Genetic hitch-hiking in spatially extended populations Journal Article

Author(s): Barton, Nicholas H; Etheridge, Alison M; Kelleher, Jerome; Véber, Amandine
Article Title: Genetic hitch-hiking in spatially extended populations
Affiliation IST Austria
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.
Keywords: coalescence; Spatial structure; Hitchhiking; Surfing; Selective sweeps; Fisher-KPP
Journal Title: Theoretical Population Biology
Volume: 87
Issue 1
ISSN: 0040-5809
Publisher: Academic Press  
Date Published: 2013-01-01
Start Page: 75
End Page: 89
DOI: 10.1016/j.tpb.2012.12.001
Notes: We thank two referees for their valuable suggestions and Christine Krebs for her assistance with the figures. The first author’s work was supported by European Research Council grant 250152. The second author’s work was supported in part by EPSRC grant EP/I01361X/1. The third author’s work was supported by EPSRC grant EP/I013091/1. The fourth author’s work was supported by the chaire Modélisation Mathématique et Biodiversité of Veolia Environment - École Polytechnique - Museum National d’Histoire Naturelle - Fondation X and by the ANR project MANEGE (ANR-09-BLAN-0215).
Open access: yes (repository)
IST Austria Authors
  1. Nick Barton
    252 Barton
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