Rate Matrix Estimation From Site Frequency Data

A procedure is described for estimating evolutionary rate matrices from observed site frequency data. The procedure assumes (1) that the data are obtained from a constant size population evolving according to a stationary Wright-Fisher model; (2) that the data consist of a multiple alignment of a moderate number of sequenced genomes drawn randomly from the population; and (3) that within the genome a large number of independent, neutral sites evolving with with a common mutation rate matrix can be identified. No restrictions are imposed on the scaled rate matrix other than that the off-diagonal elements are positive and <<1, and that the rows sum to zero. In particular the rate matrix is not assumed to be reversible. The key to the method is an approximate stationary solution to the forward Kolmogorov equation for the multi-allele neutral Wright-Fisher model in the limit of low mutation rates.