Polymorphism Data Assist Estimation of the Nonsynonymous over Synonymous Fixation Rate Ratio ω for Closely Related Species

The ratio of nonsynonymous over synonymous sequence divergence, dN/dS, is a widely used estimate of the nonsynonymous over synonymous fixation rate ratio omega, which measures the extent to which natural selection modulates protein sequence evolution. Its computation is based on a phylogenetic approach and computes sequence divergence of protein-coding DNA between species, traditionally using a single representative DNA sequence per species. This approach ignores the presence of polymorphisms and relies on the indirect assumption that new mutations fix instantaneously, an assumption which is generally violated and reasonable only for distantly related species. The violation of the underlying assumption leads to a time-dependence of sequence divergence, and biased estimates of omega in particular for closely related species, where the contribution of ancestral and lineage-specific polymorphisms to sequence divergence is substantial. We here use a time-dependent Poisson random field model to derive an analytical expression of dN/dS as a function of divergence time and sample size. We then extend our framework to the estimation of the proportion of adaptive protein evolution alpha. This mathematical treatment enables us to show that the joint usage of polymorphism and divergence data can assist the inference of selection for closely related species. Moreover, our analytical results provide the basis for a protocol for the estimation of omega and alpha for closely related species. We illustrate the performance of this protocol by studying a population data set of four corvid species, which involves the estimation of omega and alpha at different time-scales and for several choices of sample sizes.