The classical hitchhiking model with continuous mutational pressure and purifying selection.

Detecting selective sweeps driven by strong positive selection and localizing the targets of selection in the genome play a major role in modern population genetics and genomics. Most of these analyses are based on the classical model of genetic hitchhiking proposed by Maynard Smith and Haigh (1974, , 23, 23). Here, we consider extensions of the classical two-locus model. Introducing mutation at the strongly selected site, we analyze the conditions under which soft sweeps may arise. We identify a new parameter (the ratio of the beneficial mutation rate to the selection coefficient) that characterizes the occurrence of multiple-origin soft sweeps. Furthermore, we quantify the hitchhiking effect when the polymorphism at the linked locus is not neutral but maintained in a mutation-selection balance. In this case, we find a smaller relative reduction of heterozygosity at the linked site than for a neutral polymorphism. In our analysis, we use a semi-deterministic approach; i.e., we analyze the frequency process of the beneficial allele in an infinitely large population when its frequency is above a certain threshold; however, for very small frequencies in the initial phase after the onset of selection we rely on diffusion theory.