Spatial Simulation: Exploring Pattern and Process

✍ Scribed by David O'Sullivan, George L. W. Perry

• Publisher: Wiley-Blackwell
• Year: 2013
• Tongue: English
• Leaves: 342
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Cover......Page 1
Title Page......Page 5
Copyright......Page 6
Contents......Page 9
Foreword......Page 15
Preface......Page 17
Acknowledgements......Page 21
Introduction......Page 23
About the Companion Website......Page 27
Chapter 1 Spatial Simulation Models: What? Why? How?......Page 29
1.1 What are simulation models?......Page 30
1.1.1 Conceptual models......Page 32
1.1.3 Mathematical models......Page 35
1.1.4 Empirical models......Page 36
1.1.5 Simulation models......Page 37
1.2 How do we use simulation models?......Page 40
1.2.2 Models as guides to data collection......Page 41
1.2.3 Models as tools to think with'......Page 42<br>1.3 Why do we use simulation models?......Page 43<br>1.3.1 When experimental science is difficult (or impossible)......Page 44<br>1.3.2 Complexity and nonlinear dynamics......Page 46<br>1.4.1 The strengths and weaknesses of highly general models......Page 51<br>1.4.2 From abstract to more realistic models: controlling the cost......Page 55<br>Chapter 2 Pattern, Process and Scale......Page 57<br>2.1.1 What is a pattern?......Page 58<br>2.1.2 What is a process?......Page 59<br>2.1.3 Scale......Page 60<br>2.2 Using models to explore spatial patterns and processes......Page 66<br>2.2.1 Reciprocal links between pattern and process: a spatial model of forest structure......Page 67<br>2.2.2 Characterising patterns: first- and second-order structure......Page 68<br>2.2.3 Using null models to evaluate patterns......Page 71<br>2.2.4 Density-based (first-order) null models......Page 74<br>2.2.5 Interaction-based (second-order) null models......Page 76<br>2.2.6 Inferring process from (spatio-temporal) pattern......Page 77<br>2.2.7 Making the virtual forest more realistic......Page 81<br>2.3 Conclusions......Page 84<br>Chapter 3 Aggregation and Segregation......Page 85<br>3.1 Background and motivating examples......Page 86<br>3.1.1 Basics of (discrete spatial) model structure......Page 87<br>3.2 Local averaging......Page 88<br>3.2.1 Local averaging with noise......Page 91<br>3.3 Totalistic automata......Page 92<br>3.3.1 Majority rules......Page 93<br>3.3.2 Twisted majority annealing......Page 96<br>3.3.3 Life-like rules......Page 97<br>3.4 A more general framework: interacting particle systems......Page 98<br>3.4.1 The contact process......Page 99<br>3.4.2 Multiple contact processes......Page 101<br>3.4.3 Cyclic relationships between states: rock-scissors-paper......Page 104<br>3.4.4 Voter models......Page 106<br>3.4.5 Voter models with noise mutation......Page 108<br>3.5 Schelling models......Page 111<br>3.6.1 Iterative subdivision......Page 114<br>3.6.2 Voronoi tessellations......Page 115<br>3.7 Applying these ideas: more complicated models......Page 116<br>3.7.1 Pattern formation on animals' coats: reaction-diffusion models......Page 117<br>3.7.2 More complicated processes: spatial evolutionary game theory......Page 119<br>3.7.3 More realistic models: cellular urban models......Page 121<br>4.1 Background and motivating examples......Page 125<br>4.2.1 Simple random walks......Page 127<br>4.2.2 Random walks with variable step lengths......Page 130<br>4.2.3 Correlated walks......Page 131<br>4.2.4 Bias and drift in random walks......Page 136<br>4.2.5 L´evy flights: walks with non-finite step length variance......Page 137<br>4.3 Walking for a reason: foraging and search......Page 139<br>4.3.1 Using clues: localised search......Page 143<br>4.3.2 The effect of the distribution of resources......Page 144<br>4.4 Moving entities and landscape interaction......Page 147<br>4.5 Flocking: entity-entity interaction......Page 149<br>4.6 Applying the framework......Page 153<br>4.6.1 Animal foraging......Page 154<br>4.6.2 Humanhunter-gatherers'......Page 156
4.6.4 Constrained environments: pedestrians and evacuations......Page 157
4.6.5 Concluding remarks......Page 159
5.1 Motivating examples......Page 161
5.2.1 What is percolation?......Page 165
5.2.2 Ordinary percolation......Page 166
5.2.3 The lost ant......Page 170
5.2.4 Invasion percolation......Page 173
5.3 Growth (or aggregation) models......Page 176
5.3.1 Eden growth processes: theme and variations......Page 177
5.3.2 Diffusion-limited aggregation......Page 183
5.4.1 Landscape pattern: neutral models and percolation approaches......Page 186
5.4.2 Fire spread: Per Bak's `forest fire model' and derivatives......Page 190
5.4.3 Gullying and erosion dynamics: IP $+$ Eden growth $+$ D......Page 194
5.5 Summary......Page 196
Chapter 6 Representing Time and Space......Page 197
6.1.1 Synchronous and asynchronous update......Page 198
6.1.2 Different process rates......Page 200
6.1.3 Discrete time steps or event-driven time......Page 201
6.1.4 Continuous time......Page 202
6.2.1 Grid or lattice representations......Page 203
6.2.2 Vector-based representation: points, lines, polygons and tessellations......Page 205
6.3.1 Distance in grids and tessellations......Page 207
6.3.2 Neighbourhoods: local spatial relationships......Page 209
6.3.3 Networks of relationships......Page 211
6.4.1 Finite model space......Page 213
6.4.2 Infinitely extensible model space......Page 214
6.4.3 Toroidal model space......Page 215
6.5 Complicated spatial structure without spatial data structures......Page 216
6.6 Temporal and spatial representations can make a difference......Page 218
7.1 Introducing uncertainty......Page 221
7.2 Coping with uncertainty......Page 222
7.2.1 Representing uncertainty in data and processes......Page 223
7.3 Assessing and quantifying model-related uncertainty......Page 226
7.3.2 Sensitivity analysis......Page 228
7.3.3 Uncertainty analysis......Page 230
7.3.4 Analysis of model structural uncertainty......Page 232
7.3.5 Difficulties for spatial data and models......Page 234
7.3.6 Sensitivity and uncertainty analysis for a simple spatial model......Page 235
7.4 Confronting model predictions with observed data......Page 239
7.4.1 Visualisation and difference measures......Page 240
7.4.2 Formal statistical tests......Page 242
7.5.1 Occam's razor......Page 244
7.5.2 Likelihood......Page 245
7.5.3 Multi-model inference......Page 248
7.6 Pattern-oriented modelling......Page 250
7.6.1 POM case-study: understanding the drivers of treeline physiognomy......Page 252
7.7 More to models than prediction......Page 254
Chapter 8 Weaving It All Together......Page 257
8.1 Motivating example: island resource exploitation by hunter-gatherers......Page 258
8.2 Model description......Page 259
8.2.1 Overview......Page 260
8.2.2 Design concepts......Page 264
8.2.3 Details......Page 266
8.3.1 The model development process......Page 272
8.3.2 Model refinement......Page 274
8.4.1 Baseline dynamics......Page 275
8.4.2 Sensitivity analysis......Page 282
8.4.3 Uncertainty analysis......Page 286
8.5 Conclusions......Page 290
9.1 On the usefulness of building-block models......Page 293
9.2 On pattern and process......Page 294
9.3 On the need for careful analysis......Page 296
References......Page 299
Index......Page 327
Supplemental Images......Page 335