Confidence Limits on Phylogenies With a Molecular Clock

For three species in the presence of a molecular clock, it is possible to compute how many steps a phylogeny must have to be significantly worse than the most parsimonious phylogeny. This analysis extends the pioneering work of Cavender (1978, 1981) by taking advantage of the constraints imposed by the assumption of a molecular clock. The distribution of two statistics is obtained by direct enumeration of all possible outcomes in a worst-case phylogeny which has a trifurcation. The two statistics are the number of fewer steps in the best tree than in the next best tree, and the number of “phylogenetically informative” characters supporting the best tree. These two statistics prove to be approximately equivalent in statistical power, and tables of 95%-significance values are provided for each. The possible extension of these results to more than three species is discussed. The enumeration of all outcomes also allows us to compute exact tail probabilities for Templeton's (1983) test of one tree against another. His test is not exactly correct, but usually is conservative when used as a two-tailed test.