The Coalescent and Infinite-Site Model of a Small Multigene Family

The infinite-site model of a small multigene family with two duplicated genes is studied. The expectations of the amounts of nucleotide variation within and between two genes and linkage disequilibrium are obtained, and a coalescent-based method for simulating patterns of polymorphism in a small multigene family is developed. The pattern of DNA variation is much more complicated than that in a single-copy gene, which can be simulated by the standard coalescent. Using the coalescent simulation of duplicated genes, the applicability of statistical tests of neutrality to multigene families is considered.

The Amount of DNA Polymorphism Maintained in a Finite Population When the Neutral Mutation Rate Varies Among Sites

The expectations of the average number of nucleotide differences per site (π), the proportion of segregating site (s), the minimum number of mutations per site (s*) and some other quantities were derived under the finite site models with and without rate variation among sites, where the finite site models include Jukes and Cantor's model, the equal-input model and Kimura's model. As a model of rate variation, the gamma distribution was used. The results indicate that if distribution parameter α is small, the effect of rate variation on these quantities are substantial, so that the estimates of θ based on the infinite site model are substantially underestimated, where θ = 4Nv, N is the effective population size and vis the mutation rate per site per generation. New methods for estimating θ are also presented, which are based on the finite site models with and without rate variation. Using these methods, underestimation can be corrected.