Kinetics of synonymous codon change for an amino acid of arbitrary degeneracy

The kinetics of synonymous codon change and species divergence is described in a matrix formalism that is equally applicable to all levels of codon degeneracy and all levels of codon or nucleotide bias. Based on the formalism it is possible to calculate the sum of all the synonymous substitution rate constants from the observed sequence differences between two species. This sum, the relaxation rate, is equivalent to the LogDet transformation that has recently been proposed as a new measure of evolutionary distance (Lockhardt et al.Mol. Biol. Evol. 11(4): 605–612, 1994). The relationship between this measure and the average number of base changes per site (K) is discussed. The formalism is tested on some sets of simulated sequence divergence data.