Differentiation among populations with migration, mutation, and drift: implications for genetic inference

Populations may become differentiated from one another as a result of genetic drift. The amounts and patterns of differentiation at neutral loci are determined by local population sizes, migration rates among populations, and mutation rates. We provide exact analytical expressions for the mean, variance, and covariance of a stochastic model for hierarchically structured populations subject to migration, mutation, and drift. In addition to the expected correlation in allele frequencies among populations in the same geographic region, we demonstrate that there is a substantial correlation in allele frequencies among regions at the top level of the hierarchy. We propose a hierarchical Bayesian model for inference of Wright's F-statistics in a two-level hierarchy in which we estimate the among-region correlation in allele frequencies by substituting replication across loci for replication across time. We illustrate the approach through an analysis of human microsatellite data, and we show that approaches ignoring the among-region correlation in allele frequencies underestimate the amount of genetic differentiation among major geographic population groups by approximately 30%. Finally, we discuss the implications of these results for the use and interpretation of F-statistics in evolutionary studies.