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1、EvolutionarrestsinvasionsofcooperativepopulationsKirillS.KorolevDepartmentofPhysicsandGraduatePrograminBioinformatics,∗BostonUniversity,Boston,Massachusetts02215,USAPopulationexpansionstriggermanybiomedicalandecologicaltransitions,fromtumorgrowthtoinvasionsofnon-nativespecies.Althoug
2、hpopulationspreadingoftenselectsformoreinvasivephenotypes,weshowthatthisoutcomeisfarfrominevitable.Incooperativepopulations,mutationsreducingdispersalhaveacompetitiveadvantage.Suchmutationsthensteadilyaccumulateattheexpansionfrontbringinginvasiontoahalt.Ourfindingsarearareexampleofevo
3、lutiondrivingthepopulationintoanunfavorablestateandcouldleadtonewstrategiestocombatunwelcomeinvaders.Inaddition,weobtainanexactanalyticalexpressionforthefitnessadvantageofmutantswithdifferentdispersalrates.PACSnumbers:87.23.Kg,05.60.Cd,64.60.-i,87.23.CcLocustswarms,cancermetastasis,and
4、epidemicsareAlleethresholdissufficientlyhigh.Numericalsimula-somefearedexamplesofspatialinvasions.Spatialtionsconfirmedthatevolutioninsuchpopulationsgrad-spreadingistheonlymechanismforspeciestobecomeuallyreducesdispersalandeventuallystopstheinvasionhighlyabundant,whetherweareconsidering
5、abacterialevenwhenmultiplemutantscouldcompetesimultane-colonygrowingonapetridish[1,2]orthehumanexpan-ouslyandothermodelassumptionswererelaxed.sionacrosstheglobe[3].ManyinvasionsareunwelcomeSelectivepressureonthedispersalratecanbeun-becausetheythreatenbiodiversity[4],agriculture[5],or
6、derstoodmostreadilyfromthecompetitionoftwohumanhealth[6].Unfortunately,effortstocontrolortypes(mutants,strains,orspecies)withdifferentdisper-slowdowninvadersoftenfailinpartbecausetheybe-salabilitiesastheyinvadenewterritory.Forsimplicity,comemoreinvasiveovertime[7].Theevolutionofinva-we
7、focusonshort-rangedispersalthatcanbedescribedsivetraitsandinvasionaccelerationhasbeenrepeatedlybyeffectivediffusionandonlyconsiderthedynamicsinobservedinnaturefromthetakeoverofAustraliabycanethedirectionofspreading.Mathematically,themodelistoads[8]totheprogressionofhumancancers[9,10].e
8、xpressedasSe