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1、EvolutionofcooperationbymultilevelselectionArneTraulsenandMartinA.Nowak*ProgramforEvolutionaryDynamics,DepartmentsofOrganismicandEvolutionaryBiologyandMathematics,HarvardUniversity,Cambridge,MA02138EditedbySimonA.Levin,PrincetonUniversity,Princeton,NJ,andapprovedMay25,2006(receivedforreviewMarch
2、28,2006)Weproposeaminimaliststochasticmodelofmultilevel(orgroup)Oursimplemodelhassomeinterestingfeatures.Theentireselection.Apopulationissubdividedintogroups.Individualsevolutionarydynamicsaredrivenbyindividualfitness.Onlyinteractwithothermembersofthegroupinanevolutionarygameindividualsareassign
3、edpayoffvalues.Onlyindividualsrepro-thatdeterminestheirfitness.Individualsreproduce,andoffspringduce.Groupscanstaytogetherorsplit(divide)whenreachingareaddedtothesamegroup.Ifagroupreachesacertainsize,itacertainsize.Groupsthatcontainfitterindividualsreachthecansplitintotwo.Fasterreproducingindivid
4、ualsleadtolargercriticalsizefasterand,therefore,splitmoreoften.Thisconceptgroupsthatsplitmoreoften.Inourmodel,higher-levelselectionleadstoselectionamonggroups,althoughonlyindividualsemergesasabyproductofindividualreproductionandpopulationreproduce.Thehigher-levelselectionemergesfromlower-levelst
5、ructure.Wederiveafundamentalconditionfortheevolutionofreproduction.Remarkably,thetwolevelsofselectioncanop-cooperationbygroupselection:ifbc>1nm,thengroupposeeachother.selectionfavorscooperation.TheparametersbandcdenotetheAnyevolutionarygamecanbeanalyzedinourframework,butbenefitandcostofthealtr
6、uisticact,whereasnandmdenotethehere,wefocusontheinteractionbetweencooperatorsandmaximumgroupsizeandthenumberofgroups.Themodelcanbedefectors.Cooperatorspayacost,c,whichensuresthatotherextendedtomorethantwolevelsofselectionandtoincludemembersofthesamegroupreceiveabenefit,b.Defectorspaymigration.no
7、costandprovidenobenefit.Defectorsbenefitfromcooper-atorsthatarepresentinthesamegroup.Inanymixedgroup,finitepopulationsprisoner’sdilemmagroupselectiondefectorshaveahigherpayoffthancooperators.Inhomoge-fixationprobabilitysto
