Statistics of divergence times

Abstract

Given the number of nucleotide substitutions between two species (K) and the substitution rate v, the expectation of the corresponding divergence time is usually calculated as K/(2v). This is strictly true only if v is regarded as a constant because the ratio of two random variables, such as K/(2v), has distributional properties different from those of the distribution of K. Therefore, both the mean and any confidence interval for divergence times are unknown in this situation. We model the distribution of K and v using the Gamma distribution and calculate the mean and 95% confidence interval for the corresponding divergence time. These calculations are compared with results obtained by bootstrapping sequence data from the model plant Arabidopsis thaliana and its relatives. We show that for nonoverlapping pairs of phylogenetic distances, our method approaches the bootstrap results very closely. In contrast, regarding the mutation rate as a constant leads to strong underestimation of the confidence interval. An implementation of our method of computing divergence times is accessible through a web interface at http://www.soft.ice.mpg.de/cite.