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

Nei and Gojobori (1986) developed a simple method to estimate the numbersof synonymous (ds) and nonsynonymous (dN) substitutions per site. In thepresent paper, we have developed a method for computing variances andcovariances of ds's and dN's and of the proportions of synonymous (ps) andnonsynonymous (pN) differences. We also have developed a method forcomputing the variances of mean dS, dN, pS, pN, without constructing aphylogenetic tree of the genes. We have conducted computer simulationsbased on simple evolutionary models and have shown that the new methodgives good estimates of variances and covariances.