Abstract
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.
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