Unbiased Estimate of Synonymous and Nonsynonymous Substitution Rates with Nonstationary Base Composition

The measurement of synonymous and non-synonymous substitution rates (dS and dN) is useful for assessing selection operating on protein sequences or for investigating mutational processes affecting genomes. In particular, the ratio dNdS is expected to be a good proxy for ω, the ratio of fixation robabilities of non-synonymous mutations relative to that of neutral mutations. Standard methods for estimating dN, dS or ω rely on the assumption that the base composition of sequences is at the equilibrium of the evolutionary process. In many clades, this assumption of stationarity is in fact incorrect, and we show here through simulations and analyses of empirical data that non-stationarity biases the estimate of dN, dS and ω. We show that the bias in the estimate of ω can be fixed by explicitly taking into onsideration non-stationarity in the modeling of codon evolution, in a maximum likelihood framework. Moreover, we propose an exact method for estimating dN and dS on branches, based on stochastic mapping, that can take into account non-stationarity. This method can be directly applied to any kind of codon evolution model, as long as neutrality is clearly parameterized.