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1、Vol441
2、25May2006
3、doi:10.1038/nature04605LETTERSAsimplerulefortheevolutionofcooperationongraphsandsocialnetworks1,222,32HisashiOhtsuki,ChristophHauert,ErezLieberman&MartinA.NowakAfundamentalaspectofallbiologicalsystemsiscooperation.Inourmodel,theplayersofanevolutionarygame
4、occupytheCooperativeinteractionsarerequiredformanylevelsofbiologicalverticesofagraph.Theedgesdenotelinksbetweenindividualsin14organizationrangingfromsinglecellstogroupsofanimals.termsofgamedynamicalinteractionandbiologicalreproduction.Humansocietyisbasedtoalargeextentonme
5、chanismsthatWeassumethatthegraphisfixedforthedurationoftheevolutionary57promotecooperation.Itiswellknownthatinunstructureddynamics.ConsiderapopulationofNindividualsconsistingofpopulations,naturalselectionfavoursdefectorsovercooperators.cooperatorsanddefectors.Acooperatorhe
6、lpsallindividualstoThereismuchcurrentinterest,however,instudyingevolutionarywhomitisconnected.Ifacooperatorisconnectedtokother817gamesinstructuredpopulationsandongraphs.Theseeffortsindividualsandiofthosearecooperators,thenitspayoffisrecognizethefactthatwho-meets-whomisnot
7、random,butbi2ck.Adefectordoesnotprovideanyhelp,andthereforehasno1824determinedbyspatialrelationshipsorsocialnetworks.Herecosts,butitcanreceivethebenefitfromneighbouringcooperators.Ifwedescribeasurprisinglysimplerulethatisagoodapproxi-adefectorisconnectedtojcooperators,then
8、itspayoffisbj.mationforallgraphsthatwehaveanalysed,includingcycles,Thefitnessofanindividualisgivenbyaconstantterm,denotingspatiallattices,randomregulargraphs,randomgraphsandscale-thebaselinefitness,plusthepayoffthatarisesfromthegame.Strong25,26freenetworks:naturalselectionf
9、avourscooperation,iftheselectionmeansthatthepayoffislargecomparedtothebaselinebenefitofthealtruisticact,b,dividedbythecost,c,exceedsthefitness;weakselectionmeansthepayoffissmallcomparedtotheaveragenumberofneighbours,k,whichmeansb/c>k.Inthisbaselinefitness.Theideabehindweakse
10、lectionisthatmanydifferentcase,cooperationcanevolveasaconsequenceofsocialviscosityfactorscontrib