Variance and covariances of the numbers of synonymous and nonsynonymous substitutions per site

Abstract

Nei and Gojobori (1986) developed a simple method to estimate the numbers of synonymous (d(S)) and nonsynonymous (d(N)) substitutions per site. In the present paper, we have developed a method for computing variances and covariances of d(S)'s and d(N)'s and of the proportions of synonymous (p(S)) and nonsynonymous (p(N)) differences. We also have developed a method for computing the variances of mean d(S), d(N), p(S), p(N), without constructing a phylogenetic tree of the genes. We have conducted computer simulations based on simple evolutionary models and have shown that the new method gives good estimates of variances and covariances.