Geographical invariance in population genetics

Various quantities of evolutionary interest are shown to be independent of geographical structure. A diploid, monoecious population is subdivided into a finite number of panmictic colonies that exchange migrants. The migration pattern is fixed and ergodic, but otherwise arbitrary. Generations are discrete and non-overlapping; the analysis is restricted to a single locus. Previous results are generalized in the neutral multiallelic case. With selection, it is assumed that there are only two alleles, dominance is absent, selection has the same intensity in all demes, migration does not change the subpopulation numbers, and all evolutionary forces are weak. A diffusion approximation is established for the gene frequencies, and the invariance of the fixation probability and of the moments of the conditional and unconditional total heterozygosities before absorption is demonstrated by a martingale argument.