Estimating selective coefficients of allelic substitutions from patterns of interspecific allozymic mobility difference

Abstract

The neutral hypothesis of molecular evolution predicts that there should be a 1:1 ratio between allozymes in a species which are faster or slower than allozymes at the corresponding loci in a second species. Methods are presented in this paper for estimating selective differentials from observed values of r, the deviation from a fraction of 1/2 in the proportion of substitutions conferring a mobility change in a specified direction. Although the methods were developed for allozymes, they are readily applied to cases where two taxa may differ in other properties, such as DNA sequence. r is related to the selection coefficient s under a ‘genic selection’ model. If a change in one direction is favoured in one species and a change in the other direction is equally favoured in the second species, both s and N are assumed constant and only one substitution has occurred at each locus, then the estimate of s is approximately (ln(1/2+r) − ln(1/2 − r))/4N. If selective coefficients follow an unspecified distribution f(s) and N is assumed constant, then the average value of s lies between r/2N(1/2 + r) and r/2N(1/2 − r). Specifying the distribution of s to enable point estimation of E(s) is mathematically difficult for the usual probability density functions. A new family of distributions is suggested to overcome these difficulties. The analysis is extended to cover estimation of r where more than one substitution has occurred. The range of the various estimates of s provided by these methods from electrophoretic data is usually below 1/N and mostly substantially so.