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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 A John Wiley & Sons, Ltd., Publication Thiseditionfirstpublished2013©2013byJohnWiley&Sons,Ltd Registeredoffice: JohnWiley&Sons,Ltd,TheAtrium,SouthernGate,Chichester,WestSussex,PO198SQ,UK Editorialoffices: 9600GarsingtonRoad,Oxford,OX42DQ,UK TheAtrium,SouthernGate,Chichester,WestSussex,PO198SQ,UK 111RiverStreet,Hoboken,NJ07030-5774,USA Fordetailsofourglobaleditorialoffices,forcustomerservicesandforinformationabouthowto applyforpermissiontoreusethecopyrightmaterialinthisbookpleaseseeourwebsiteat www.wiley.com/wiley-blackwell. Therightoftheauthortobeidentifiedastheauthorofthisworkhasbeenassertedinaccordance withtheUKCopyright,DesignsandPatentsAct1988. Allrightsreserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystem,or transmitted,inanyformorbyanymeans,electronic,mechanical,photocopying,recordingor otherwise,exceptaspermittedbytheUKCopyright,DesignsandPatentsAct1988,withoutthe priorpermissionofthepublisher. Designationsusedbycompaniestodistinguishtheirproductsareoftenclaimedastrademarks.All brandnamesandproductnamesusedinthisbookaretradenames,servicemarks,trademarksor registeredtrademarksoftheirrespectiveowners.Thepublisherisnotassociatedwithanyproductor vendormentionedinthisbook.Thispublicationisdesignedtoprovideaccurateandauthoritative informationinregardtothesubjectmattercovered. LimitofLiability/DisclaimerofWarranty:Whilethepublisherandauthorhaveusedtheirbest effortsinpreparingthisbook,theymakenorepresentationsorwarrantieswiththerespecttothe accuracyorcompletenessofthecontentsofthisbookandspecificallydisclaimanyimplied warrantiesofmerchantabilityorfitnessforaparticularpurpose.Itissoldontheunderstandingthat thepublisherisnotengagedinrenderingprofessionalservicesandneitherthepublishernorthe authorshallbeliablefordamagesarisingherefrom.Ifprofessionaladviceorotherexpertassistance isrequired,theservicesofacompetentprofessionalshouldbesought. LibraryofCongressCataloging-in-PublicationData 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 AcataloguerecordforthisbookisavailablefromtheBritishLibrary. Wileyalsopublishesitsbooksinavarietyofelectronicformats.Somecontentthatappearsinprint maynotbeavailableinelectronicbooks. Coverimage:PhotoisofShinobazuPondintheUenodistrict,Tokyo,April2012. Photocredit:DavidO’Sullivan. CoverdesignbyNickyPerry. Typesetin10.5/13ptTimesTen-RomanbyLaserwordsPrivateLimited,Chennai,India. FirstImpression2013 To Fintan & Malachy and Leo & Ash 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