Bayesian estimation of nonsynonymous/synonymous rate ratios for pairwise sequence comparisons

The nonsynonymous/synonymous rate ratio (omega = d(N)/d(S)) is an important measure of the mode and strength of natural selection acting on nonsynonymous mutations in protein-coding genes. The simplest such analysis is the estimation of the d(N)/d(S) ratio using two sequences. Both heuristic counting methods and the maximum likelihood (ML) method based on a codon substitution model are widely used for such analysis. However, these methods do not have nice statistical properties, as the estimates can be zero or infinity in some datasets, so that their means and variances are infinite. In large genome-scale comparisons, such extreme estimates (either 0 or infinity) of omega and sequence distance (t) are common. Here, we implement a Bayesian method to estimate omega and t in pairwise sequence comparisons. Using a combination of computer simulation and real data analysis we show that the Bayesian estimates have better statistical properties than the ML estimates, because the prior on omega and t shrinks the posterior of those parameters away from extreme values. We also calculate the posterior probability for omega > 1 as a Bayesian alternative to the likelihood ratio test. The new method is computationally efficient and may be useful for genome-scale comparisons of protein-coding gene sequences.