[Evaluation and extension of Markov process models for the evolution of DNA]

Markov process models of nucleotide substitution are evaluated. A model proposed by Lanave et al (1984), alleged to need no priori assumption about the substitution pattern, is found to have the assumption of reversibility. Calculations based on the 2-p, 4-p, and 6-p substitution schemes show that site variation of substitution speed leads to serious under-estimation of sequence divergence by various methods. Spatial pattern variation also leads to under-estimation, but the discrepancy is slight. A nonhomogeneous Markov process model is used to study the temporal variations of rates and it is shown that the estimated number of substitutions reflects a rate averaged over time. The implications of those results to evolutionary phylogenetics are discussed.