Mutation Rate Varies Among Sites

The expectations of the average number of nucleotide differences per site (x), 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 a is small, the effect of rate variation on these quantities are substantial, so that the estimates of 6 based on the infinite site model are substantially underestimated, where 6 = 4Nv, N is the effective population size and vis the mutation rate per site per generation. New methods for estimating 6 are also presented, which are based on the finite site models with and without rate variation. Using these methods, underestimation can be corrected. T HE amount of DNA polymorphism maintained in a population can be estimated from the average number of painvise nucleotide differences per site (lr ) or from the proportion of segregating site ( s ) among a sample of DNA sequences. When the population is panmictic and at equilibrium and when mutations are selectively neutral, KIMURA (1969) and WATTERSON ( 1975) showed by using the infinite site model that the expectations of lr and s are given by E ( T ) = 8 and E ( s ) = a l ( n ) 8 , (1) where 8 = 4Nv, N is the effective population size, u is the neutral mutation rate per site per generation, and