Site-specific evolutionary rates in proteins are better modeled as non-independent and strictly relative

Motivation: In a nucleotide or amino acid sequence, not all sites evolve at the same rate, due to differing selective constraints at each site. Currently in computational molecular evolution, models incorporating rate heterogeneity always share two assumptions. First, the rate of evolution at each site is assumed to be independent of every other site. Second, the values of these rates are assumed to be drawn from a known prior distribution. Although often assumed to be small, the actual effect of these assumptions has not been previously quantified in the literature. Results: Herein we describe an algorithm to simultaneously infer the set of n-1 relative rates that parameterize the likelihood of an n-site alignment. Unlike previous work (a) these relative rates are completely identifiable and distinct from the branch-length parameters, and (b) a far more general class of rate priors can be used, and their effects quantified. Although described in a Bayesian framework, we discuss a future maximum likelihood extension. Conclusions: Using both synthetic data and alignments from the Myc, Max and p53 protein families, we find that inferring relative rather than absolute rates has several advantages. First, both empirical likelihoods and Bayes factors show strong preference for the relative-rate model, with a mean Delta 1nP=-0.458 per alignment site. Second, the computed likelihoods and Bayes factors were essentially independent of the relative-rate prior, indicating that good estimates of the posterior rate distribution are not required a priori. Third, a novel finding is that rates can be accurately inferred even when up to approximate to 4 substitutions per site have occurred. Thus biologically relevant putative hypervariable sites can be identified as easily as conserved sites. Lastly, our model treats rates and tree branch-lengths as completely identifiable, allowing for the first time coherent simultaneous inference of branch-lengths and site-specific evolutionary rates.