Sampling theory for neutral alleles in a varying environment

We develop a sampling theory for genes sampled from a population evolving with deterministically varying size. We use a coalescent approach to provide recursions for the probabilities of particular sample configurations, and describe a Monte Carlo method by which the solutions to such recursions can be approximated. We focus on infinite-alleles, infinite-sites and finite-sites models. This approach may be used to find maximum likelihood estimates of parameters of genetic interest, and to test hypotheses about the varying environment. The methods are illustrated with data from the mitochondrial control region sampled from a North American Indian tribe.