The estimate of total nucleotide substitutions from pairwise differences is biased

Abstract

A nomographic method is presented that estimates the number of nucleotide substitutions since the common ancestor of two nucleotide sequences with no assumption about the proportion of transition and transversion substitutions except that it is constant over time. Of two previous methods of estimating this number, that of M. Kimura (Proc. natn. Acad. Sci. U.S.A. 78, 454-458 (1981) obtains the same result, and is thus confirmed by this work, while that of W. M. Brown, E. M. Prager, A. Wang & A. C. Wilson (J. molec. Evol. 18, 225-239 (1982] does not get the same result. The method presented here also obtains the fraction of all substitutions that are transitions. If one has three or more homologous sequences to compare, one can test the validity of the model by examining the constancy of the estimated proportion of substitutions that are transitions across the various pairs of sequences in a simple visual way. The method is general for any pair of mutually exclusive nucleotide substitutional categories, not just transitions and transversions. Mitochondrial data provide evidence that, for this and probably other current models correcting for superimposed substitutions, one or more of the underlying assumptions is incorrect. This is because there is some unknown systematic bias affecting this evolutionary process. It is suggested that at least part of the bias arises from incorrectly assuming that all sites are variable. In the absence of evidence that this bias is not present in other data, all estimates of the number of substitutions based upon pairs of sequences and current methods of estimating superimposed substitutions at a single site should be viewed as uncertain.