polygenic adaptation

Coop G & Ralph PL 2012 Patterns of neutral diversity under general models of selective sweeps. Genetics, in press.
doi:10.1534/genetics.112.141861

• 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
• 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
• 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
• 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
• the limiting coalescent model under a high rate of sweeps to low frequency is identical to the standard neutral model

• the rate of neutral genetic drift is independent of recombination rate
• this positive correlation between recombination rates and diversity offers good evidence that linked selection plays a substantial role in the fate of alleles, especially in low recombination regions

• in humans (and other species) there is no strong skew towards rare alleles in low recombination regions
• which ... suggests that full sweeps may have been rare, and that background selection may be the main mode of linked selection, in humans and a number of other species

• fluctuating environments ... and changing genetic backgrounds may often act to prevent alleles achieving rapid fixation within the population
• if multiple mutations affecting the adaptive phenotype segregate during the sweep then it may be that no one of these alleles sweeps to fixation

• we develop a coalescent-based model of patterns of diversity surrounding a selected allele that sweeps into the population but not necessarily to fixation
• if the initial rise of the selected allele is rapid then the coalescent process is primarily affected by this stage, and relatively insensitive to the subsequent dynamics of the selected allele
• we then develop a coalescent model of recurrent sweeps on patterns of neutral diversity in which selected alleles may only reach intermediate frequency

• sweeps that go to intermediate frequency can lead to a greater proportion of high frequency derived alleles than under a full sweep model
• a single, recent full sweep leads to high frequency derived alleles through hitchhiking
• under a recurrent full sweep model these alleles are then fixed in the population by subsequent sweeps and drift
• therefore removed from the frequency spectrum

• the requirement of a high rate of sweeps implies that interference between the sweeps may occur
• although to interfere, the sweeps must begin at very similar times at loci separated by a low recombination rate
• a very high rate of sweeps is needed indeed before interference will have an appreciable impact on the hitchhiking effect

• it seems likely that such full sweeps constitute only a small proportion of the selected loci whose frequency changes in response to adaptation

• the strength of the positive relationship between substitution rates and diversity depends on the fate of alleles that sweep into the population
• this positive relationship may be weak, and a poor predictor of the total reduction in diversity, if the majority of adaptive alleles that initially sweep into the population are eventually lost
• partial sweeps also have a strong effect on linkage disequilibrium and haplotype diversity, a signature that has been exploited in scans for selection