Simulating Probability Distributions in the Coalescent

Abstract We describe some computational algorithms for computing probability distributions for sample configurations from the finite-sites models in population genetics. One particular interest is the development of computational methods for estimating substitution rates for DNA sequence data using likelihood techniques. The approach uses a recursion satisfied by the sampling probabilities to construct a Markov chain with a set of absorbing states in such a way that the required sampling distribution is the mean of a functional of the process up to the absorption time. This provides a conceptually simple framework for simulating the likelihood of the data for a set of parameter values. The method is particularly attractive in practice: it is simple to program and can be extended to cover other features of interest such as the infinitely-many-sites process, recombination, selection, and variable population size.