Modeling Multiallelic Selection Using a Moran Model

Abstract

Abstract We present a Moran-model approach to modeling general multiallelic selection in a finite population and show how it may be used to develop theoretical models of biological systems of balancing selection such as plant gametophytic self-incompatibility loci. We propose new expressions for the stationary distribution of allele frequencies under selection and use them to show that the continuous-time Markov chain describing allele frequency change with exchangeable selection and Moran-model reproduction is reversible. We then use the reversibility property to derive the expected allele frequency spectrum in a finite population for several general models of multiallelic selection. Using simulations, we show that our approach is valid over a broader range of parameters than previous analyses of balancing selection based on diffusion approximations to the Wright–Fisher model of reproduction. Our results can be applied to any model of multiallelic selection in which fitness is solely a function of allele frequency.