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Geo-mathematical modelling: models from complexity science
Sir Alan Wilson, Centre for Advanced Spatial Analysis, University College London
Mathematical and computer models for a complexity science tool kit
Geographical systems are characterised by locations, activities at locations, interactions between them and the infrastructures that carry these activities and flows. They can be described at a great variety of scales, from individuals and organisations to countries. Our understanding, often partial, of these entities, and in many cases this understanding is represented in theories and associated mathematical models.
In this book, the main examples are models that represent elements of the global system covering such topics as trade, migration, security and development aid together with examples at finer scales. This provides an effective toolkit that can not only be applied to global systems, but more widely in the modelling of complex systems. All complex systems involve nonlinearities involving path dependence and the possibility of phase changes and this makes the mathematical aspects particularly interesting. It is through these mechanisms that new structures can be seen to 'emerge', and hence the current notion of 'emergent behaviour'. The range of models demonstrated include account-based models and biproportional fitting, structural dynamics, space-time statistical analysis, real-time response models, Lotka-Volterra models representing 'war', agent-based models, epidemiology and reaction-diffusion approaches, game theory, network models and finally, integrated models.
Geo-mathematical modelling:
Presents mathematical models with spatial dimensions.
Provides representations of path dependence and phase changes.
Illustrates complexity science using models of trade, migration, security and development aid.
Demonstrates how generic models from the complexity science tool kit can each be applied in a variety of situations
This book is for practitioners and researchers in applied mathematics, geography, economics, and interdisciplinary fields such as regional science and complexity science. It can also be used as the basis of a modelling course for postgraduate students.
Contents
Notes on Contributors xv
Acknowledgements xxi
About the Companion Website xxiii
Part I APPROACHES
1 The Toolkit 3
Alan G. Wilson
Part II ESTIMATING MISSING DATA: BI-PROPORTIONAL FITTING AND PRINCIPAL COMPONENTS ANALYSIS
2 The Effects of Economic and Labour Market Inequalities on Interregional Migration in Europe 9
Adam Dennett
2.1 Introduction 9
2.2 The Approach 12
2.3 Data 12
2.4 Preliminary Analysis 13
2.5 Multinomial Logit Regression Analysis 15
2.6 Discussion 22
2.7 Conclusions 24
References 25
3 Test of Bi-Proportional Fitting Procedure Applied to International Trade 26
Simone Caschili and Alan G. Wilson
3.1 Introduction 26
3.2 Model 27
3.3 Notes of Implementation 28
3.4 Results 30
References 32
4 Estimating Services Flows 33
Robert G. Levy
4.1 Introduction 33
4.2 Estimation Via Iterative Proportional Fitting 34
4.3 Estimating Services Flows Using Commodities Flows 37
4.4 A Comparison of The Methods 40
4.5 Results 45
4.6 Conclusion 49
References 50
5 A Method for Estimating Unknown National Input-Output Tables Using Limited Data 51
Thomas P. Oléron Evans and Robert G. Levy
5.1 Motivation and Aims 51
5.2 Obstacles to The Estimation of National Input-Output Tables 52
5.3 Vector Representation of Input-Output Tables 53
5.4 Method 54
5.5 In-Sample Assessment of The Estimates 58
5.6 Out-of-Sample Discussion of The Estimates 63
5.7 Conclusion 67
References 68
Part III DYNAMICS IN ACCOUNT-BASED MODELS
6 A Dynamic Global Trade Model With Four Sectors: Food, Natural Resources, Manufactured Goods and Labour 71
Hannah M. Fry, Alan G. Wilson and Frank T. Smith
6.1 Introduction 71
6.2 Definition of Variables for System Description 73
6.3 The Pricing and Trade Flows Algorithm 73
6.4 Initial Setup 75
6.5 The Algorithm to Determine Farming Trade Flows 77
6.6 The Algorithm to Determine The Natural Resources Trade Flows 80
6.7 The Algorithm to Determine Manufacturing Trade Flows 81
6.8 The Dynamics 83
6.9 Experimental Results 84
References 90
7 Global Dynamical Input-Output Modelling 91
Anthony P. Korte and Alan G. Wilson
7.1 Towards a Fully Dynamic Inter-country Input-Output Model 91
7.2 National Accounts 92
7.3 The Dynamical International Model 97
7.4 Investment: Modelling Production Capacity: The Capacity Planning Model 100
7.5 Modelling Production Capacity: The Investment Growth Approach 103
7.6 Conclusions 121
References 122
Appendix 123
A.1 Proof of Linearity of the Static Model and the Equivalence of Two Modelling Approaches 123
Part IV SPACE-TIME STATISTICAL ANALYSIS
8 Space-Time Analysis of Point Patterns in Crime and Security Events 127
Toby P. Davies, Shane D. Johnson, Alex Braithwaite and Elio Marchione
8.1 Introduction 127
8.2 Application in Novel Areas 132
8.3 Motif Analysis 138
8.4 Discussion 147
References 148
Part V REAL-TIME RESPONSE MODELS
9 The London Riots -1: Epidemiology, Spatial Interaction and Probability of Arrest 153
Toby P. Davies, Hannah M. Fry, Alan G. Wilson and Steven R. Bishop
9.1 Introduction 153
Contents ix
9.2 Characteristics of Disorder 156
9.3 The Model 158
9.4 Demonstration Case 162
9.5 Concluding Comments 166
References 166
Appendix 168
A.1 Note on Methods: Data 168
A.2 Numerical Simulations 169
10 The London Riots -2: A Discrete Choice Model 170
Peter Baudains, Alex Braithwaite and Shane D. Johnson
10.1 Introduction 170
10.2 Model Setup 170
10.3 Modelling the Observed Utility 172
10.4 Results 176
10.5 Simulating the 2011 London Riots: Towards a Policy Tool 181
10.6 Modelling Optimal Police Deployment 187
References 190
Part VI THE MATHEMATICS OF WAR
11 Richardson Models with Space 195
Peter Baudains
11.1 Introduction 195
11.2 The Richardson Model 196
11.3 Empirical Applications of Richardson's Model 202
11.4 A Global Arms Race Model 204
11.5 Relationship to a Spatial Conflict Model 206
11.6 An Empirical Application 207
11.7 Conclusion 212
References 213
Part VII AGENT-BASED MODELS
12 Agent-based Models of Piracy 217
Elio Marchione, Shane D. Johnson and Alan G. Wilson
12.1 Introduction 217
12.2 Data 219
12.3 An Agent-based Model 221
12.4 Model Calibration 232
12.5 Discussion 232
References 235
13 A Simple Approach for the Prediction of Extinction Events in Multi-agent Models 237
Thomas P. Oléron Evans, Steven R. Bishop and Frank T. Smith
13.1 Introduction 237
13.2 Key Concepts 238
13.3 The NANIA Predator-prey Model 241
13.4 Computer Simulation 247
13.5 Period Detection 249
13.6 A Monte Carlo Approach to Prediction 252
13.7 Conclusions 263
References 264
Part VIII DIFFUSION MODELS
14 Urban Agglomeration Through the Diffusion of Investment Impacts 269
Minette D'Lima, Francesca R. Medda and Alan G. Wilson
14.1 Introduction 269
14.2 The Model 270
14.3 Mathematical Analysis for Agglomeration Conditions 272
14.4 Simulation Results 275
14.5 Conclusions 279
References 279
Part IX GAME THEORY
15 From Colonel Blotto to Field Marshall Blotto 283
Peter Baudains, Toby P. Davies, Hannah M. Fry and Alan G. Wilson
15.1 Introduction 283
15.2 The Colonel Blotto Game and its Extensions 285
15.3 Incorporating a Spatial Interaction Model of Threat 286
15.4 Two-front Battles 288
15.5 Comparing Even and Uneven Allocations in a Scenario with Five Fronts 289
15.6 Conclusion 292
References 292
16 Modelling Strategic Interactions in a Global Context 293
Janina Beiser
16.1 Introduction 293
16.2 The Theoretical Model 294
16.3 Strategic Estimation 295
16.4 International Sources of Uncertainty in the Context of Repression and Rebellion 297
16.5 International Sources of Uncertainty Related to Outcomes 299
16.6 Empirical Analysis 301
16.7 Results 303
16.8 Additional Considerations Related to International Uncertainty 304
16.9 Conclusion 304
References 305
17 A General Framework for Static, Spatially Explicit Games of Search and Concealment 306
Thomas P. Oléron Evans, Steven R. Bishop and Frank T. Smith
17.1 Introduction 306
17.2 Game Theoretic Concepts 307
17.3 Games of Search and Security: A Review 310
17.4 The Static Spatial Search Game (SSSG) 314
17.5 The Graph Search Game (GSG) 324
17.6 Summary and Conclusions 335
References 336
Part X NETWORKS
18 Network Evolution: A Transport Example 343
Francesca Pagliara, Alan G. Wilson and Valerio de Martinis
18.1 Introduction 343
18.2 A Hierarchical Retail Structure Model as a Building Block 344
18.3 Extensions to Transport Networks 345
18.4 An Application in Transport Planning 347
18.5 A Case Study: Bagnoli in Naples 350
18.6 Conclusion 360
References 361
19 The Structure of Global Transportation Networks 363
Sean Hanna, Joan Serras and Tasos Varoudis
19.1 Introduction 363
19.2 Method 364
19.3 Analysis of the European Map 366
19.4 Towards a Global Spatial Economic Map: Economic Analysis by Country 368
19.5 An East-west Divide and Natural Economic Behaviour 373
19.6 Conclusion 376
References 377
20 Trade Networks and Optimal Consumption 378
Robert J. Downes and Robert G. Levy
20.1 Introduction 378
20.2 The Global Economic Model 379
20.3 Perturbing Final Demand Vectors 380
20.4 Analysis 384
20.5 Conclusions 393
Acknowledgements 394
References 394
Appendix 396
Part XI INTEGRATION
21 Research Priorities 399
Alan G. Wilson
Index 403
