My slides on this topic provide an overview on this work. Below is a brief description of the work, see the paper for references and more.
There is now good evidence that linked selection plays an important role in shaping patterns of genetic diversity in many of the species examined to date. For example, levels of diversity are lower in regions of low recombination and near genes, which is exactly where linked selection should be more prevalent. However, current models of linked selection are often overly simplistic. For example, the dominant model of positive linked selection — the recurrent full sweep model — assumes that all selected alleles sweep rapidly to fixation. While this may be true of some sweeps, due to changing external and genomic environments many selected alleles may sweep into the population but not be destined for rapid fixation.
Peter and I show that these models can be generalized, as in large populations only the initial fast behavior of selected alleles affects the coalescent at partially linked sites. We develop a flexible model of selective sweeps in a multiple coalescent framework, and show that sweeps to intermediate frequencies can have a profound effect on levels of diversity, but can strongly modify other predictions of the hitchhiking model.
These results suggest that one promising way forward is to estimate the distribution of multiple merger sizes in the coalescent. We are now working on inference machinery to this end, and extending our results to soft sweeps.