A ground-up approach to explaining dynamic spatial modelling for an interdisciplinary audience.Across broad areas of the environmental and social sciences, simulation models are an important way to study systems inaccessible to scientific experimental and observational methods, and also an essential complement to those more conventional approaches. The contemporary research literature is teeming with abstract simulation models whose presentation is mathematically demanding and requires a high level of knowledge of quantitative and computational methods and approaches. Furthermore, simulation models designed to represent specific systems and phenomena are often complicated, and, as a result, difficult to reconstruct from their descriptions in the literature. This book aims to provide a practical and accessible account of dynamic spatial modelling, while also equipping readers with a sound conceptual foundation in the subject, and a useful introduction to the wide-ranging literature.Spatial Simulation: Exploring Pattern and Process is organised around the idea that a small number of spatial processes underlie the wide variety of dynamic spatial models. Its central focus on three 'building-blocks' of dynamic spatial models - forces of attraction and segregation, individual mobile entities, and processes of spread - guides the reader to an understanding of the basis of many of the complicated models found in the research literature. The three building block models are presented in their simplest form and are progressively elaborated and related to real world process that can be represented using them. Introductory chapters cover essential background topics, particularly the relationships between pattern, process and spatiotemporal scale. Additional chapters consider how time and space can be represented in more complicated models, and methods for the analysis and evaluation of models. Finally, the three building block models are woven together in a more elaborate example to show how a complicated model can be assembled from relatively simple components.To aid understanding, more than 50 specific models described in the book are available online at patternandprocess.org for exploration in the freely available Netlogo platform. This book encourages readers to develop intuition for the abstract types of model that are likely to be appropriate for application in any specific context. Spatial Simulation: Exploring Pattern and Process will be of interest to undergraduate and graduate students taking courses in environmental, social, ecological and geographical disciplines. Researchers and professionals who require a non-specialist introduction will also find this book an invaluable guide to dynamic spatial simulation.

Foreword xiiiPreface xvAcknowledgements xixIntroduction xxiAbout the Companion Website xxv1 Spatial Simulation Models: What? Why? How? 11.1 What are simulation models? 21.1.1 Conceptual models 41.1.2 Physical models 71.1.3 Mathematical models 71.1.4 Empirical models 81.1.5 Simulation models 91.2 How do we use simulation models? 121.2.1 Using models for prediction 131.2.2 Models as guides to data collection 131.2.3 Models as 'tools to think with' 141.3 Why do we use simulation models? 151.3.1 When experimental science is difficult (or impossible) 161.3.2 Complexity and nonlinear dynamics 181.4 Why dynamic and spatial models? 231.4.1 The strengths and weaknesses of highly general models 231.4.2 From abstract to more realistic models: controlling the cost 272 Pattern, Process and Scale 292.1 Thinking about spatiotemporal patterns and processes 302.1.1 What is a pattern? 302.1.2 What is a process? 312.1.3 Scale 322.2 Using models to explore spatial patterns and processes 382.2.1 Reciprocal links between pattern and process: a spatial model of forest structure 392.2.2 Characterising patterns: first- and second-order structure 402.2.3 Using null models to evaluate patterns 432.2.4 Density-based (first-order) null models 462.2.5 Interaction-based (second-order) null models 482.2.6 Inferring process from (spatio-temporal) pattern 492.2.7 Making the virtual forest more realistic 532.3 Conclusions 563 Aggregation and Segregation 573.1 Background and motivating examples 583.1.1 Basics of (discrete spatial) model structure 593.2 Local averaging 603.2.1 Local averaging with noise 633.3 Totalistic automata 643.3.1 Majority rules 653.3.2 Twisted majority annealing 683.3.3 Life-like rules 693.4 A more general framework: interacting particle systems 703.4.1 The contact process 713.4.2 Multiple contact processes 733.4.3 Cyclic relationships between states: rock-scissors-paper 763.4.4 Voter models 783.4.5 Voter models with noise mutation 803.5 Schelling models 833.6 Spatial partitioning 863.6.1 Iterative subdivision 863.6.2 Voronoi tessellations 873.7 Applying these ideas: more complicated models 883.7.1 Pattern formation on animals' coats: reaction-diffusion models 893.7.2 More complicated processes: spatial evolutionary game theory 913.7.3 More realistic models: cellular urban models 934 Random Walks and Mobile Entities 974.1 Background and motivating examples 974.2 The random walk 994.2.1 Simple random walks 994.2.2 Random walks with variable step lengths 1024.2.3 Correlated walks 1034.2.4 Bias and drift in random walks 1084.2.5 L¿evy flights: walks with non-finite step length variance 1094.3 Walking for a reason: foraging and search 1114.3.1 Using clues: localised search 1154.3.2 The effect of the distribution of resources 1164.3.3 Foraging and random walks revisited 1194.4 Moving entities and landscape interaction 1194.5 Flocking: entity-entity interaction 1214.6 Applying the framework 1254.6.1 Animal foraging 1264.6.2 Human 'hunter-gatherers' 1284.6.3 The development of home ranges and path networks 1294.6.4 Constrained environments: pedestrians and evacuations 1294.6.5 Concluding remarks 1315 Percolation and Growth: Spread in Heterogeneous Spaces 1335.1 Motivating examples 1335.2 Percolation models 1375.2.1 What is percolation? 1375.2.2 Ordinary percolation 1385.2.3 The lost ant 1425.2.4 Invasion percolation 1455.3 Growth (or aggregation) models 1485.3.1 Eden growth processes: theme and variations 1495.3.2 Diffusion-limited aggregation 1555.4 Applying the framework 1585.4.1 Landscape pattern: neutral models and percolation approaches 1585.4.2 Fire spread: Per Bak's 'forest fire model' and derivatives 1625.4.3 Gullying and erosion dynamics: IP + Eden growth + DLA 1665.5 Summary 1686 Representing Time and Space 1696.1 Representing time 1706.1.1 Synchronous and asynchronous update 1706.1.2 Different process rates 1726.1.3 Discrete time steps or event-driven time 1736.1.4 Continuous time 1746.2 Basics of spatial representation 1756.2.1 Grid or lattice representations 1756.2.2 Vector-based representation: points, lines, polygons and tessellations 1776.3 Spatial relationships: distance, neighbourhoods and networks 1796.3.1 Distance in grids and tessellations 1796.3.2 Neighbourhoods: local spatial relationships 1816.3.3 Networks of relationships 1836.4 Coordinate space: finite, infinite and wrapped 1856.4.1 Finite model space 1856.4.2 Infinitely extensible model space 1866.4.3 Toroidal model space 1876.5 Complicated spatial structure without spatial data structures 1886.6 Temporal and spatial representations can make a difference 1907 Model Uncertainty and Evaluation 1937.1 Introducing uncertainty 1937.2 Coping with uncertainty 1947.2.1 Representing uncertainty in data and processes 1957.3 Assessing and quantifying model-related uncertainty 1987.3.1 Error analysis 2007.3.2 Sensitivity analysis 2007.3.3 Uncertainty analysis 2027.3.4 Analysis of model structural uncertainty 2047.3.5 Difficulties for spatial data and models 2067.3.6 Sensitivity and uncertainty analysis for a simple spatial model 2077.4 Confronting model predictions with observed data 2117.4.1 Visualisation and difference measures 2127.4.2 Formal statistical tests 2147.5 Frameworks for selecting between competing models 2167.5.1 Occam's razor 2167.5.2 Likelihood 2177.5.3 Multi-model inference 2207.6 Pattern-oriented modelling 2227.6.1 POM case-study: understanding the drivers of treeline physiognomy 2247.7 More to models than prediction 2268 Weaving It All Together 2298.1 Motivating example: island resource exploitation by hunter-gatherers 2308.2 Model description 2318.2.1 Overview 2328.2.2 Design concepts 2368.2.3 Details 2388.3 Model development and refinement 2448.3.1 The model development process 2448.3.2 Model refinement 2468.4 Model evaluation 2478.4.1 Baseline dynamics 2478.4.2 Sensitivity analysis 2548.4.3 Uncertainty analysis 2588.5 Conclusions 2629 In Conclusion 2659.1 On the usefulness of building-block models 2659.2 On pattern and process 2669.3 On the need for careful analysis 268References 271Index 299