THE STRONG-MIGRATION LIMIT FOR THE GENEALOGICAL PROCESS IN GEOGRAPHICALLY STRUCTURED POPULATIONS

In this article we assume that the entire population is subdivided into a finite number of panmictic colonies, each of which consists of a respective number of haploid individuals. We also assume that random genetic drift occurs in each colony and migration among colonies, which is independent of time and ergodic. We study the genealogical process of sampled genes from geographically structured populations. We prove that if the actual total population number is replaced by the effective population number, the mean coalescence time converges to that in a panmictic population in the strong migration limit. We also obtain the geographical distribution of the common ancestor.