Countering inbreeding with migration 1. Migration from unrelated populations

Abstract

The eff'ecto f migrationo n inbreedingi s moclelledfb r small populationsw ith immigrantsf rom a largeu nrelatedp opulation. Different migration rates and numbers fbr the two sexes are assumed, and a general recursion equation for inbreeding progressd erived,w hich can be shownt o leadt o an equilibriumi nbreedingc oeftlcientw heret he ef-fbctso f geneticc lrift and migration balance each other. For small migration rates and large numbers of breeding animals it is shown that migration of only the scarcers ex will minimizet he equilibriumi nbreedingM. igrationf rom only one sexw ill alsob e an advantage in small populationsw ith largem igrationr ates.I n smallp opulationsw ith largem igrationr atesf -ewemr igrantsa ren ecessary for a givene quilibriumi nbreedingc oetficienth ani n largep opulationsw ith smallm igrationr ates.F inally,a n equation is derived for situations where the number of femaies is so large that their contribution to inbreeding can be ignored. Simple tablesa re given for the equilibriumi nbreedingc oefficientsw heret he numbero f migrantsa nclh erd sizesa ret akeni nto consideration. The general impression fiom these tables is that, for equal numbers of the two sexes, the provision of 2-4 migrantst o a populations houlds tabilizein breedingI.n populationws ith low malet o femaler atios,w hereo nly rhei nbreeding fiom the males idei s importanto, neo r two malem igrantss houlds tabilizeth e inbreedins.

Die effek van migrasieo p intelingi s gemodelleevr ir kiein bevolkingsn iet immigranteu it 'n grooto nverwanteb evolking. Verskillendem igrasietempo'esn aantallem anlikee n vrouliked ierei s verondersteeln 'n algemenere kursievergelyking vir die vorderingv an intelingi s afgelei.S o'n rekursievergelykinlegi tot'n ewewigsintelingskoeffisiewnata rd ie uitwerking van genetiesem onsteringe n migrasiei n balansi s. In die gevalv an klein migrasietempo'esn 'n groot aantalt eelcliere worcl daarb ewysd at migrasiev and ie geslagm etd ie kleinstea antatl eeldierec liee wewigsintelinsga lm inimaliseerM. igrasiev an eeng eslags al ook'n voordeelh 0 in klein bevolkingsm et grootm igrasietempo'sIn. klein bevolkingsm et gepaardgaancle grootm igrasietempo'iss minderm igranten odigv ir 'n gegewee wewigsintelin-qskoefflsaiesni nt grootb evolkings met klein migrasietempo'sA. s grensgevails 'n vergelykinga fgeleiw aard ie aantalv roulikei ndividues o gioot is dat hulle bydraet ot inteling weglaatbaakr lein is. Gebruiksvriendeliktea bellev ir ewewigsintelingw ord gegeew aark uclclegrootteesn die aantal migrantei n ag geneemw ord. Die algemenein druki n hierclieta bellei s dat 2-4 migrantei ntelings al beheerv ir ,n gelyke aantalm anlike en vroulike diere. Met groot genoega antallev roulike diere,s odath ulle bydraet ot inteling negeerbaaiir ,behoo( eeno f twee manliked ierei nteling binnea anvaarbarger enset e hou.

Keywords: Inbreeding, migration, sex differences.