VARIANCE TO MEAN RATIO, R(T), FOR POISSON PROCESSES ON PHYLOGENETIC TREES

The ratio of expected variance to mean, R(t), of numbers of DNA base substitutions for contemporary sequences related by a ''star'' phylogeny is widely seen as a measure of the adherence of the sequences' evolution to a Poisson process with a molecular clock, as predicted by the ''neutral theory'' of molecular evolution under certain conditions. A number of estimators of R(t) have been proposed, all predicted to have mean 1 and distributions based on the chi2. Various genes have previously been analyzed and found to have values of R(t) far in excess of 1, calling into question important aspects of the neutral theory. In this paper, I use Monte Carlo simulation to show that the previously suggested means and distributions of estimators of R(t) are highly inaccurate. The analysis is applied to star phylogenies and to general phylogenetic trees, and well-known gene sequences are reanalyzed. For star phylogenies the results show that Kimura's estimators (''The Neutral Theory of Molecular Evolution,'' Cambridge Univ. Press, Cambridge, 1983) are unsatisfactory for statistical testing of R(t), but confirm the accuracy of Bulmer's correction factor (Genetics 123: 615-619, 1989). For all three nonstar phylogenies studied, attained values of all three estimators of R(t), although larger than 1, are within their true confidence limits under simple Poisson process models. This shows that lineage effects can be responsible for high estimates of R(t), restoring some limited confidence in the molecular clock and showing that the distinction between lineage and molecular clock effects is vital. However, these results also indicate that R(t) may be a poor statistic for analyzing the accuracy of Poisson process models and the molecular clock and that tests based on the whole likelihood function are more suitable. (C) 1994 Academic Press, Inc.