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 (pi), 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 alpha is small, the effect of rate variation on these quantities are substantial, so that the estimates of theta based on the infinite site model are substantially underestimated, where theta = 4Nv, N is the effective population size and v is the mutation rate per site per generation. New methods for estimating theta are also presented, which are based on the finite site models with and without rate variation. Using these methods, underestimation can be corrected.