Effects of the shape of distribution of mutant effect in nearly neutral mutation models

Abstract

Models of the theory of nearly neutral mutation incorporate a continuous distribution of mutation effects in contrast to the theory of purely neutral mutation which allows no mutations with intermediate effects. Previous studies of one such model, namely the house-of-cards mutation model, assumed normal distribution of mutation effect. Here I study the house-of-cards mutation model in random-mating finite populations using the weak-mutation approximation, paying attention to the effects of the distribution of mutant effects. The average selection coefficient, substitution rate and average heterozygosity in the equilibrium and transient states were studied mainly by computer simulation. The main findings are: (i) Very rapid decrease of the substitution rate and very slow approach to equilibrium as selection becomes stronger are characteristics of assuming normal distribution of mutant effect. If the right tail of the mutation distribution decays more rapidly than that of the normal distribution, the decrease of substitution rate becomes slower and equilibrium is achieved more quickly. (ii) The dispersion index becomes smaller or larger than 1 depending on the time and the intensity of selection, (iii) LetN be the population size. When selection is strong the ratio of 4N times the substitution rate to the average heterozygosity, which is expected to be 1 under neutrality, is larger than 1 in earlier generations but becomes less than 1 in later generations. These findings show the importance of the distribution of mutant effect and time in determination of the behaviour of various statistics frequently used in the study of molecular evolution.