Some effects of subdivision of finite populations on genetic diversity measures

Abstract

<p>Random genetic drift and mutation in subdivided populations are considered in terms of the infinite-alleles Wright-Fisher model.;Moments of the multidimensional frequency spectrum of order n correspond to probabilities of identity for n genes drawn from specified subpopulations. Recursions are developed for moments of arbitrary order.;Several authors have studied the second moments of frequency spectrums for certain population structures. They point out that these second moments can be used to approximate expectations, under the neutrality hypothesis, of some common measures of genetic identity and distance. In the present work, fourth moments and related probabilities are used to approximate variances of these measures. Specific examples are given for two demes, the island model, and the circular stepping stone model.;It stands to reason that the effects of subdivision should vanish if there are large rates of migration among the demes. An analytic proof of this result has recently been given by Nagylaki (1980). This result is confirmed and the effects of smaller migration rates are studied for certain population structures. Even when the population as a whole is not effectively panmictic, the individual subpopulations are, although their effective sizes may be considerably larger than their actual sizes. Moreover, it seems that the distribution of genes in k of the P subpopulations is similar to that of a population with exactly k subpopulations, where the deme sizes and migration rates are so chosen to give the same second moments of the frequency spectrum as from the original population.;Since the distribution of genes can be approximated in this fashion, variances of the genetic identity or distance between two demes of an arbitrary subdivided population can be approximated using a two deme model with appropriate effective migration, mutation and size parameters. Similarly, when the appropriate effective parameters can be found, covariances of distance can be approximated via a four deme model.;;Reference;Nagylaki, T. 1980. The strong-migration limit in geographically structured populations. J. Math. Biol. 9:101-114.</p>