Estimating the variability of substitution rates.

Suppose that amino acid or nucleotide data are available for a homologous gene in several species which diverged from a common ancestor at about the same time and that substitution rates between all pairs of species are calculated, correcting as necessary for multiple substitutions and for back and parallel substitutions. The variances and covariances of these corrected substitution rates are evaluated, and are used to construct a new test for uniformity (constancy of the molecular clock) and to find the best estimates of substitution rates in individual lineages with their standard errors. A substantial bias may arise if the effect of correcting the pairwise substitution rates is ignored.