Fixation probability of an allele in a subdivided population with asymmetric migration

Abstract

The question of loss of genetic diversity in spatially structured populations has been considered by many authors, who have either assumed symmetric migration between subpopulations or restricted the analysis to two subpopulations and allowed asymmetric migration. In this paper we briefly discuss the two-subpopulation case that has been dealt with by other authors and then find a general formula for fixation probabilities for a population divided into three and four subpopulations. The number of individuals in the subpopulations can be different, but the size of each subpopulation is constant over time. Migration between the subpopulations may be asymmetric, that is the number of migrants moving from subpopulation i to subpopulation j is not the same as the number of migrants moving from subpopulation j to subpopulation i. When migration is symmetric, the results of previous authors are confirmed. The result for asymmetric migration shows that the influence a subpopulation has on the fixation probability for the whole population is determined by its size and the net amount of gene flow out of the subpopulation, directly and indirectly, to the whole population. The position of a subpopulation relative to the other subpopulations (that is, edge versus centre) is only important in that it can determine the amount of net gene flow from a subpopulation. Some examples are given of how this result can be applied, and of applications to conservation genetics. We conclude that when considering a management plan with the intention of maintaining genetic diversity, the relative strength and direction of migration must be considered.