Implications of long tails in the distribution of mutant effects

Long-tailed distributions possess an infinite variance, yet a finite sample that is drawn from such a distribution has a finite variance. In this work we consider a model of a population subject to mutation, selection and drift. We investigate the implications of a long-tailed distribution of mutant allelic effects on the distribution of genotypic effects in a model with a continuum of allelic effects. While the analysis is confined to asexual populations, it does also have implications for sexual populations. We obtain analytical results for a selectively neutral population as well as one subject to selection. We supplement these analytical results with numerical simulations, to take into account genetic drift. We find that a long-tailed distribution of mutant effects may affect both the equilibrium and the evolutionary adaptive behaviour of a population.