  Two major sources of stochasticity in the dynamics of neutral alleles result
from resampling of finite populations (genetic drift) and the random genetic
background of nearby selected alleles on which the neutral alleles are found
(linked selection). There is now good evidence that linked selection plays an
important role in shaping polymorphism levels in a number of species. One of
the best investigated models of linked selection is the recurrent full sweep
model, in which newly arisen selected alleles fix rapidly. However, the bulk of
selected alleles that sweep into the population may not be destined for rapid
fixation. Here we develop a general model of recurrent selective sweeps in a
coalescent framework, one that generalizes the recurrent full sweep model to
the case where selected alleles do not sweep to fixation. We show that in a
large population, only the initial rapid increase of a selected allele affects
the genealogy at partially linked sites, which under fairly general assumptions
are unaffected by the subsequent fate of the selected allele. We also apply the
theory to a simple model to investigate the impact of recurrent partial sweeps
on levels of neutral diversity, and find that for a given reduction in
diversity, the impact of recurrent partial sweeps on the frequency spectrum at
neutral sites is determined primarily by the frequencies achieved by the
selected alleles. Consequently, recurrent sweeps of selected alleles to low
frequencies can have a profound effect on levels of diversity but can leave the
frequency spectrum relatively unperturbed. In fact, the limiting coalescent
model under a high rate of sweeps to low frequency is identical to the standard
neutral model. The general model of selective sweeps we describe goes some way
towards providing a more flexible framework to describe genomic patterns of
diversity than is currently available.
