Evolutionary distances for protein-coding sequences: modeling site-specific residue frequencies.

Estimation of evolutionary distances from coding sequences must take into account protein-level selection to avoid relative underestimation of longer evolutionary distances. Current modeling of selection via site-to-site rate heterogeneity generally neglects another aspect of selection, namely position-specific amino acid frequencies. These frequencies determine the maximum dissimilarity expected for highly diverged but functionally and structurally conserved sequences, and hence are crucial for estimating long distances. We introduce a codon-level model of coding sequence evolution in which position-specific amino acid frequencies are free parameters. In our implementation, these are estimated from an alignment using methods described previously. We use simulations to demonstrate the importance and feasibility of modeling such behavior; our model produces linear distance estimates over a wide range of distances, while several alternative models underestimate long distances relative to short distances. Siteto-site differences in rates, as well as synonymous/nonsynonymous and first/second/third-codon-position differences, arise as a natural consequence of the site-to-site differences in amino acid frequencies.