Estimating synonymous and nonsynonymous substitution rates

Partitioning the total substitution rate into synonymous and nonsynonymous components is a key aspect of many analyses in molecular evolution. Numerous methods exist for estimating these rates. However, until recently none of the estimation procedures were based on a sound statistical footing. In this paper, the evolutionary model of Muse and Gaut (1994) is used as the basis for two sets of parameters quantifying silent and replacement substitution rates. The parameters are shown to be equal when the four nucleotides are equally frequent and unequal otherwise. Maximum-likelihood estimation of these parameters is described, and the performance of these estimates is compared to that of existing estimation procedures. It is shown that the estimates of Nei and Gojobori (1986) are not unbiased for either set of parameters, although they provide very good estimates for one set as long as sequence divergence is not too high. However, some disturbing properties are found for the Nei and Gojobori estimates. In particular, it is shown that the expected value of the Nei and Gojobori estimate of silent substitution rate is a function of both the silent and replacement substitution rates. The maximum-likelihood estimates have no such problems.