The variance of pairwise nucleotide differences in two populations with migration

Abstract

The variances of three measures of pairwise difference are derived for the case of two populations that exchange migrants. The resulting expressions can be used to place standard errors on estimates of population genetic parameters. The three measures considered are the average number of intrapopulation nucleotide differences, the average number of interpopulation nucleotide differences, and the net number of nucleotide differences between the two populations. The expectations of these statistics are previously known and suggest that they might be used to the quantify the divergence between populations. However, the standard errors of all three statistics are shown to be quite large relative to their expectations. Thus, our ability to quantify divergence between populations with them is limited, at least using available data. An analysis of mitochondrial DNA sequences from grey-crowned babblers illustrates the application of the theory. The variances derived here for migration are compared to previously published results for two populations that have been completely isolated from one another for some length of time. All three variances are greater under migration than under isolation, suggesting that a test to distinguish these two demographic situations could be developed.