Monte Carlo inference methods in population genetics

We study the distribution of summary statistics of the sample configuration of DNA sequences taken from a large population that has evolved with deterministically varying population size. We study the information available in the number of alleles and segregating sites for estimating the substitution rate, and for making inferences about the time to the most recent common ancestor of the sample. We exploit a Monte Carlo method for solving recurrence equations that define the requisite sampling probabilities. The methods are illustrated with some mitochondrial control region data.