The ages of mutations in gene trees

Under the infinitely many sites mutation model, the mutational his-tory of a sample of DNA sequences can be described by a unique gene tree. We show how to find the conditional distribution of the ages of the mutations and the time to the most recent common ancestor of the sam-ple, given this gene tree. Explicit expressions for such distributions seem impossible to find for the sample sizes of interest in practice. We resort to a Monte Carlo method to approximate these distributions. We use this method to study the effects of variable population size and variable muta-tion rates, the distribution of the time to the most recent common ancestor of the population and the distribution of other functionals of the underlying coalescent process, conditional on the sample gene tree. 1. Introduction. The seminal paper of Kimura and Ohta (1973) exploited diffusion theory to derive the expected age and the variance of the age of a neutral mutation observed to have frequency x in a population. This paper stimulated many authors to study the distribution of the age of an allele; th