Decay of genetic variability in geographically structured populations.

The ultimate rate and pattern of approach to equilibrium of a diploid, monoecious population subdivided into a finite number of equal, large, panmictic colonies are calculated. The analysis is restricted to a single locus in the absence of selection, and every mutant is assumed to be new to the population. It is supposed that either the time-independent backward migration pattern is symmetric in the sense that the probability that an individual at position x migrated from y equals the probability that one at y migrated from x, or it depends only on displacements and not on initial and final positions. Generations are discrete and nonoverlapping. Asymptotically, the rate of convergence is approximately (I-u)2t[I-(2NT)-1]t, where u, NT, and t denote the mutation rate, total population size, and time in generations, respectively; the transient part of the probability that two homologous genes are the same allele is approximately independent of their spatial separation. Thus, in this respect the population behaves as if it were panmictic.