On investigating the statistical properties of the populous path algorithm by computer simulation

Goodman et al.'s (1974) populous path algorithm for estimating hidden mutational change in protein evolution is designed to be used as an adjunct to the maximum parsimony method. When the algorithm is so used, the augmented maximum parsimony distances, far from being overestimates, are underestimates of the actual number of nucleotide substitutions which occur in Tateno and Nei's (1978) computer simulation by the Poisson process model, even when the simulation is carried out at two and a half times the sequence density. Although underestimates, our evidence shows that they are nevertheless more accurate than estimates obtained by a Poisson correction. In the maximum parsimony reconstruction, there is a bias towards overrepresenting the number of shared nucleotide identities between adjacent ancestral and descendant nodal sequences with the bias being stronger in those portions of the evolutionary tree sparser in sequence data. Because of this particular property of maximum parsimony reconstructed sequences, the conclusions of Tateno and Nei concerning the statistical properties of the populous path algorithm are invalid. We conclude that estimates of protein evolutionary rates by the maximum parsimony - populous path approach will become more accurate rather than less as larger numbers of closely related species are included in the analysis.