each of the five parameters. Each set of parameters, combining a value for each of them, is evaluated according to the simulation output it produces. This evaluation measures the proximity between the simulation outputs and the objective functions defined for the model and thus measures the ability of a certain set of parameter values to reproduce the stylized facts that the simulation should best approach. The settings receiving the best evaluations are then used as a basis to generate new parameter sets that are then tested.

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5.3.4.2. Exploration of the parameter space under objective constraint The SimpopLocal model being stochastic, the simulation results vary from one simulation to another for the same parameter settings. Therefore, the evaluation of the parameter settings according to the three objectives must take this variability into account. We verified that about 100 simulations for each set of parameters were sufficient to capture this variability without significantly increasing the duration of the calculation. Each objective function has a corresponding measurement evaluating the quality of the simulated result. The model’s ability to produce a log-normal distribution is measured by the difference between the simulated distribution and a theoretical log-normal distribution, having the same mean and standard deviation according to a Kolmogorov–Smirnov test. The maximum population objective quantifies the model’s ability to generate larger or smaller cities, and the result of a simulation is tested by calculating the difference between the size of the largest agglomeration and the expected value of 10,000 inhabitants: ((population of the largest urban area 10,000) /10,000). The simulation duration objective quantifies the model’s ability to generate an expected configuration within a historically plausible time frame. The difference between the number of iterations of the simulation and the expected value of 4,000 simulation steps is calculated: ((duration simulation 4,000)/4,000). These three error calculations are standardized in order to compare the degree of success of a simulation with each of the three objectives. However, since it is not possible to aggregate the three calculations to produce a single global quality measure, a multi-objective algorithm is needed to determine which simulations are most satisfactory for approaching the desired final configuration. This type of algorithm calculates compromise solutions such that none dominates all others for all objectives. These solutions are called Pareto compromises and together they form what is called a “Pareto front”. The use of global exploration methods such as genetic algorithms to calibrate a multi-agent model (and in particular a stochastic multi-agent model) involves a very high computation cost (Sharma and Singh 2006). This type of load is too large to run on local computers, and supercomputers are very expensive and are not readily available in most laboratories. Computer grids offer a solution to solve these computationally intensive problems. However, computing on such a large scale requires orchestrating the execution of tens of thousands of instances of the model on computers distributed around the world. The cumulative probability of local failures

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and the problem of optimally distributing the workload on the grid make it very difficult for a lay researcher to use it, as mentioned above. It is, among other things, to overcome these difficulties that the OpenMOLE platform was built (Reuillon et al. 2010, 2013). This example of the calibration of the SimpopLocal model shows how OpenMOLE helps modelers to bridge the technical and methodological gap between them and high-performance computing. The grid infrastructure (EGI) allowed us to use such computing power that half a billion model executions could be performed for SimpopLocal calibration, which otherwise would have required about 20 years of computing with a single computer (Schmitt et al. 2015). 5.3.4.3. The calibration profile, a great epistemological progress for SHS The result of the calibration process only ensures that the model can reproduce the stylized characteristics of the emergence of a city system, with a fairly accurate assessment of the values of the parameters that together contribute to this evolution. However, it says nothing about how often parameter sets produce plausible behaviors, and how each parameter contributes to changing the model’s behavior. For example, it would be interesting to know when certain parameter values prevent the system from achieving plausible behavior and not to limit itself to knowing only one set of “optimal” parameter values. A new method has been developed to represent the sensitivity of the model to variations in a single parameter, independent of variations in all other parameters (Reuillon et al. 2015). By means of a function that calculates a single numerical value describing the calibration quality for the model, the profile algorithm calculates the lowest possible calibration error when the value of a given parameter is set and the others are free. The algorithm calculates this minimum error for the entire variation range of the studied parameter. For each value of a parameter, the algorithm tries to identify the value sets of the other parameters that produce the best fit of the model to the expected data (the smallest possible error). A graph then represents the variations of this optimal adjustment value according to the variations of the studied parameter. The calibration profile thus shows several possible shapes for this curve. When it shows a clear inflection toward the lowest values for calibration error, for a very small range of variation in the values of the parameter under study, it can be concluded that

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the order of magnitude of the parameter that satisfies the requirements in terms of model behavior has really been identified. If one of these curves remains flat, it indicates that the parameter has no effect on the model’s behavior and can, therefore, be eliminated. Thus, in the case of SimpopLocal, a parameter imagined as the lifetime of an innovation was finally excluded because variations had no effect on the quality of fit of the model, all things being equal with variations in the other parameters (Schmitt 2014). We, therefore, have the opportunity here to assess the extent to which the mechanisms devised to build the model are not only sufficient but also necessary to produce the expected behavior. Within the limits of the theoretical framework and the selection of the stylized facts selected, this is the first time that SHS researchers can reach this type of essential scientific conclusion, thanks to a validation method that is finally effective for multiagent simulation models. This marks a huge advancement in the social sciences from an epistemological point of view. Of course, this is a relative certitude that remains always related to the theoretical framework given by the objects, attributes, and mechanisms selected by researchers to be representative of the observed system. A complementary form of validation of the model could then be imagined if archeological historians tried to recalibrate it with data from their observations. Indeed, the estimated set of parameters contains values that generate the desired dynamics for a fictitious system but are not fixed in absolute terms. They are related to each other, on the one hand, and to the fictitious data entered, on the other. If the latter are modified to make them compatible with a historically observed settlement system, the model’s ability to simulate its development would then be confirmed not only by reconstructing the trajectories of the population evolution of the inhabited places considered but also by maintaining the relative orders of magnitude of the parameters that generate these dynamics. 5.4. Other examples of OpenMOLE applications: network– territory interaction models In this section, we propose to illustrate the application of OpenMOLE’s exploration methods and intensive computing alongside another thematic issue: that of interactions between networks and territories. This question has fueled many scientific debates, for which most of the problems remain relatively open. For example, the problem of the “structuring effects of transport infrastructure” (Bonnafous and Plassard 1974), presented by Offner

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(1993) as a “scientific myth” invoked to justify the cost of a new infrastructure by its impact on regional development, not always observed in the medium term, may, according to A. Bretagnolle (in Offner et al. 2014), be observed for larger territories and over time, while taking into account local fluctuations in the dynamics of systems of cities. The debate is thus fueled by contradictory results according to the places and periods studied, and also according to the time lags allowed to measure a relationship between a “cause” and its “effect”. The empirical difficulty of extracting general stylized facts, as well as the conceptual difficulty of geographical entities that are, in fact, in circular causal relationships, is bypassed by a model of the co-evolution of transport networks and territories proposed by Raimbault (2018b). The results obtained are closely linked to the use of OpenMOLE and its exploration and calibration algorithms, of which we will give some illustrations. The application of multi-objective calibration is essential to the experiment with models of systems of cities corresponding to real situations. For example, Raimbault (2018a) introduces a model of the evolution of a system of cities over time, similar to the model of Favaro and Pumain (2011), but focusing on the effect of the physical transport network. The growth rates of cities are determined by the superposition of several effects: (i) endogenous growth captured by a fixed growth rate corresponding to the Gibrat model; (ii) interactions between cities by a gravity model; and (iii) feedback of flows circulating in the network on the evolution of the population of the crossed cities. This model is calibrated in a non-stationary way over time, i.e. over sliding time windows, in order to take the change in the nature of urban dynamics into account, as observed by Bretagnolle and Franc (2018) with, for example, the changes in transport networks, on the French system of cities between 1830 and 2000. To calibrate the model, the simulated populations are compared to the observed populations. At this stage, the use of a multi-objective calibration algorithm (the NSGA2 algorithm implemented in OpenMOLE) is essential. Indeed, the adjustment can be made, for example, on the basis of an average square error over time and for all cities. However, given the disparities in city size linked to the urban hierarchy, it quickly appears that a single-objective optimization on this error will amount to adjusting the size of the largest cities to the detriment of the majority of cities in the system. The addition of a second objective, taken, for example, as an average square error on population logarithms, makes it possible to better consider all cities. An important result of Raimbault (2018a) is then the emergence of Pareto fronts for these two objectives, for all the time windows considered. This shows that this type of

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model must be applied by making a compromise between the adjustment of populations for medium-sized cities and populations for larger cities. This result is possible, thanks to the multi-objective optimization by the genetic algorithm of OpenMOLE. Another example of the application of the platform’s methods, which illustrates its crucial role, is given by the search for co-evolution regimes, i.e. different forms of correlation over time between the development of a network and the growth of a city or region. If the correlation keeps the same sign, it means that the growth of the territory can precede and, therefore, cause that of the network or vice versa, whereas if it varies over time, its changes make it possible to detect circular causalities and, therefore, a coevolution between network and territory. According to Raimbault (2017b), the study of the reasons for time-delayed correlation makes it possible to isolate typical regimes of interaction between network variables and territorial variables. More precisely, Raimbault (2018b) defines co-evolution as the existence of causal circular relationships, at the level of a set of entities in a certain spatial realm. In the case of networks and territories, network properties must be locally caused by those of the territories and vice versa. Unidirectional causalities from networks to territories then correspond to the “structuring effects” mentioned above. This definition of co-evolution makes it possible to capture the “congruence” (Offner 1993) between these objects, in a way, their dynamic reciprocal adaptation. It also allows the construction of an operational method proposed by Raimbault (2017b), which statistically looks for causal links between corresponding variables. In practice, the weak notion of Granger causality3 is mobilized, allowing flexibility with regard to the necessary data and the temporal and spatial frameworks of estimation. This causality is quantified by the delayed correlations between variations in network variables (such as centralities or accessibility) and variations in territorial variables (such as population, employment, real estate transactions, etc.). The existence of significant maxima at non-zero delays (stronger correlation between the values of one and the growth of the other with a time lag) gives a causal direction (the growth of a network variable precedes and, therefore, leads to the growth of a territory variable or vice versa, for the region and period considered). A typology of these delayed correlation profiles provides what are called                                         3 Low causality according to the Granger concept is derived from correlations measured over time series, such causality is assumed when one variable provides results useful for predicting the value of another variable.

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“causality regimes”, including co-evolution regimes where two variables “territory” and “network” are in reciprocal causality. The question is then, for a given case study, to identify the regimes present from observed data or data simulated by a model, in particular those that correspond to a co-evolution. The demonstration of the existence of such regimes at the end of a “co-evolution model” is not expected a priori since the processes included at the microscopic level where the influences are, indeed, reciprocal and do not imply a reciprocal causality at the macroscopic level of the indicators. Indeed, the models considered are complex and reflect an emergence. The delayed correlation method is applied to a macroscopic co-evolution model by Raimbault (2019a), which extends the Raimbault model (2018a) by adding rules for the evolution of network link capacities. Direct sampling, which consists of a random draw of a fixed number of values or “points” of parameters (e.g. by Latin Hypercube sampling maximizing point spacing), is a first experiment allowed by OpenMOLE to gain an insight into the model’s ability to produce co-evolution. This experiment makes it possible to isolate a number of coevolution regimes that can potentially be produced by the model: 33 regimes for 729 possible regimes for the variables considered, i.e. 4.5% (in this case, populations are considered as territory variables, and proximity centrality and accessibility as network variables, which corresponds to six directed pairs of variables, and therefore 36 = 729 possible regimes, each pair being able to have a positive, negative, or non-existent delayed correlation). Among the 33 isolated co-evolution regimes, there are 19 whose existence could not be intuitively predicted. The existence and variety of these regimes are an important result, showing that it is possible to model a co-evolution in the statistical sense given earlier. The application of the Pattern Space Exploration algorithm (Chérel et al. 2015), which aims to achieve diversity in the regimes produced, allows this conclusion to be considerably extended since this algorithm produces 260 co-evolution regimes (35.7%). This is a typical example where the strong nonlinearity of the outputs considered can lead to partial or even biased conclusions and where the use of a specific method is crucial. The results are made more robust and extensive, thanks to the application of a specific method integrated into the OpenMOLE platform. This method also allows models to be compared with each other. Thus, Raimbault (2019b) applied this method to the SimpopNet model introduced by Schmitt (2014), which is also a macroscopic co-evolution model and has

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a large number of similarities with Raimbault’s (2019a) co-evolution model, particularly in the variables considered, i.e. the calculable output indicators. SimpopNet then produces a smaller number of interaction and co-evolution regimes, confirming, on the one hand, that it is not immediate for a model designed for co-evolution (SimpopNet) to actually bring about co-evolution regimes and suggesting, on the other hand, that its stronger constraints in network evolution rules induce a greater difficulty in producing a diversity of regimes. 5.5. Perspectives The development of the OpenMOLE platform has made it possible to create an original axis, or even a field of research, one of the remarkable aspects of which is a high level of interdisciplinarity between the human sciences and more technical disciplines such as computer science. According to Banos (2017), this leads to the production of a broader and deeper knowledge, like the virtuous spiral of Banos (2013) between discipline and interdisciplinarity. In addition, the single-platform philosophy (mentioned above, through the strong interaction between the three axes of model loading, access to innovative exploration methods, and transparent access to intensive computing environments) opens up many perspectives, both technical and theoretical and methodological and thematic. We give some illustrations in the following, reflecting a present state of possible futures for OpenMOLE. 5.5.1. Methods The integration of new exploration methods is a key focus of OpenMOLE’s development. For example, the comprehensive resolution of inverse problems (Aster et al. 2018) is not currently included. The resolution of a reverse problem consists of determining the entire history of a given objective in the output space of the model. Calibration algorithms solve similar problems but do not guarantee the exhaustiveness of the solutions produced, which can be a major problem in the case of equifinality (ReyCoyrehourcq 2015), i.e. parameter configurations or initial conditions leading by different trajectories to an identical result. A reverse problem heuristic based on Pattern Space Exploration (PSE) mechanisms is currently being developed for integration into OpenMOLE.

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The use of Bayesian inference methods is another avenue being explored. Indeed, in the case of highly stochastic models where the attached distributions have non-standard shapes, an estimate of the probability distribution of the parameters can be provided by this type of method. In the case of simulation models, the Approximate Bayesian Computation method (Csilléry et al. 2010) allows, for a set of observed data, the provision of the probability distribution of the parameters that most likely led to these data. It is thus an extended calibration, with a probabilistic produced knowledge allowing uncertainty to be taken into account. A specification of this method proposed by Lenormand et al. (2013), designed to reduce the number of simulations in the case of models with significant computation time, is also being adapted to parallel computation and integrated into the platform. We should also mention various methodological disciplines that are also under investigation: (i) the question of high dimensionality quickly becomes a problem in the use of the PSE algorithm since the number of output configurations is potentially subject to the curse of dimensionality, i.e. execution time or size are exponential functions of the number of dimensions – reducing the number of simulated configurations subject to the PSE algorithm by imposing a diversity of selected configurations criterion would solve this problem and take into account a much greater wealth of outputs; (ii) the issue of sensitivity to initial spatial conditions already mentioned (Raimbault et al. 2018) is particularly relevant for geographical models, and a Scala library including synthetic generators of population configurations at different scales is currently being developed, including, for example, the neighborhood generators studied by Raimbault and Perret (2019); and (iii) the implementation of information criteria for model performance, already mentioned in Chapter 4 and which are a cornerstone of multi-modeling approaches, is also under study, as the POMIC criterion proposed by Piou et al. (2009). 5.5.2. Tools During its development, OpenMOLE was always at the forefront in terms of the tools used and developed. The choice of the Scala language to replace Java from the first versions of OpenMOLE is an innovative technological choice, made particularly relevant by the functional programming possibilities but also the object programming it provides, making it a more powerful language in terms of flexibility than other functional languages, such as Haskell (Oliveira and Gibbons 2010). However, the underlying Java

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infrastructure is retained, allowing high portability to any operating system and any type of hardware, which is very important for distributing calculations over heterogeneous grid nodes. Properties such as line mixing make Scala particularly relevant for multi-modeling (Odersky and Zenger 2005). In addition, properties such as implicit conversions or case classes make Scala ergonomic for DSL development (Sloane 2008), which, as already mentioned, is an essential aspect of OpenMOLE. Questions of program loading, and of models by extension, remain an active field of research, particularly in relation to reproducibility. The docker program, which uses containers, allows the embedding of an identical execution environment regardless of the operating system and hardware. Hung et al. (2016) propose coupling dockers with a graphical interface for scientific reproducibility. Similar programs such as Singularity are specifically dedicated to the reproducibility of HPC experiments (Kurtzer et al. 2017). The core of OpenMOLE’s embedding strategy is not based on such a program (Singularity), yet some tasks based on running programs with a complicated environment are embedded in OpenMOLE by a task using docker (e.g. for the R language that requires the installation of a complete R environment). An improvement in the integration of dockers in OpenMOLE is an active and important research axis for the future extension of the genericity of the programs that can be embedded in the platform. OpenMOLE would thus be at the forefront of technical research in terms of scientific reproducibility. Similarly, the question of the scalability of experiments (i.e. the ability of programs to deal with problems of increasing magnitude) is at the heart of the platform’s philosophy, and research is being conducted to, for example, automate the deployment of multiple instances of OpenMOLE on a cluster and to facilitate its use within communities of thematicians. 5.6. Conclusion The exploration of simulation models continued in geography through initiatives such as the development of the OpenMOLE platform. This development has been carried out in a highly interdisciplinary and reciprocal framework, thus constituting a win–win relationship between computer scientists and geographers (Pumain 2019), but also through an unprecedented integration of knowledge domains (Raimbault 2017a), i.e. empirical, theoretical, and modeling knowledge, but also tools and methods, which strongly interact with one another in each of these domains. The

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OpenMOLE adventure, and its branch related to geography within the framework of the ERC GeoDiverCity, testifies to a new way of producing geographical knowledge, making it possible to produce scientific evidence in the social sciences. It thus gives weight to geography and, more broadly, to the human and social sciences, in the face of hard sciences such as physics, which claim a monopoly on the identification of evidence relating to the functioning of social systems (Dupuy and Benguigui 2015). It now remains to promote this research position, as well as the tools and methods that make it possible, in cooperation with the new emerging disciplines of City Science and Urban Analytics described by Batty (2019), within the field of Theoretical and Quantitative Geography.

6 Model Visualization

6.1. Introduction Geographers know the essential role of cartography in analyzing, understanding, and describing the spaces they study. For Philippe Pinchemel (1979, pp. 246–247), “only the cartographic representation highlights geographical organizations, structures, and systems. The map and the cartographic language also appear as the expression, as the privileged developer of geography. Geographical thinking can be seen in cartographic representations”. In geographical modeling1, it is, therefore, not surprising that cartography and data visualization in a broader sense are essential media for the expressiveness of a model. In their latest manual linking agent-based modeling (ABM) and geographic information systems (GIS), Crooks et al. (2019) describe the importance of visualization, applied here to simulation results: Building effective modeling outcomes, modeling, is a vital Good-quality maps

visualizations of spatial analysis and be they derived from GIS or agent-based final component of the analysis process. and visualizations not only explain the

                                        Chapter written by Robin CURA. 1 In this chapter, we will use the term modeling to refer to computer modeling, formalized in algorithmic form rather than mathematical, thus excluding both statistical and mathematical modeling (e.g. around game theory), as well as more common types of modeling in geography such as graphic modeling (“chorematic”) or qualitative systemic modeling (often formalized as sagittal diagrams, for example). Among the types of computer modeling, it should be noted that the emphasis here is on simulation models and, like most of this book, on agent-based simulation models.

Geographical Modeling: Cities and Territories, First Edition. Edited by Denise Pumain. © ISTE Ltd 2019. Published by ISTE Ltd and John Wiley & Sons, Inc.

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outcomes of the analysis, but also aid interpretation by allowing observers to easily draw out insights. (Crooks et al. 2019, p. 117) Moreover, even when modeling is not geographical, there are many semantic parallels between geographic space and the modeling environment: agents interact in a virtual “world”, a world that refers to a continuous, geographical space, or more often than not, a discretized space, composed of patches or cells, which can themselves constitute agents (as in cellular automata models, for example). In the field of agent-based models, agents are generally inseparable from the support space in which they operate, which can itself evolve independently. Agent-based modeling platforms clearly illustrate the strong relationship between ABM and visualization or even mapping: the home pages of the majority of these platforms highlight screenshots, most of which offer cartographic representations of running simulation models. However, despite the close link between agent-based modeling and geography, on the one hand, and geography and visualization, on the other, there is little reference in the scientific literature to graphical and, in particular, cartographic representation methods, including in the most appropriate articles (Kornhauser et al. 2009; Lee et al. 2015). A review of the literature shows this quite widely (Angus and Hassani-Mahmooei 2015, Table 4): in the journal JASSS (Journal of Artificial Societies and Social Simulation), which is predominant in the field of agent-based social simulation, there are many more tables (233 identified), schematic diagrams (218), and code extracts (111) than statistical graphics (43) or maps (29)2. In the world of ABM, data visualization, therefore, seems to be largely neglected and marginal, even though researchers recognize its importance (Kornhauser et al. 2009). In addition, visualizations are used more often to communicate results than as tools for model analysis or presentation (Angus and Hassani-Mahmooei 2015), while researchers generally agree on the importance of visualization in the model construction process3. In this chapter, we therefore wish to present and to illustrate the advantages that can be gained from the use of data visualization, either                                         2 It should be noted, however, that the authors identify 135 screenshots in this corpus, a significant proportion of which probably contain statistical graphs and maps. 3 For example, through face validation methods, to which we will return in section 6.3.2.

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statistical or cartographic, in the practice of geographic data modeling. For this reason, it seems important to establish the parallels that exist between the practice of modeling and that of visualization. These methods appear to be largely similar in terms of both practices and aims. Once these parallels have been established, it will be possible to highlight the peculiarities and main applications of geographic model visualization in each of the phases of their design. We will thus see how visualization can help to verify a model, both in itself and with respect to the numerical assumptions on which it is built, and more generally to evaluate it. By extrapolating these strengths from model visualization, it will be possible to show when and how visualization can be useful in comparing models, in understanding their particularities, as well as in distinguishing models within a model family (see Chapter 4, section 4.4). Finally, visualization is relevant in the different phases of communication surrounding the finished models, i.e. in terms of presentation, scientific valorization, and dissemination. However, some obstacles and locks remain to correctly visualize the ABM simulation data, and we will propose a few leads to solve these. 6.2. Visualization as modeling Simulation and visualization are scientific fields studied by very different and quite hermetically sealed disciplinary communities. In each of these fields, computing and computer scientists play a major role: they design and build the technical concepts, methodologies, and tools on which practitioners can rely on in order to model the desired systems or (geo)-visualize the available information. However, by focusing on these practitioners, there is greater disciplinary diversity. On the modeling side, practitioners can be ecologists, engineers, sociologists, archeologists, and so on. They share quantitative approaches to study the relationships between humans and their environments (natural or social). On the visualization research side (here in the sense of data visualization, or Information Visualization – InfoVis), the community is growing toward both creative and artistic as well as technical approaches, bringing together, for example, designers, data-journalists, or practitioners of new disciplines related to data, data scientists. Geographers interested in modeling (in the broad sense, including graphic forms of modeling) are quite widely dispersed among these approaches, perhaps for historical reasons as much as for thematic interests.

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However, there are many similarities and parallels between visualization and modeling. In the broad sense, there is a tight link because a visualization is a model, whether one takes Minsky’s (1965) definition or a more general one. A visualization is thus a representation of a data set, necessarily partial and dedicated to a task (see, for example, section 4.2.1 of Chapter 4). As much as models, visualization uses thematic and technical knowledge – and therefore often involves interdisciplinarity – but it is also concerned with equifinality (there are potentially as many ways to visualize a data set as there are visualization designers) or evaluation (some visualizations will be more valid than others to shed light on an aspect of a data set representing a system). Overall, the nine “strong principles” identified by Banos (2013, pp. 76–84) apply at least as much to data visualization as to computer modeling: without respecting their order or going into detail, these principles can provide an entry point for drawing a portrait of the similarities between modeling and visualization, and moreover, when it comes to designing visualizations as part of a modeling activity. Principle

Applicable to visualization?

Principle 1

Modeling is learning

Yes

Principle 2

The modeler is not omnicompetent

Yes

Principle 3

Simulation models must take root in the data

Yes

Principle 4

The behavior of each model must be known about in a precise way

No

Principle 5

The modeler must cease to propose unique and optimal solutions to complex problems

Yes

Principle 6

The modeler is not the “guardian of proven truth”; their and its models must be accessible in their entirety in order to be reproduced

Yes

Principle 7

The models are not only children anymore

Yes

Principle 8

The models should be coupled

Yes

Principle 9

Mathematics is not a universal modeling language

No

Table 6.1. The “strong principles” of modeling by Banos (2013) and their relevance to the question of the visualization of data

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6.2.1. Visualization as a tool for interdisciplinarity Modelers know the importance of dialog in building a model. In his second principle, Banos (2013) makes the following clarification: The modeler must be aware of the fundamentally limited nature of his skills. What can be perceived as a weakness is for me a strength. Assumed, this reality naturally leads to collaboration. In a very general way, I would even say that modelling a complex system is an essentially collaborative act (p. 77). Similarly, it seems obvious that visualization is an “essentially collaborative act”. Visualization is a communication tool for the transmission and diffusion of a message. Without taking into account its reception by its readers, there is a high risk of designing a medium that is not very comprehensible and, therefore, not very useful. Feedback from the target audience is therefore important, especially when visualization must help support or transmit a complex message that requires thematic expertise, as is often the case in a modeling project. Therefore, the visualization designer cannot act alone in the same way that the modeler cannot be satisfied with their expertise alone. 6.2.1.1. Visualization and co-construction Visualization, like modeling, also encourages the practice of a true co-design that takes advantage of the other’s knowledge. In the design of a simulation model, the diversity of the designers’ profiles makes it possible to arrive at a richer model and, above all, one that aims to satisfy the thematic and methodological research of its authors: everyone must find their benefit. The more diversified the perspectives, the more robust the model will be in each of its aspects. This can be illustrated by means of an interdisciplinary co-construction experiment – between geography, geographical information science (GISc), archeology, and history – a simulation model of spatial dynamics over time. This model, called SimFeodal (Cura et al. 2017b), aims to study how the European area was restructured between the 9th and 13th Centuries, moving from a predominantly dispersed peasant population to a spatial distribution concentrated in hamlets, villages, and small towns. The members of the project had in common a willingness to test general hypotheses; for example, the polarization effect of castles and aggregates of emerging populations, or the influence of the establishment of the religious system around parishes on

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the fixation of the population. Each having its own disciplinary and thematic speciality, the logic and mechanisms of the model were adopted, between consensus and compromise, particularly for the choice of the level of detail of the model, and between specificity and generality. Once the model was built, and in order to explore its functioning, the visualization of the data from the model made it possible to reflect the overall logic, and also made each of the thematic experts want to observe the results at different levels. For the archeologist, a specialist of parishes, it was essential that the results of the model correspond to empirical knowledge on the number, spatial distribution, and spacing measurements of the parishes at the time. For the historian, a specialist in medieval agrarian communities, it was interesting to observe their emergence and to understand the advantage they conferred to their members toward the power of the emerging feudal system. For the modeling geographer, the distribution of population aggregate sizes was an important issue, for example to determine whether or not the model resulted in a hierarchy of the settlement system as a whole. To answer each of these questions, the visualization designer (and modeler) had to design a large collection of graphical outputs, illustrating both the general trends of the model and the specific thematic aspects. To do this, in the same way that the model was created in co-construction, (geo)visualizations also had to be codesigned, in order to guarantee both their usefulness to each member and their adequacy to each other’s disciplinary practices in order to re-use them, for example, in specialized journals. 6.2.1.2. Visualization as a mediation tool In the same way that the model can be a mediation tool by expressively formalizing for each of the observations of the modeled system (in relation to principle 9), visualization fulfills the same purpose. Data visualization imposes a high degree of transparency in what is represented and how it is represented. Where the model explains and formalizes the components of a system that one wishes to represent, visualizations explain and formalize the model itself. Visualization makes it possible, around an intuitive common language (the graphic representation), to explain the inputs, mechanisms, behaviors, and outputs of a model. To build on these, for example, it may be useful to represent the evolution of the attributes of a set of agents over time. In the SimFeodal model, “peasant households” agents are provided with a satisfaction variable and tend to migrate when it is too low. This push mechanism, similar in spirit to that of a Schelling model (Schelling 1971), is supplemented by a pull mechanism, with migrant agents being attracted

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preferentially to the most attractive poles (population aggregates, parish churches, castles, etc.). The details of the mechanisms governing these general rules are complex and may only be due to implementation particularities. However, when we try to study, in graphical form, the correlations between the attraction of a place and the mass of attracted peasant households, many questions emerge: is the stated satisfaction of peasant households calculated and recorded before or after migration? Is the attractiveness of the poles, which depends in particular on the number of farming households concentrated there, in the same way representative of a pre- or post-migration state? Visualization raises these questions to a large extent because we have to decide what we are going to represent. In the same way that modeling requires precision and explanation of everything that is modeled, visualization requires precision and explanation of how everything is modeled (what Amblard et al. (2006) call “internal validation”). Visualization, therefore, increases the mediation role of the model, allowing a more general mediation to clarify its functioning. A. Banos insists that mathematical formalism is not the most suitable for exchange (principle 9). We could go further here by adding that computer formalism, made of lines of code or pseudo-codes, is not fundamentally more accessible, whereas visualization makes it possible to put all researchers involved in understanding and describing a model on an equal footing. In the words of Banos (2013, p. 83), when he expresses the interest of agent formalism in relation to mathematical formalism: “I am convinced that by revealing, visually, the functioning of even sophisticated methods, and by allowing the user to manipulate them, to interact with them, we can partly break down this barrier of formal languages. Giving a good intuition of methods is the best way to ensure that they are used correctly, but also that their users eventually give themselves the more formal means to understand them”. 6.2.1.3. Visualization and interdisciplinarity It should be noted that this equality in relation to visualization is somewhat misleading: many contemporary works highlight the existence of visual literacy or data literacy, which express inequalities in the ability to understand visual or digital information. Apart from these inequalities, which often relate to acculturation to graphic visualization, (i.e. to the habit of reading certain types of graphs and, therefore, to the ability to quickly understand their message – geographers must nevertheless learn to read

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maps), it can be noted that the different disciplinary cultures also have different habits in terms of types of visualizations. In climatology, it is a common practice to evaluate numerical climate models by representing deviations from observed data on a graph, called a Taylor diagram (Taylor 2001), which summarizes three statistical indicators related to this deviation into a single two-dimensional graph. For a geographer, this type of representation is at the very least unusual, and therefore, it requires a strong acculturation to intuitively conduct a visual evaluation of the results of a model. As part of his thesis research between transport geography, agent-based modeling, and climatology, Emery (2016) carried out interdisciplinary work to evaluate the model he was developing, based in particular on this type of graph (Figure 6.1). In order to make this diagram understandable to the project members, it was therefore necessary to explain it, i.e. to detail its construction, the way it was read, and of course, to show many applications, before its visual analysis became intuitive and it could thus constitute an evaluation tool adapted to the model developed. This example of interdisciplinarity around a model representation illustrates how visualization, in the context of a modeling project, can serve as a catalyst for interdisciplinary transfers.

Figure 6.1. Using the Taylor diagram to validate the results of a road traffic simulation model in Dijon, France (Emery 2016, p. 256). For a color version of this figure, see www.iste.co.uk/pumain/geographical.zip

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Even when the disciplinary habits related to visualization are similar, visualization can also help to foster dialog and encourage explicitness. We can take the example of rank-size curves (see Chapter 3 and Figure 6.2): quantitative geographers, among others, are often confronted with them and are, therefore, used to this representation based on bi-logarithmic plots. They will have no difficulty reading them and will quickly see in the slope of the curve, or its evolution, valuable clues about the hierarchy of a settlement system. However, these curves may not be very meaningful for researchers from different disciplines, or may even be understood inversely by some (Pumain 2012, p. 36). Thus, while geographers traditionally represent the common logarithm (base 10) of the ranks on the abscissa and that of the populations on the ordinate, economists and physicists frequently reverse these axes. In addition, at least for the example shown in Figure 6.2, it can be noted that economists use the natural logarithm (base 2) rather than the common, which can again lead to significant misinterpretation. It is therefore necessary to be particularly careful in reading these curves and to explain their content and the results they contain even more clearly.

Figure 6.2. Different habits represented in row-size curves. Left: in geography (Cura et al. 2017a, Figure 2, p. 369). Right: in economics (according to Gabaix (1999), Figure 1, p. 740)

Because we cannot conceive model visualization without real collaboration, which in an interdisciplinary framework can only lead to thematic and methodological transfers and acculturations to the specificities of each individual, visualization is, therefore, an important interdisciplinary tool. Visualization requires that both the objects represented and the methods of representation be explained, thus constituting a common and universal formalism subject to acculturation to the modes of representation. Moreover,

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as in agent-based modeling, it does not require any significant mathematical prerequisites, which are often limited in the fields of social sciences (Banos 2013). 6.2.2. Visualization and reproducibility In the sixth principle (Table 6.1, Banos 2013), the importance of practical and theoretical reproducibility of the models is recalled. For agent-based modeling, the proposed standard for describing models, “ODD” (Grimm et al. 2017), has been widely adopted, although its authors insist on the inadequacy of this method and on the need to also communicate the numerical elements of a model: input data, source codes, software dependencies, and so on. The world of visualization does not have such a commonly adopted standard, even though, in practice, the tools dedicated to visualization are now often part of a formalized, grammatical logic of visualization design and specification: the grammar of graphics (Wilkinson 2006 [1999]). 6.2.2.1. Rooting in data This way of formalizing the graphical representation types is in line with the current major trends in visualization that is strongly connected to data, data visualization or dataviz. This practice, which is still largely based on legacies from the 1960s and 1970s – such as John Tukey and exploratory data analysis (Tukey 1977), for example, or the semiology of graphics by Jacques Bertin (1973), well known to geographers – benefits considerably from the availability of free software that draws inspiration in particular from the grammar of graphics, and therefore allows data to be represented graphically in a relatively agnostic way with regard to the software and technical platforms used4. These tools, which are closely linked to data, make it possible to adapt quickly to updates in the data or to the inclusion of new data sets – if their structure is similar – which is extremely valuable in a modeling context                                         4 Based on the grammar of graphics, it is easy to generate visualizations in R with the ggplot2 graphical library (Wickham 2016) or in Python via the Altair module (VanderPlas et al. 2018), or generate web visualizations (JavaScript) via Vega (Satyanarayan et al. 2016). The code describing the production of a plot from each of these libraries is extremely close, and in any case, systematically understandable by the user of one or the other of these tools.

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where the modeler performs hundreds or thousands of simulations (or even millions – see section 5.3.4 of Chapter 5) and may, therefore, feel the need to visualize a large part of them. In a reproducibility approach, this also implies that a visualization cannot live alone and should, therefore, systematically be accompanied by its computer code, especially by the data it helps to understand. 6.2.2.2. Reproducibility of visual exploration Chapter 5 (section 5.3.4) presents the dedicated methods for exploring the behaviors of a simulation model, which Banos (2013, principle 4) considered essential. If the platforms mentioned in Chapter 5 make it possible to base these explorations on documented and reproducible practices, for example by pushing for the communication of their source code, the stakes are the same for the visualizations that result from them. Communicating on a model using non-reproducible graphical results invalidates the entire process of making the models accessible. Sébastien Rey-Coyrehourcq et al. (2017) compare the replicability of a model (Figure 6.3A) and that of its actual exploration (Figure 6.3B) and carry out the experiment of reproducibility (conceptual as well as practical in this research) to its conclusion, thus proposing a total availability of all the elements necessary to the reproduction of a model, its exploration, and the visualization of the outputs resulting from this exploration (Rey-Coyrehourcq et al. 2017, pp. 429–433).

Figure 6.3. The replicability levels of a simulation model and its exploration (Rey-Coyrehourcq et al. 2017, Figure 3, p. 427). For a color version of this figure, see www.iste.co.uk/pumain/geographical.zip

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6.2.3. Visualizing a model means learning Throughout his text, Arnaud Banos highlights a major interest (principle 1) in modeling: modeling is learning (Banos 2016). Banos explains this learning by basing modeling upon an iterative and abductive approach: “modeling is indeed a fundamentally iterative process which – and all the more so if it is guided by an abduction principle – implies a strong interaction between the model developed and the progressively constructed vision of the phenomenon in question” (Banos 2013, p. 77). It seems to us that the iterative process characterizes the modeling process in general. It is not more characteristic of abductive approaches – which Livet et al. (2014) associate with KISS models, for example – than of empirical-inductive (or deductive) models such as KIDS models (see Chapter 2). Iteration is at the heart of any modeling approach, whether it goes from hypotheses to concepts, from data to hypotheses, or alternates between the three. The visualization of model data is part of a very comparable logic, also by promoting this iterative, abductive posture itself (Banos 2005, pp. 239–40). Even if the data from the model would not be likely to evolve, we can conceive the realization of a visualization or visual exploration process in the same terms as the modeling process (Andrienko et al. 2018). The visualization of data from the model is, therefore, in itself an iterative process. It also reinforces this iteration by allowing the model to evolve as the visualizations shed light on its understanding. Visualization, therefore, makes it possible to gain an understanding of the model – which is why it is originally mobilized – and also of the system modeled itself, by including the modeling–visualization process in a feedback loop resulting in new knowledge on the target system (Figure 6.4).

Figure 6.4. Iterations between models and visualizations to enrich knowledge (from Keim et al. 2008, Figure 1, p. 156)

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It is also important to note the significance of manipulation, i.e. interaction with the model. It is by interacting with the model, for example by playing with the cursors of its parameters, that one can obtain insight into the effects they have on the model’s mechanisms. Outside of geography, it is on these almost tangible interactions with simulations that several research avenues have been developed, at the interface between computer science, design, and pedagogy, particularly around the “Explorable Explanations” community (Case 2015). For the proponents of these methods, it is through direct manipulation of the parameters, inputs and outputs that we can understand how a system works, in a purely visual way, as summarized by Bret Victor (2009): “Model, Watch, Learn”. While the modeled systems can take many forms (mathematical, physical, or statistical models), there is an excellent pedagogical experience around the Schelling model (Schelling 1971). The experiment presents the Schelling model as an interactive computer game (Parable of the Polygons, Hart and Case 2014). This allows lessons from this model to be taken up much more intuitively than a traditional research article. Applied to simulation models, visualization means creating a model in the model: it allows us to enrich a large part of the intrinsic qualities provided by modeling. Visualization thus makes it possible to increase the interdisciplinary scope of a model, to increase its reproducibility, and to gain in understanding of the model itself as well as of the spatial phenomenon that is being modeled. 6.3. Visualize to evaluate In the modeling process, the most frequent – or most documented – use of visualization is in the different phases of model evaluation. It should be noted at the outset that this term is used here in the broadest sense, i.e. as a set of processes and techniques designed to qualify and quantify the ability of a simulation model to reproduce the selected elements of the modeled system. Evaluation is thus registered as a generic term corresponding to verification, accreditation (Balci 1997), validation – internal or external (Amblard et al. 2006) – or evaludation5 (Augusiak et al. 2014). It is common practice to divide the practice of evaluation into two main categories related to the object to be evaluated: either the                                         5 The authors use this portmanteau word to “describe the entire process of model’s quality”.

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correspondence of an implemented model to the empirical, theoretical, or conceptual model on which it is based (model verification or internal validation6), or the correspondence between the implemented model and the stylized facts of the system it seeks to reproduce (model validation or external validation7). However, this chapter does not focus on model evaluation per se, and this distinction will thus not be followed. We would prefer a chronological breakdown8, identifying the phases of the modeling where visualization can be an important asset. It will therefore be necessary to describe the potentialities of the applied visualization before, during, and after the simulation. 6.3.1. Visualize before modeling Some models base their hypotheses on empirical studies based on statistical data (principle 3 of Table 6.1, for example). In these cases, the visualization makes it possible to verify the results of digital processing, which could be inaccurate, or even invalid, due to the lack of a sufficiently detailed visual observation of the data. Indeed, many analysts tend, for the sake of speed, to confine themselves to examining the numerical results resulting from data aggregations or modeling and to use these results as a basis for formulating their assumptions. However, forgetting that these numerical models, because of the reduction in dimensionality that constitutes their core, necessarily have the effect of impoverishing the underlying data of summarizing them in a small number of indicators, therefore paves the way for wrongful interpretations. It should be noted that the problem is not new. It is in response to the same observation that a major field of statistics has emerged: exploratory data analysis. Once upon a time, statisticians only explored. Then they learned to confirm exactly – to confirm a few things exactly, each under very specific circumstances. As they emphasized exact confirmation, their techniques inevitably became less flexible. The connection of the most used techniques with past insights was weakened. Anything to which a confirmatory procedure                                         6 According to the dedicated expression: “model verification deals with building the model right” (Balci 1994, p. 165). 7 “Model validation deals with building the right model” (Balci 1994). 8 At least in terms of model progress, pure chronology being undermined by the iterative nature of the modeling.

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was not explicitly attached was decried as “mere descriptive statistics”, no matter how much we had learned from it. […] Today, exploratory and confirmatory can – and should – proceed side by side (Tukey 1977, Preface, p. vii). In this book, John Wilder Tukey introduces, in particular, the representation of shapes of distribution using box plots, which make it possible to identify outliers and to isolate them from the more general shape of a distribution (quartiles and deciles). In the same vein, Anscombe’s (1973) work shows that indicators relating to central and dispersion values as well as correlation indices can be misleading by making very different point patterns appear similar (Figure 6.5).

Figure 6.5. Different data sets with identical means, medians, variances, and correlation coefficients. From Matejka and Fitzmaurice (2017) and Cairo (2016) (for the figure of the dinosaur Anscombosaurus). NB: The blue lines correspond to the regression line of the correlation; it is almost identical (and low) in all of these data sets. For a color version of this figure, see www.iste.co.uk/pumain/geographical.zip

This figure illustrates another known statistical bias that visualization can help to identify: the slant_up data set shows a generally negative correlation (the regression line has a negative slope), while the data set appears, visually, to consist of five subsets that would each independently have a positive slope. This is Simpson’s paradox (1951), which can have extremely perverse effects in agent modeling: if the aggregate trend is the reverse of individual trends, without verification of these statistical biases, the modeler can design a mechanism that would oppose empirical knowledge and observations. These few examples illustrate the importance of visualization when different statistical biases and effects (Stan Openshaw’s MAUP (1983a) could also be cited) can lead modelers to misconceive their model regarding agents’ individual or aggregate behaviors. The visualization of all output

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data makes it possible to improve the verification of modeled phenomena, and thus enriches the steps prior to modeling. 6.3.2. Visualize during the simulation In the model evaluation process, among the phases involving visualization, the most well-known is probably the face validation step. This step is one of the first recommended practices to ensure a certain plausibility, at least in appearance, of the implemented model (Figure 6.6). Face validation is a visual verification, based on intuitions as to the expected behavior, of the plausibility of the model, i.e. the potential adequacy between the progress and outcome of a simulation, on the one hand, and the expert knowledge of the modeled system, on the other hand.

Figure 6.6. The classic phases of evaluating a simulation model. From Klüg (2008, Figure 1, p. 42)

Franziska Klüg (2008, pp. 41–42) details this process by including three components that are based on the creation of model visualizations: – Animation assessment: evaluation of the process of a simulation as a whole. This involves judging the plausibility of the dynamics (on the scale of the system as a whole, or of its components) reproduced in the simulation, via a live observation of the simulation. – Output assessment: qualitative evaluation of outputs produced by the simulation, either through verification of values (an approach found in more formal evaluation methods, through automation of these types of evaluation)

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by an expert, or through the analysis of co-variations and temporal changes in different output indicators. The evaluation of outputs can not only be applied to the modeled system as a whole but also to each type of agent involved. – Immersive assessment: the aim here is to evaluate the model through the likelihood of the individual actions and reactions of the agents that interact with it. The focus is therefore on the plausibility of the agents’ behavior (micro level) rather than on the resulting macroscopic dynamics. Various agent-based modeling software highlight the two methods that are carried out directly from the simulation, i.e. process evaluation and immersive evaluation (see section 6.1). The proposed visualization tools are therefore designed to be as intuitive as possible and to provide visualizations of the model from the beginning of its implementation, for example in the prototyping phases. These visualizations almost systematically include one or more (Figure 6.8) maps of the modeled world where agents are represented and where their movements and changes in their attributes can, therefore, be visualized, for example by representing them as proportional symbols (quantitative attributes) or by assigning different symbols to agents (qualitative attributes) (Figure 6.7). These maps are often supplemented by statistical plots, such as the evolution of an indicator during a simulation (the different plots occupying the left parts of the images in Figures 6.7 and 6.8).

Figure 6.7. AccesSim Model (Delage et al. 2009), developed with the NetLogo software (Tisue and Wilensky 2004). For a color version of this figure, see www.iste.co.uk/pumain/geographical.zip

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Figure 6.8. BSNM (Brown plant hopper Surveillance Network Model) (Truong et al. 2012), developed with the Gama software (Taillandier et al. 2018). For a color version of this figure, see www.iste.co.uk/pumain/geographical.zip

Live visualization (online visualization according to Grignard and Drogoul (2017a)) is necessarily constrained by the visual space presented to the modeler. As we wish to refine the observation of model behaviors, we tend to add new visualizations, multiplying the number of indicators to be monitored during a simulation. It may therefore be useful to conduct ex-post observations, i.e. by visualizing different indicators – and their evolution – once the simulation has been completed. Simulation platforms adopt different strategies to meet this recurring need. Some (e.g. Gama) propose multiplying the tabs dedicated to visualization, among which one can then alternate in order to carry out a more advanced face validation (Figure 6.8). This ensures that the overall display of the model is not overloaded and that it remains in a summarizing role. Other platforms (NetLogo, etc.) offer an extremely practical mechanism that consists of being able to replay a simulation, i.e. to allow the modeler to move back and forth in time steps once the execution of the model has been completed. This way, modelers can focus on a few indicators or even add new ones interactively when the platform allows it. In any case, and because modeling is a highly iterative task, modelers are strongly advised to save, in the outputs of a model, the states of the different agents at each simulation time step. This makes it possible not only to carry out more in-depth subsequent analyses (for example, using spatial analysis

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methods that are not implemented in generic agent-based modeling software) but also to allow subsequent re-examinations of past simulations, even if new versions of the model have been implemented in the meantime. 6.3.3. Visualizing after the simulation Retrospective visualization is important in the evaluation of a model: if all of the elements (e.g. agents and attributes) have been saved during the execution of a simulation, it allows us to come back at any time to the results of a simulation, either to specify the analysis or to compare the results to those of other simulations. 6.3.3.1. Analysis of simulation results Agent-based modeling platforms increasingly provide statistical and geostatistical analysis methods, (geo)visualization capabilities, and integrated data mining tools as a whole. For internal validation or face validation tasks, a large number of the analyses can therefore already be carried out without leaving the technical environment of the modeling platforms. However, this is not the primary purpose of these platforms, and ad hoc analysis tools and environments are much more suitable for more advanced analyses. When simulation data have a strong spatial component, it will be much more efficient to analyze them within dedicated software like GISs. However, GISs have their shortcomings. On the one hand, they are probably the simplest and most powerful tools for integrating and manipulating spatial data, particularly because they are based on intuitive and user-friendly point-and-click graphical interfaces. On the other hand, interactive manipulation prevents the automation (and replicability) of analysis steps. Thus, with each new simulation, it is necessary to reproduce the processing chain applied to the simulation data in the same way, manually, interactively, in order to obtain comparable results. In the construction phase of a model, where many simulations can be analyzed every day, the limits of this type of tool are quickly reached. For that, at the cost of lower interactivity, the modeler and/or evaluator will benefit from using data analysis tools, geographical or not, built on command line interfaces, i.e. on lines of source code. With the now widespread tools dedicated to automatic report creation (Notebooks), it is possible to create once and for all a series of advanced analyses leading to the production of tabular and (carto)graphical outputs, or even to add interactivity to all of these elements. The languages dedicated to data

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analysis (R, Python, Julia, etc.) all simplify the creation of these interactive automatic reports (R Markdown, Jupyter Notebooks, Weave.jl), which can be generated again with a single click on the results of a new simulation. 6.3.3.2. Analysis of the results of several replicates These reproducible and automatic reporting practices also make it possible to consider the stochasticity of a model, i.e. the amount of randomness it contains. In agent-based modeling, agents execute a set of behaviors, often in a predefined order. However, the order in which agents are called, i.e. the priority given to each agent to execute his or her own behaviors, is most often a function of a hazard that allows the stability of a model to be tested against the results generated. In the Schelling model (Schelling 1971), for example, dissatisfied agents move, at each time step, to an empty location. Depending on the order in which the agents are called, the results of the model (in terms of the speed of reaching an equilibrium, for example) can change quite significantly: if the most dissatisfied agents are migrated first, there is a greater chance that all agents reach an acceptable level of satisfaction more quickly. On the contrary, if at each time step the slightly dissatisfied agents are moved, there is a risk of pendulum-swing phenomena, i.e. some agents being caught in infinite loops of migration. By introducing randomness into the order of agents’ calls, i.e. by modifying it at each time step without taking into account any determinism (here their satisfaction), we obtain a potentially average, neither optimized nor excessively unstable, behavior. However, once randomness is introduced, the results of a single simulation cannot be relied upon to judge the overall behavior of the model: another random simulation may yield different results. It is therefore essential to take into account the stochasticity of a simulation model by conducting replications, i.e. different simulations where the random seed will vary. Retrospective visualization allows us to take this stochasticity into account and thus to highlight the main central trends of a model. Numerical indicators of dispersion and/or variability exist, but like the usual statistical summaries (Figure 6.5), they do not reflect the diversity of achievements of a simulation model. On the contrary, a visual analysis of the outputs of each replication makes it possible to visually embrace the diversity of the outputs and also the common points between them (Figure 6.9).

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Figure 6.9. Visualization of SimpopLocal model trends and variabilities (see Chapter 5, section 5.3.2). The representation combining rank-size curves and box plots makes it possible to represent the general shape of the population distribution of the human installations of the model while displaying a higher variability at the top of the hierarchy. From Schmitt et al. (2015, Figure 3, p. 312). For a color version of this figure, see www.iste.co.uk/pumain/geographical.zip

6.3.3.3. Toward a visual evaluation However, the qualitative foundations of face validation analyses raise doubts among many authors. For Charles Hermann, for example: Although face validity has value in the early stages of model building or for quick checks during actual operation, its severe limitations should be recognized. […] The acceptance of face validity as a rough, first approximation might be improved if the simulator explicitly stated in advance what observations would constitute indications that an aspect of the observable universe had been successfully captured. In summary, face validity in its usual form suffers from the lack of explicit validity criteria (Hermann 1967, p. 222). However, the suggestions for improvement he suggests could lead to a real evaluation procedure based on visualization. By specifying an upstream grid of criteria and expectations for simulation results (as in the POM methodology discussed in Chapter 4, section 4.2.3), and by ensuring that the evaluators are each experts in the part of the model to be evaluated9, a certain rigor can be obtained in a visual analysis. The most traditional                                         9 The analysis of the overall behavior of a model, at the macroscopic scale, can thus be based on expertise that is different from that of the microscopic behavior of each of the agents involved.

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quantitative evaluation approaches quantify differences between the behavior of the model and the expected objectives (optimization of a fitness function, for example). Visual comparison, which qualitatively estimates the differences between the results of the model and expert thematic knowledge, can also offer a completely rigorous and enriching method with regard to the knowledge acquired on the functioning of the model as well as on that relating to the model system itself. The proposed method is thus like any non-formal evaluation procedure, based on the comparison between empirical knowledge and theoretical results from the simulation. In terms of comparison, visualization can excel: “At the heart of quantitative reasoning is a single question: compared to what? Small multiple designs, multivariate and data bountiful, answer directly by visually enforcing comparisons of changes, of the differences among objects, of the scope of alternatives” (Tufte 1998 [1990], p. 67). 6.4. Visualizing to compare Visualization is a good tool for comparing statistical results if the methods used are appropriate. As part of a modeling activity, comparable elements must be identified and compared using appropriate visual modalities. 6.4.1. Which models should be compared?

Figure 6.10. A graphical representation of the difference between iteration and incrementality, from Patton (2017). For a color version of this figure, see www.iste.co.uk/pumain/geographical.zip

Modeling is intrinsically a hybrid process between iteration and incrementality (Figure 6.10). The construction of a model can thus only be

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carried out by adding the different parts (types of agents, mechanisms, etc.) that compose it successively (incrementality, Figure 6.10, right), but at the same time it is part of a process of refinement and improvement (iteration, Figure 6.10, left) of what has already been implemented. These two methods can be opposed, and each poses its own obstacles to visual comparison, for example when trying to compare different successive or alternative versions of the same model. 6.4.1.1. Comparing different versions of a model When developing a model, in order to carry out internal validation for each addition, the first difficulty encountered is the comparison of successive versions (iterative). In the same way that mechanisms are refined over time, indicators and analytical filters also tend to be specified and clarified. For example, in a simple evolution model summarized by a Gibrat process (Cura et al. 2017a), it is sufficient in the early versions of the model to verify that the population structure tends to rank well. To do this, we can simply measure the evolution of the slope of the rank-size curve as the model unfolds: if the difference between the starting slope and the slope at the end of the simulation is positive, we can say that the system is ranked. However, as versions are developed to approach empirical observations, it is then possible to compare the difference between the simulated slope obtained at the end of the simulation and the slope observed in the data. If we did only record the relative values of the slope evolution, and now observe the exact values at the end of the simulation, we would obtain two non-comparable indicators, either visually or numerically. In developing a model, it is therefore very important to take into account from the outset the complexity of the indicators that we wish to compare. This is in line with the logic of the visual evaluation proposals described earlier: it is better to define the evaluation criteria of the model well in advance and implement its recording in the model from the beginning of its construction. 6.4.1.2. Comparing different models The incrementality of the modeling leads to another problem: the results of several versions of a model cannot be compared ceteris paribus because they would not all integrate the same mechanisms and/or types of agents, regardless of implementation and design variants. This is a problem that is also encountered in the development of families of models or in multimodeling practices. The authors of Chapter 4 identify the difficulty in comparing the different models produced as an important limitation

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(section 4.5.4). In these cases, it is difficult to make rigorous quantitative comparisons because the information available is fundamentally different. It seems to us that visual comparisons, which are more qualitative, can at least provide insights into the effectiveness of a particular mechanism or submodel, if only by focusing on visualizations of global structures. This can then play the role of the lowest common denominator. 6.4.2. How should visual comparison be done? These obstacles lead us to specify the means of the visual comparison, both graphically and conceptually. We postulate that the visual analysis of model data is not fundamentally different from the visual analysis of conventional data, and that the visual information-seeking mantra is therefore just as applicable: Overview first, zoom and filter, then details on demand (Shneiderman 1996, p. 2). By transposing this mantra to the visualization of data from geographical modeling, we can therefore encourage top-down data exploration, i.e. by devoting the first visual analyses to the global, spatial, and social structures produced by the model, before analyzing more specific parts of the model if necessary. 6.4.2.1. Comparing overviews Many methods allow the visual comparison of data, both statistical and spatial (Figure 6.11).

Figure 6.11. Some types of graphs for visual comparison (Ribecca 2018a). For a color version of this figure, see www.iste.co.uk/pumain/geographical.zip

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However, one of the difficulties in visualizing simulated data is the stochasticity of the models. In terms of visualizations, this implies that a comparison of two versions of a model cannot be based on the comparison of two data sets, but rather on the comparison of two sets of data sets. Where most manuals make a strong distinction between the representation for the purpose of comparison and the representation for data aggregation, the visualization of simulated data involves linking the two. For example, it will therefore be necessary to compare the evolution of a quantitative attribute over the duration of the simulation and to add a representation of uncertainty or variance to the classical time series representations – see, for example, Wilke (2019, Chapters 13 and 16) – such as via box plot representations (Figure 6.9). Similarly, for geographical data, the visual vocabulary of uncertainty can also be used to represent on a map, e.g. in proportional symbols, the minimum and maximum values that a spatial object can achieve depending on replication or by replacing proportional symbols with mini-plots indicating this variability (Figure 6.12).

Figure 6.12. An example of a map showing variability using integrated plots in a discretized spatial cartogram. From Ribecca (2018b)

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6.4.2.2. Filters and details on demand In the same way that a model evaluation approach generally begins with a macroscopic analysis before going into the details of microscopic behaviors, Shneiderman (1996) recommends gradually refining the visual exploration of a data set by zooming, filtering, and interacting with visualizations. In face validation analyses, this is a classic approach that agent-based modeling platforms make as intuitive as possible. The static data analysis framework is not well suited to this, especially when it is part of the use of tools with command-line interfaces, which is recommended earlier. However, this observation is likely to change rapidly, given the emergence and democratization of many tools10 which make it accessible and fairly simple to create interactive graphical interfaces – for example allowing us to present different visualizations of data in a linked way, i.e. by reflecting interactions with one view (filtering, zooming, etc.) on the others. These tools are part of the current process of creating interactive dashboards, which aim in particular to facilitate this process of filtering and visual evaluation of a complex set of indicators; see, for example, Few (2006) in general, and Kitchin et al. (2015) for urban geography. From a static point of view, this visual exploration can be enabled by presenting illustrations that are representative of different levels of granularity. Figure 6.13 illustrates this approach: it provides information on the diversity of patterns in the evolution of the former Soviet Union system of cities that can be obtained with the MARIUS model (Cottineau 2014). To do this, the plot on the left summarizes the variability of possible outcomes, using two indicators (population growth and system ranking). The strong abstraction of the relative positioning of the simulations is explained and detailed in the second plot, which shows nine examples of demographic trajectories of the system under study; the examples are located in the different quadrants and ends of the first graph. This way, by exemplifying the most different final configurations, we give an understanding, by means of a visual comparison, of the total diversity of configurations that can result from this model.

                                        10 Examples include shiny (Chang et al. 2017) and flexdashboard (Iannone et al. 2018) in R, Dash (Plotly 2017) and Bokeh Development Team (2014) in Python, or Vega-lite (Satyanarayan et al. 2017) in JavaScript.

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Figure 6.13. Visualization and characterization of the different behaviors (patterns) expressed by the MARIUS model (Cottineau 2014) using the PSE (Pattern Space Exploration) method of Chérel et al. (2015). For a color version of this figure, see www.iste.co.uk/pumain/geographical.zip

Whether it is to explore successive versions of a model, a set of random replications, or the result of a massive exploration of the potential behaviors of a family of models, the visual comparison approach makes it possible to provide knowledge about both the model(s) and to force reflexivity on what is modeled. Visualization tools are multiple and scattered, but generally tend to be simplified, around increasingly shared graphical concepts and technologies, largely free, which are moving toward a homogenization of the possibilities of representations and interactions offered. The previous example (Figure 6.13) illustrates the importance of visual comparison, particularly its ability to provide insights to a modeler – or to a scientific audience – on different levels of observation of a model. This last point allows us to return to a fundamental property of visualization: we do not necessarily visualize for ourselves, and depending on the target audiences (model designers, thematic experts, scientists, stakeholders, or the general public), we do not visualize the same objects, and we do not represent them in the same way, either. This has been illustrated, for example, in the field of cartography by the famous cube of cartographic practices (Figure 6.14). In this figure, the three displayed dimensions (task, level of interaction, and level of expertise of users) are linked and only one visualization path is possible, ranging from exploratory to restitution visualization. The use of visualization, as a graphic language, can thus help to communicate the ideas and results of a model throughout its

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life cycle, from its initial design to its mobilization as an awareness tool, if it is adapted at each step to the new target audience.

Figure 6.14. MacEachren’s “Cartography3” Mapping Practices Cube (Livet et al. 2004 [1995]), updated by Çöltekin et al. (2018)

6.5. Visualizing to communicate Concepts related to data visualization are often rooted in the lexical field of language: from the semiology of graphics of Jacques Bertin (1973) to the grammar of graphics of Leland Wilkinson (2006 [1999]), via the “languages of art” of Nelson Goodman (1968) and the “visual explanations” of Edward Tufte (1997), many researchers find in visualization characteristics similar to those of the language. Without going into detail, we can nevertheless retain a strong common point in terms of usage: like a language, visualization is used – or at least allows us – to communicate information. By pointing out the importance of visualization in an interdisciplinary modeling process, it has already been shown that visualization makes it possible to communicate with an audience of experts involved in a common project. However, we would like to highlight other uses of visualization as a means of communicating a model: first, as a tool for dissemination – i.e. for presentation and dialog around the results of a model, within a scientific community or not – and as

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a tool for raising awareness or, in other words, as an instrument for teaching about the social issues raised by a model. 6.5.1. Visualizing to disseminate The study on visualization practices in modeling articles mentioned in section 6.1 (Angus and Hassani-Mahmooei 2015) considers that the majority of visualizations are used in the presentation of model results. Modelers are thus accustomed to the graphical representation of their results, i.e. to illustrate the processes generated by their models. We would like to make a case here for going beyond the simple static visualization of these results. We stated that it has become relatively easy to create interactive visualizations and arrange them within interactive dashboards (section 6.4.2). It seems to us that this practice, made more systematic in the restitution of models, would combine many advantages. First, gathering all the data and visualizations related to a model in a single place would allow the modelers themselves to have a unique, interactive, and accessible resource to extract the visualizations (static or interactive) to be inserted in the different means of communication around their model: by producing a platform for visualization and exploration of the model’s outputs, one guarantees oneself an easy access to these data and their representations. This ease of access for oneself is combined with ease of exchange and communication between the different members involved, whatever the degree and nature of this involvement, in the design and construction of the model: what better tool to discuss internally the results and improvements to be made to a model than a common platform gathering everybody involved around quickly accessible identical visualizations? Second, these internal gains to the modelers can be turned into external communication gains: by presenting a model associated with a data mining tool, an evaluator, a colleague, or any member of public can explore the results themselves and thus understand the message that the model conveys (on the same logic as the “Explorable Explanations” – see section 6.2.3). By making an exploration platform available, the public is thus able to really grasp what is presented, which will probably lead them to pay more attention to the model and its results than if a static description was given: changing an audience from external observer to involved explorer via an intuitive and user-friendly tool can only increase their interest in what is presented.

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A final point relates to one of the requirements of modeling discussed earlier: allowing the data (both inputs and outputs) of a model to be seen and manipulated improves its reproducibility. By using only graphic representations that anyone can faithfully reproduce using a similar interactive visualization platform, the reproducibility of the analyses presented is certified, moreover, if the sources of the platform itself are also made available (Figure 6.15). These practices seem to be extremely virtuous and advantageous for modelers, and we are convinced that the community would benefit from taking greater control of them11.

VARIUS (Cottineau 2015), dedicated to the exploration of the MARIUS model (Cottineau 2014)

                                        11 To our knowledge, such tools are still very rare, both in absolute terms and in terms of the number of model-related publications. Examples can be found in Figure 6.15.

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GibratSim, simulation and exploration of the dynamics of systems of cities (Cura et al. 2017a) Figure 6.15. Examples of interactive model exploration platforms. For a color version of this figure, see www.iste.co.uk/pumain/geographical.zip

6.5.1.1. Visualize to raise awareness Apart from the challenge of promoting a model to a scientific community, visualization can also be part of an approach to raise awareness among a wider and more heterogeneous public. A whole range of modeling in itself focuses on these objectives, particularly in action–research trends, where these approaches are called Companion Modeling or ComMod (2015), Participatory Agent-Based Simulation (Le Page and Perrotton 2018), or Serious Game (e.g. Banos et al. 2018). These approaches support an awareness approach (to climate, civic, and development issues, etc.) based on the use of models, built by modelers or sometimes co-constructed with the target audience. The models can be of different forms (simulation models of course, but also graphic models or even board games), but they are always used as mediation tools between experts in the field, on the one hand, and a wider audience whose awareness is being raised, on the other hand (citizens, populations at risk, public or private stakeholders, etc.).

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These approaches, although old, now seem to be returning to the forefront of science, as shown by the recent call for contributions from the journal NetCom (Henriot and Molines 2019). In the latter, we find in particular an axis that seems to resonate with the comments made above: Contributions are expected: on the relationship of the serious game to its support, as well as on the importance of the indicator table. If the paper format can make the game easily transportable, the digital format ensures a certain playability, by drawing, or by quickly building the players’ intentions. Overall, contributions are expected to discuss the question of the model, simulation and the contribution of real-time indicators, to optimize decisions in the case of games that seek to be plausible and that are part of a technical approach, or on the contrary, by introducing a share of randomness to force players to leave the utopia that everything can be controlled. This seems to fully illustrate the need to create and reflect on graphical, interactive interfaces dedicated to the visualization of models and the exploration of their results, particularly in what it can bring in terms of awareness and involvement of a wider audience rather than the scientific community alone who is interested in modeling. 6.6. Some obstacles inherent in model visualization Throughout this chapter, we have shown how and when visualization, be it static or interactive, can contribute to a better knowledge of a model. The chosen methodological angle was aimed more at encouraging modelers to practice visualization than at providing specific technical advice on the precise modalities of its implementation. To do this, we refer to the plethora of existing resources, several of which have been cited throughout these pages, from the most conceptual works (Bertin 1973; Keim et al. 2008; Tufte 1998 [1990]; Tukey 1977; Wilkinson 2006 [1999]) to the most applied (Kornhauser et al. 2009; Ribecca 2018a; Wilke 2019). In these references and in this chapter, simulation data, variables, and inputs are treated as conventional spatiotemporal data. However, it seems important to note the specifics – or at least the peculiarities – of simulation data compared to the more traditional data that geographers are used to manipulating and visualizing.

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6.6.1. Producing and visualizing massive data The analysis and visualization of simulation data can quickly be based on big data. This refers to data that are potentially too large in volume to be processed on a personal computer using traditional methods and tools. Simulation data can hardly be compared to big data from new data sources, the size of which is only one of the difficulties faced by the analysis12. The need to keep all data related to a simulation has been stressed several times in this chapter, whether for reproducibility reasons or simply to ensure an ability to retrospectively explore behaviors that would not have been considered useful to study in the first place. In this case, the size of data produced during the design and evaluation of a simulation model increases very significantly, until it becomes very largely unusable without using the most recent database management and high-performance computing (HPC) analytical processing methods (Table 6.2). It could be argued that the computing power of personal computers and computer servers is steadily increasing, especially now through the use of graphics processing units (GPUs) rather than conventional processors (CPUs), and that this amount of data would, therefore, not really be an issue. However, this would overlook the fact that model exploration methods are increasing just as much, if not more, resulting in tools that allow us to get to know the models better and better at the cost of a considerable increase in simulations to be performed (see the methods presented in Chapter 5, for example). Furthermore, the storage capacities available to the wide audience increase significantly slower than the ability to produce big data. Mass production thus raises questions at several levels. We cannot pretend to solve these problems here, but we will nevertheless try to give some suggestions that we think deserve to be tried.

                                        12 The characteristics of big data can be summarized using the famous 3Vs: Volume, Velocity and Variety, to which we often add Veracity and Variability. Simulation models produce large but slow-moving and slightly-varying data since they are produced on demand (during simulation) and generated according to the modalities decided by the modeler (who programs the recording of outputs in the format and structure that they wish).

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Data Quantity Memory size

1000 [agents] 100 [time steps] 100 [replications] 100 [experiments] 1000 [explorations]

An agent

1 row

~10 bytes

A time step

1,000 rows

~10 kB

A simulation

100,000 rows

~1 MB

An experiment

1 million ~100 MB rows

A calibrated model

100 million rows

~10 GB

An explored/ known model

100 billion rows

~ 10 TB

Storage and analysis Storage infrastructure

Analysis and visualization tools

Text file

ABM software

Spreadsheet

Interactive statistical tool

Database Command-line management interface system (DBMS) statistical tool Distributed DBMS

Highperformance computing

Table 6.2. Massification of simulation data

6.6.1.1. Data logging The question of the mass of data arises as soon as the simulations are launched: saving a lot of data comes with a substantial cost in terms of the speed of execution of a model due to the time required to write the data. In addition to this cost, there is a significant amount of disk space usage, which can even be one of the bottlenecks in running models through massively parallel solutions such as grid computing (see Chapter 5, section 5.3.4). Most often, data are recorded in plain-text formats, which are not very efficient for recording purposes and require a large amount of disk space. These formats have the advantage of universality and interoperability: they are easy to consult and manipulate regardless of the tools used. By using binary data formats optimized for analytical processing, we can reduce the disk footprint and speed up data recording to a level that makes this step negligible. Examples include the data formats of the Apache Arrow

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consortium13, or the use of in-memory database formats to be serialized at the end of the simulation (for example, SQLite14). It should be noted, however, that these methods must be implemented within agent-based modeling software for greater efficiency and that it is therefore relevant to the developers of these tools to implement them. This can only be encouraged by user requests. 6.6.1.2. Structuring, durability, and querying of data The problem does not stop with the recording of data: whether it is generated in traditional text formats or in more efficient files, their structuring, simulation by simulation, makes their durable and efficient use difficult. When we analyze the simulations one by one, or even aggregate their replications, the support does not matter: the mass and heterogeneity of the queried data remain reasonable. When we want to historicize the versions of a model, or simply compare successive versions or different models (several models resulting from a multi-modeling process, for example), it becomes more complex: the mass of data increases, as does the probability that slight differences in model implementations and outputs could happen. If several sensitivity or calibration analyses are conducted at different stages of a model’s evolution, the mass of data and their heterogeneity can even become a major obstacle to their concomitant analysis. To prevent such bottlenecks, we believe that it is important, from the beginning of a modeling project, to think about how the data will be structured over time. This is now common in the field of geographic data, where the realization of abstract data models is a taught and encouraged practice, but remains too rare in modeling where the computer implementation of the model gives rise to more requirements than the storage of its productions. Table 6.2 gives the amount of data that can be achieved: to cope with it, traditional approaches to re-organization and subsequent restructuring of data do not seem to be desirable or feasible. The use of the methodological cores of the data organization, for example in relational databases, remains a guarantee of reproducibility and external accessibility, and therefore of the durability of stored and archived data. However, traditionally, mobilized                                         13 https://arrow.apache.org. 14 www.sqlite.org.

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tools – personal and centralized databases, such as Access, SQLite, or traditional relational database management systems (DBMS) such as MySQL and PostgreSQL – do not easily meet the constraints imposed by the need for efficient querying and massive storage that simulation data impose15. Modelers are therefore increasingly forced to turn to high-performance DBMS, for example NoSQL mobility or online analytical processing environments (OLAP, column-oriented DBMS, etc.). 6.6.1.3. Data visualization From a thematic point of view, the (geo)visualization of data is relatively unaffected by the amount of input data. The rules and modes of representation or interaction with data do not change significantly, whether the data are big or more traditional. From a technical point of view, however, this poses many problems that any cartographer will have noticed: it is trivial to create a choropleth map of the cities of a U.S. state, whatever the technical solution chosen, but much more difficult to produce such a map on the scale of all 30,000 U.S. incorporated cities: when the software succeeds, the time needed to create the map in practice is considerably longer. These are problems of graphic rendering, i.e. drawing on one canvas all the elements that must be represented. When the data increase, the number of elements that will have to be drawn and rendered (displayed) also increases, sometimes in a more than proportional way. Overall, while visualization, including in geography, has gradually freed itself from display resolution problems by turning to vector representations (pdf, svg, etc.) rather than rasters (images in the most common sense), increasingly big data now often require us to go back using hybrid solutions such as tiling (tile grids, vector or raster) or graphics rendering solutions based on the computing power of graphics processing units (GPUs), such as OpenGL and WebGL. To be able to mobilize such technologies, the practice of visualization cannot be based on traditional tools (e.g. CAD) and will necessarily be rendered on external platforms with strong graphic computing capabilities.

                                        15 For example, with a database composed of 100 million lines, the slightest query in a classic DBMS will take several tens of seconds (indexed PostgreSQL) or even minutes (classic, unoptimized MySQL).

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6.6.2. Visualization of aggregated data The replication dimension of simulation data is another major obstacle to their visual exploration by conventional methods. It has been mentioned above that there are graphical methods for reporting the variability of different replications of a simulation, for example by showing their extremes or by representing the values of dispersion measures (e.g. with box plots). However, it will appear to the modeling geographer that these solutions do not allow them to look at all of the information produced by a model, and therefore to understand the specifics of each replication. 6.6.2.1. Aggregation and variability This is the intrinsic problem in data aggregation processes: it is used to summarize all the modalities of a data distribution into a single (or a few) measure(s). To do this, the overall trend is usually to summarize into central values: mean or median. Sometimes, as in box plots, we also show some additional values, relative to the dispersion of distributions. However, all these measures characterize the average behavior of a model rather than the variability of its outputs. We can thus be more interested in the diversity of results, for example the extreme cases that a model can produce, than in a necessarily smoothed average. This is typically what automated model exploration methods, based on pattern recognition, try to emphasize (see Chapter 5). However, in terms of visualization, most productions remain limited to the representation of average trends or at best to the exemplification of unexpected behaviors (Figure 6.13). To succeed in representing the diversity of the trajectories produced by a model, whether they are simply temporal or spatiotemporal, is thus a difficult exercise. Typologies of spatiotemporal aggregation operations exist (Bach et al. 2014), but their implementation is not easy and tends to apply to ad hoc tools more than to generic models. Figure 6.16 shows an example of such a platform, closely linked to the data of the HU.M.E. empty space colonization model (Coupé et al. 2017a), of which it sought to facilitate exploration. The ambition of the described platform (VisuAgent) was thus to focus the exploration on the diversity of aggregation methods and types of rendering more than on the construction of the usual spatiotemporal evolution indicators.

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Figure 6.16. Visualization of different aggregation methods, on replicative and temporal dimensions, with VisuAgent software (Cura et al. 2014), on HU.M.E. model outputs (Coupé et al. 2017a). For a color version of this figure, see www.iste.co.uk/pumain/geographical.zip

It seems that in a discipline such as geography, which is built by articulating the study of the general and the particular, modelers would do well to consider visual ways of reflecting the full diversity of the trajectories that the models they design can take, in order to always enrich knowledge about what these models say about the systems they represent. 6.6.2.2. Aggregation of geographical data In terms of aggregation, geographical data from simulation can pose a particular problem that is, to our knowledge, very specific to it. Many models are based on a theoretical space, often isotropic, where the likelihood of the spatial configuration as a whole is studied rather than the precise location of the elements. In the Schelling model, for example, the modeled space is not intended to correspond exactly to a real space but constitutes an abstraction of it. The pattern of segregation is more important than its absolute positioning on the plane. Space does not count as such, but it is a relative benchmark against which to judge the spatial relationships,

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distances, gaps, and clusterings that the model shapes. On the other hand, the map is probably the most effective way to communicate information on the spatial configuration to which this model can lead, allowing us to understand the spatial structure generated at a glance: segregated or uniform, made up of large homogeneous groups or islets of segregation, expressing radial segregation or concentric gradients, and so on. However, even if two results are similar in terms of their spatial structure, it is difficult to represent a synthesis map: the specificities of twodimensional statistical distributions complicate the aggregation process. An example is shown in Figure 6.17: the four spatial configurations represented are identical in terms of spatial structure indicators. The first three configurations result from axial rotations and symmetries and are, therefore, strictly transitive. The last configuration is part of the same report as long as the support space is designated as toric, as commonly adopted in the agentbased simulation in theoretical spaces. Mathematically, these four patterns are therefore analogous, a mathematical transformation that allows passage from one to the other. In terms of representation, however, it is extremely difficult to account for an aggregation of these four situations: in practice, any of these maps could be suitable for this role, but the human eye is necessary to achieve it16.

Figure 6.17. Four identical Schelling model configurations, obtained by (2) rotation, (3) axial symmetry, and (4) translation into a toric space, of the first pattern (1)

                                        16 One could, of course, imagine using machine learning methods that would test the similarities between these spatial configurations by automatically rotating, translating, reducing, and so on. However, the complexity of the analysis would increase considerably, considering all possible mathematical operations, as in the Geographical Analysis Machine (GAM) of Openshaw et al. (1987).

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Figure 6.18. Two very similar but non-aggregatable cases of spatiotemporal evolution

The situation is even more difficult in the case of less abstract theoretical spaces, for example, in continuous rather than discrete spaces. Figure 6.18 shows the evolution of two replications of a theoretical model portraying the growth of cities. Spacings, growth rates, places of appearance of new cities and all indicators are almost identical17. Again, a large number of indicators would have to be represented to show the similarity of these two replications, while a map composition largely summarizes this information. However, to the best of our knowledge, it seems to us, once again, strictly impossible to establish a common map that is capable of aggregating the information from these two replications. For the modeler, the two alternatives are therefore either to be satisfied with statistical indicators, which can be aggregated but which will not adequately reflect the spatial situation, or to carry out an observation of each of the maps corresponding to the different data produced by the replications. Similar questions even arise for one-dimensional data, for example with directional statistics (see, for example, Laloux 2015). In the case of angle measurements, in particular, traditional aggregation operations cannot be carried out: the average of two angles of 30° and 330° is not 180°, but 0°, which is immediately apparent on a compass rose, but which is contrary to the usual statistical logic.                                         17 This is not a simple mathematical transformation, hence the imperfect correspondence: the three Southeast cities in simulation A are transposed into the same configuration relative to the Northwest in simulation B, while all the other cities undergo a simple 180° rotation. To a geographer’s eye, however, these two produced spaces will be largely similar.

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This example is not transposable as such to the problem of aggregation of spatial data, and nor do the obstacles highlighted in this section have clear solutions. However, these various elements make it possible to illustrate the difficulties posed by geographical data from models, which we believe constitute stimulating avenues for reflection. 6.7. Conclusion We have shown how the contribution of visualization, widely accepted compared to conventional data, can be significant in the modeling of geographic systems. The practice of graphic representation is rooted in the disciplinary culture of geographers. At the same time, however, we can only observe the weakness of cartographic production in the field of modeling, even though multi-agent simulation software competes for this purpose. In order to encourage modelers to take up the question of visualization, we have highlighted many steps in designing a model where visualization can help the modeler and the thematic experts around them to dialog about the model around a common framework, a disciplinary interface constituted by the representation of the model’s data. Similarly, during the model evaluation process, we propose a method, called visual evaluation, based on the interactive and exploratory analysis of simulation data, always with a view to gaining knowledge of the model as well as the modeled system. These achievements would not really have any real meaning, at least in terms of a cumulative approach to knowledge (Pumain 2005), without an ability to transfer them to a wider audience, whether it be scientists, actors, or a lay public: visualization can facilitate this necessary transfer and thus contribute to the dissemination of the results and lessons of the models. For these contributions to be complete and useful to all, disciplinary transfer cannot be a one-way street: where geographers can benefit from research in data visualization, they would also benefit from addressing the issues specific to data from geographic models. One could say, as a rewording of Banos (2013, p. 76), that empowering geographers and, beyond that, humanities and social science researchers to become more autonomous in their visualization process is also an important contribution to the emergence of a true interdisciplinarity.  

 

   

 

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List of Authors

Paul CHAPRON IGN Laboratoire des Sciences et Technologies de l'Information Géographique (LaSTIG) Saint-Mandé France Clémentine COTTINEAU CNRS UMR 8097 Centre Maurice Halbwachs Paris France Robin CURA Université Paris 1 PanthéonSorbonne CNRS UMR 8504 Géographie-cités France Marion LE TEXIER Université de Rouen CNRS UMR 6266, IDEES France

Denise PUMAIN Université Paris 1 PanthéonSorbonne CNRS UMR 8504 Géographie-cités France Juste RAIMBAULT Institut des Systèmes Complexes Paris-Ile-de-France France Sébastien REY-COYREHOURCQ Université de Rouen CNRS UMR 6266, IDEES France Lena SANDERS CNRS UMR 8504 Géographie-cités Paris France Cécile TANNIER CNRS UMR 6049, ThéMA Besançon France  

Geographical Modeling: Cities and Territories, First Edition. Edited by Denise Pumain. © ISTE Ltd 2019. Published by ISTE Ltd and John Wiley & Sons, Inc.

 

Index

A, B, C accessibility, 11, 13, 17, 34, 38, 55, 63, 64, 66–70, 72, 76, 78, 107, 121, 132, 145, 146, 154, 157, 161, 176, 179, 185 aggregation, 15, 58–60, 79, 80, 83, 93, 95, 98, 101, 102, 141, 155, 157, 165, 175, 185, 187–191 artificial society, 133, 152 big data, 183 calibration, 39, 110, 118, 123, 128, 130, 132, 139, 141–144, 147, 148, 184, 185 cartography, see map, 6, 15, 86, 95–98, 112, 121, 128, 151–153, 178, 186, 191 cellular automata, 25, 129, 152 centrality, 5, 13, 14, 16–18, 23, 92, 93, 127, 146 co-evolution, 21, 144–146 complexity, 1, 38, 44, 52, 95, 97, 98, 102, 106–110, 113, 116–122, 125, 126, 129, 131, 135, 146, 154, 155, 157, 173, 176, 185, 189 configuration, see pattern, 5, 9, 10, 12, 14, 17, 23, 26, 32,

38–41, 43, 53, 55, 57, 66, 69, 72, 76–80, 83, 84, 88, 93, 94, 99, 102–105, 107, 109–111, 120, 129, 141, 147, 148, 176, 188–190 D, E determinism, 4, 8, 128, 170 distance, 4, 6, 8, 10–15, 21, 23, 25–29, 53, 98–100,102, 115, 117, 119, 128, 135, 138 dynamics, 12, 18, 23, 30, 31, 62, 95–97, 99, 102, 104, 114, 121, 122, 125, 127, 129–131, 135, 139, 140, 143, 144, 155, 166, 167, 181 emergence, 1, 2, 4, 7, 9, 14, 16–18, 28–30, 32, 37, 40, 41, 44, 45, 78, 93–96, 111, 112, 125, 128, 131, 133–135, 137, 140, 142, 144, 146, 150, 155, 157, 164, 176, 191 F, G flow, 3, 6, 7, 12, 13, 16, 25, 37, 53, 54, 61, 77, 93, 100, 102, 103, 111, 115, 131, 132, 144

Geographical Modeling: Cities and Territories, First Edition. Edited by Denise Pumain. © ISTE Ltd 2019. Published by ISTE Ltd and John Wiley & Sons, Inc.

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fractal, 14, 17, 20, 23, 60, 61, 66, 84–92 genetic algorithm, 125, 133, 139, 141, 145 geographic information system (GIS), 3, 7, 29, 131, 151, 169 graph, 58, 98, 142, 149, 152, 157, 158, 172, 174, 176, 177 gravitation model, 13, 16, 113, 115, 129, 144 growth, 18, 19, 26, 28, 33, 37, 39–41, 78, 80, 84, 107, 120, 129, 135–138, 144, 145, 153, 176, 190 H, I, K hierarchy, 5, 14, 17–21, 23, 28, 34, 40, 45, 61, 67, 77, 81, 92, 93, 96, 103, 112–116, 119, 135, 136, 144, 156, 159, 171 incremental, 17, 18, 25, 95, 96, 105, 107, 110, 111, 119, 122, 139, 172, 173 innovation diffusion, 18, 20, 25, 56, 113, 129, 138 intensive computing, 133, 134, 141, 143, 147 distributed, 125 interactivity, 14, 30, 66, 118, 163, 168, 169, 176, 179–182, 191 iteration, 45, 48, 61, 66, 77, 91, 92, 103, 109, 133, 141, 162, 164, 168, 172, 173 KIDS model, 32, 44, 46, 50, 51, 101, 162 KISS model, 32, 44, 46, 48, 50, 101, 162 L, M land use, 12, 25, 37, 56, 64, 96, 129 LUTI, 101

map, see cartography, 14, 15, 22, 26, 59, 95–98, 112, 151, 152, 158, 167, 175, 186, 189, 190 mobility daily, 103 model exploration, 115, 118, 125, 132, 156, 161, 177, 179–183, 187 transfers, 98 modeling platform, 119, 133, 152, 169, 176 multi-agent model, 23, 51, 62, 66, 78, 101, 121, 131, 133, 136, 141, 143 multi-scale model, 79, 80, 88, 94 N, O, P network, 7, 15–20, 22, 23, 25–27, 30, 31, 34, 35, 51, 53, 58, 63, 66, 69, 74, 75, 101, 112, 113, 130, 132, 135, 136, 138, 139, 143–147, 168 OpenMOLE, 126, 128, 131–134, 137, 139, 142–149 pattern, see configuration, 21, 24, 33, 34, 44, 77, 81, 87–89, 98, 105, 107, 108, 110–112, 125, 165, 176, 177, 187–189 R range (spatial), 14, 16, 27, 77, 98, 136 region, 3, 5, 7, 10, 11, 14–17, 20, 23, 25, 27, 29, 30, 35, 37, 39, 45, 46, 53, 61, 62, 78, 80–83, 85, 88, 90, 93, 95, 102, 113, 115, 127, 134, 135, 144, 145 reproducibility, 21, 39, 44, 49, 96, 103, 107, 108, 111, 112, 115, 120, 122, 129, 131, 135, 140, 142, 149, 154, 160, 161,

Index

163, 164, 166, 169, 170, 180, 183, 186 risk, 43, 112, 127, 155, 170, 181 S scale, 2, 3, 10, 13–17, 19, 20, 22, 26, 27, 29, 30, 37, 43–46, 49, 53, 95–99, 101, 110–112, 121, 127, 131, 132, 135, 141, 148, 166, 171, 186 dependence, 53 scaling laws, 19, 20, 83 self-organization, 1, 2, 16, 34, 106, 107 semiology of graphics, 160, 178 space–time compression, 25–28 spacing, 5, 11, 14, 34, 66, 128, 146, 156, 190 spatial analysis, 55, 151, 168 autocorrelation, 58, 129 inequality, 60, 136 interaction, 55–57, 99–102, 113, 129, 135, 136, 138 segregation, 101, 189 stochasticity, 128, 170, 174  

225

system of cities, 5, 16, 17, 19, 22, 25, 27, 30, 34, 40, 84, 96, 131–136, 140, 142, 144, 176, 181 T, U, V territorialization, 19, 21 trace, 37 trajectory, 2, 20, 21, 25, 37, 50, 51, 55, 66, 93, 103, 106–109, 122, 129, 130, 135, 143, 147, 176, 187, 188 transport, 12, 13, 16, 17, 26, 27, 53, 63, 64, 66–68, 71, 73–76, 78, 80, 91, 99, 101, 103, 113, 115, 130, 137, 143, 144, 158 urban functions, 113, 129, 136 urbanization, 23, 28, 63, 66, 68, 79, 88, 89, 91, 106, 114, 117 validation, 6, 86, 103, 105, 125, 126, 139, 143, 152, 157, 158, 161, 163, 164, 166, 168, 169, 171, 173, 176

 

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PELLÉ Sophie, REBER Bernard From Ethical Review to Responsible Research and Innovation (Responsible Research and Innovation Set – Volume 3) REBER Bernard Precautionary Principle, Pluralism and Deliberation: Sciences and Ethics (Responsible Research and Innovation Set – Volume 4) VENTRE Daniel Information Warfare – 2nd edition

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