A nearly-neutral biallelic Moran model with biased mutation and linear and quadratic selection

Abstract

In this article, a biallelic reversible mutation model with linear and quadratic selection is analyzed. The approach reconnects to one proposed by Kimura ( Possibility of extensive neutral evolution under stabilizing selection with special reference to nonrandom use of codons (PNAS,1981)), who starts from a diffusion model and derives its equilibrium distribution up to a constant. We use a boundary-mutation Moran model, which approximates a general mutation model for small effective mutation rates, and derive its equilibrium distribution for polymorphic and monomorphic variants in small to moderately sized populations. Using this model, we show that biased mutation rates and linear selection alone can cause patterns of polymorphism rates within and substitution rates between populations that are usually ascribed to balancing or overdominant selection. We illustrate this using a data set of short introns and fourfold degenerate sites from Drosophila simulans and Drosophila melanogaster.