Genetic hitch-hiking in spatially extended populations

Barton, Nicholas H and Etheridge, Alison M and Kelleher, Jerome and Véber, Amandine (2013) Genetic hitch-hiking in spatially extended populations. Theoretical Population Biology, 87. pp. 75-89. ISSN 0040-5809

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Abstract

When a mutation with selective advantage s spreads through a panmictic population, it may cause two lineages at a linked locus to coalesce; the probability of coalescence is exp(−2rT), where T∼log(2Ns)/s is the time to fixation, N is the number of haploid individuals, and r is the recombination rate. Population structure delays fixation, and so weakens the effect of a selective sweep. However, favourable alleles spread through a spatially continuous population behind a narrow wavefront; ancestral lineages are confined at the tip of this front, and so coalesce rapidly. In extremely dense populations, coalescence is dominated by rare fluctuations ahead of the front. However, we show that for moderate densities, a simple quasi-deterministic approximation applies: the rate of coalescence within the front is λ∼2g(η)/(ρℓ), where ρ is the population density and is the characteristic scale of the wavefront; g(η) depends only on the strength of random drift, . The net effect of a sweep on coalescence also depends crucially on whether two lineages are ever both within the wavefront at the same time: even in the extreme case when coalescence within the front is instantaneous, the net rate of coalescence may be lower than in a single panmictic population. Sweeps can also have a substantial impact on the rate of gene flow. A single lineage will jump to a new location when it is hit by a sweep, with mean square displacement ; this can be substantial if the species’ range, L, is large, even if the species-wide rate of sweeps per map length, Λ/R, is small. This effect is half as strong in two dimensions. In contrast, the rate of coalescence between lineages, at random locations in space and on the genetic map, is proportional to (c/L)(Λ/R), where c is the wavespeed: thus, on average, one-dimensional structure is likely to reduce coalescence due to sweeps, relative to panmixis. In two dimensions, genes must move along the front before they can coalesce; this process is rapid, being dominated by rare fluctuations. This leads to a dramatically higher rate of coalescence within the wavefront than if lineages simply diffused along the front. Nevertheless, the net rate of coalescence due to a sweep through a two-dimensional population is likely to be lower than it would be with panmixis.

Item Type: Article
DOI: 10.1016/j.tpb.2012.12.001
Uncontrolled Keywords: coalescence, Spatial structure, Hitchhiking, Surfing, Selective sweeps, Fisher-KPP
Subjects: 500 Science > 570 Life sciences; biology
500 Science > 570 Life sciences; biology > 576 Genetics and evolution
Research Group: Barton Group
SWORD Depositor: Sword Import User
Depositing User: Sword Import User
Date Deposited: 21 Mar 2013 15:20
Last Modified: 05 Sep 2017 14:11
URI: https://repository.ist.ac.at/id/eprint/118

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