Spatial Simulation: Exploring Pattern and Process

342 Pages·2013·15.984 MB·English

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

Spatial Simulation

Spatial Simulation
Exploring Pattern and Process
David O’Sullivan and George L. W. Perry
University of Auckland – Te Whare Wa¯nanga o Ta¯maki Makaurau,
New Zealand
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O’Sullivan,David,1966–
Spatialsimulation:exploringpatternandprocess/DavidO’Sullivan,GeorgeL.W.Perry.
pagescm
Includesbibliographicalreferencesandindex.
ISBN978-1-119-97080-4(cloth)–ISBN978-1-119-97079-8(paper)
1.Spatialdatainfrastructures–Mathematicalmodels.2.Spatialanalysis(Statistics)I.Perry,
GeorgeL.W.II.Title.
QA402.O7972013
003–dc23
2012043887
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Contents
Foreword xiii
Preface xv
Acknowledgements xix
Introduction xxi
About the Companion Website xxv
1 Spatial Simulation Models: What? Why? How? 1
1.1 Whataresimulationmodels? 2
1.1.1 Conceptualmodels 4
1.1.2 Physicalmodels 7
1.1.3 Mathematicalmodels 7
1.1.4 Empiricalmodels 8
1.1.5 Simulationmodels 9
1.2 Howdoweusesimulationmodels? 12
1.2.1 Usingmodelsforprediction 13
1.2.2 Modelsasguidestodatacollection 13
1.2.3 Modelsas‘toolstothinkwith’ 14
1.3 Whydoweusesimulationmodels? 15
1.3.1 Whenexperimentalscienceisdifficult(orimpossible) 16
1.3.2 Complexityandnonlineardynamics 18
1.4 Whydynamicandspatialmodels? 23
1.4.1 Thestrengthsandweaknessesofhighlygeneralmodels 23
1.4.2 Fromabstracttomorerealisticmodels:controllingthecost 27
2 Pattern, Process and Scale 29
2.1 Thinkingaboutspatiotemporalpatternsandprocesses 30
2.1.1 Whatisapattern? 30
viii CONTENTS
2.1.2 Whatisaprocess? 31
2.1.3 Scale 32
2.2 Usingmodelstoexplorespatialpatternsandprocesses 38
2.2.1 Reciprocallinksbetweenpatternandprocess:aspatialmodelof
foreststructure 39
2.2.2 Characterisingpatterns:first-andsecond-orderstructure 40
2.2.3 Usingnullmodelstoevaluatepatterns 43
2.2.4 Density-based(first-order)nullmodels 46
2.2.5 Interaction-based(second-order)nullmodels 48
2.2.6 Inferringprocessfrom(spatio-temporal)pattern 49
2.2.7 Makingthevirtualforestmorerealistic 53
2.3 Conclusions 56
3 Aggregation and Segregation 57
3.1 Backgroundandmotivatingexamples 58
3.1.1 Basicsof(discretespatial)modelstructure 59
3.2 Localaveraging 60
3.2.1 Localaveragingwithnoise 63
3.3 Totalisticautomata 64
3.3.1 Majorityrules 65
3.3.2 Twistedmajorityannealing 68
3.3.3 Life-likerules 69
3.4 Amoregeneralframework:interactingparticlesystems 70
3.4.1 Thecontactprocess 71
3.4.2 Multiplecontactprocesses 73
3.4.3 Cyclicrelationshipsbetweenstates:rock–scissors–paper 76
3.4.4 Votermodels 78
3.4.5 Votermodelswithnoisemutation 80
3.5 Schellingmodels 83
3.6 Spatialpartitioning 86
3.6.1 Iterativesubdivision 86
3.6.2 Voronoitessellations 87
3.7 Applyingtheseideas:morecomplicatedmodels 88
3.7.1 Patternformationonanimals’coats:reaction–diffusionmodels 89
3.7.2 Morecomplicatedprocesses:spatialevolutionarygametheory 91
3.7.3 Morerealisticmodels:cellularurbanmodels 93
4 Random Walks and Mobile Entities 97
4.1 Backgroundandmotivatingexamples 97
4.2 Therandomwalk 99
4.2.1 Simplerandomwalks 99
4.2.2 Randomwalkswithvariablesteplengths 102
4.2.3 Correlatedwalks 103
4.2.4 Biasanddriftinrandomwalks 108
4.2.5 Le´vyflights:walkswithnon-finitesteplengthvariance 109