Abstract

The Hill-Robertson effect and epistasis are often proposed to explain the prevalence of sexual reproduction and recombination. The Hill-Robertson effect occurs in small populations, where a combination of genetic drift and weak natural selection result in negative linkage disequilibrium. In a large population, however, negative epistasis is the major source of negative linkage disequilibrium. The epistasis can be calculated with two models: the additive model and multiplicative model. In populations of any size, recombination reduces the negative linkage disequilibrium, thus enhancing the population's response to selection. In our research, we examine negative epistasis under quasi-truncation selection. We also study the amount of negative linkage disequilibrium caused by both the Hill-Robertson effect and the negative epistasis under r selection, constant population size, and quasi-truncation selection. In addition, we examine the effect of epistasis calculated with either the additive model or multiplicative model on linkage disequilibrium. We find that non-epistatic selection calculated with the additive model can still generate negative linkage disequilibrium. In large populations, the negative linkage disequilibrium is noteworthily associated with negative epistasis. In addition, recombination does not always speed fixation even if the average linkage disequilibrium is weak negative.