APPROXIMATE METHODS FOR ESTIMATING THE PATTERN OF NUCLEOTIDE SUBSTITUTION AND THE VARIATION OF SUBSTITUTION RATES AMONG SITES

We propose two approximate methods (one based on parsimony and one on pairwise sequence comparison) for estimating the pattern of nucleotide substitution and a parsimony-based method for estimating the gamma pa rameter for variable substitution rates among sites. The matrix of sub stitution rates that represents the substitution pattern can be recove red through its relationship with the observable matrix of site patter n frequences in pairwise sequence comparisons. Tn the parsimony approa ch, the ancestral sequences reconstructed by the parsimony algorithm w ere used, and the two sequences compared are those at the ends of a br anch in the phylogenetic tree. The method for estimating the gamma par ameter was based on a reinterpretation of the numbers of changes at si tes inferred by parsimony. Three data sets were analyzed to examine th e utility of the approximate methods compared with the more reliable l ikelihood methods. The new methods for estimating the substitution pat tern were found to produce estimates quite similar to those obtained f rom the likelihood analyses. The new method for estimating the gamma p arameter was effective in reducing the bias in conventional parsimony estimates, although it also overestimated the parameter. The approxima te methods are computationally very fast and appear useful for analyzi ng large data sets, for which use of the likelihood method requires ex cessive computation.