Non-Equivalent Loci and the Distribution of Mutant Effects

J. J. Welch and D. Waxman

Genetics 161: 897-904 (2002)

Centre for the Study of Evolution, School of Biological Sciences, University of Sussex, Brighton BN1 9QG, Sussex UK

It has been repeatedly observed that the distribution of new mutations of a quantitative trait has a kurtosis (a statistical measure of the distribution's shape) that is systematically larger than that of a normal distribution. Here we suggest that rather than being a property of individual loci that control the trait, the enhanced kurtosis is highly likely to be an emergent property that arises directly from the loci being mutationally non-equivalent. We present a method of incorporating non-equivalent loci into quantitative genetic modelling, and give an approximate relation between the kurtosis of the mutant distribution and the degree of mutational non-equivalence of loci. We go on to ask whether incorporating the experimentally observed kurtosis through non-equivalent loci, rather than at locus level affects any biologically important conclusions of quantitative genetic modelling. Concentrating on the maintenance of quantitative genetic variation by mutation-selection balance we conclude that typically, non-equivalent loci yield a genetic variance that is of order 10% smaller than that obtained from the previous approaches. For large populations, when the kurtosis is large, the genetic variance may be less than 50% of the result of equivalent loci, with Gaussian distributions of mutant effects.