FIXATION PROBABILITY OF AN ALLELE IN A SUBDIVIDED POPULATION WITH ASYMMETRIC MIGRATION

The question of loss of genetic diversity in spatially structured popu lations has been considered by many authors, who have either assumed s ymmetric migration between subpopulations or restricted the analysis t o two subpopulations and allowed asymmetric migration. In this paper w e briefly discuss the two-subpopulation case that has been dealt with by other authors and then find a general formula for fixation probabil ities 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 t he subpopulations may be asymmetric, that is the number of migrants mo ving from subpopulation i to subpopulation j is not the same as the nu mber 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 subpop ulation has on the fixation probability for the whole population is de termined by its size and the net amount of gene flow out of the subpop ulation, directly and indirectly, to the whole population. The positio n of a subpopulation relative to the other subpopulations (that is, ed ge versus centre) is only important in that it can determine the amoun t of net gene flow from a subpopulation. Some examples are given of ho w this result can be applied, and of applications to conservation gene tics. We conclude that when considering a management plan with the int ention of maintaining genetic diversity, the relative strength and dir ection of migration must be considered.