Neutral Evolution in Spatially Continuous Populations

Barton, Nick; Depaulis, Frantz; Etheridge, Alison

doi:10.1006/tpbi.2001.1557

Cited by 145 publications

(252 citation statements)

References 13 publications

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“…The scaling is made explicit (in the neutral case) in Lemma 2.7 of Barton et al (2002); this spatial diffusion approximates a wide range of models, both discrete and continuous, provided that the distribution of dispersal distance declines fast enough that the motion of a single ancestral lineage rescales to Brownian motion. To mimic the behaviour of (3) we take N = ρ and m = σ 2 in our simulations.…”

Section: One Dimensional Waves Of Advancementioning

confidence: 99%

Genetic hitchhiking in spatially extended populations

Barton

Etheridge

Kelleher

et al. 2013

Theoretical Population Biology

100

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Section: One Dimensional Waves Of Advancementioning

confidence: 99%

Genetic hitchhiking in spatially extended populations

Barton

Etheridge

Kelleher

et al. 2013

Theoretical Population Biology

100

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“…This can remain of order one as Np', and mp0 (see Fleming & Su, 1974;Nagylaki, 1978 ;Barton et al, 2002).…”

Section: The Effect Of a Barrier In Two Dimensionsmentioning

confidence: 99%

“…When the separation between the genes is large compared with the deme spacing (r>>e), F * converges to the continuous approximation, given by equation (5a) with B=0. The probability of identity of nearby genes (and hence the standardized variance of allele frequency) depends on the local structure, and takes the form log (L/k)/ (4prs 2 ) (Slatkin & Barton, 1990 ;Barton et al, 2002).…”

Section: The Effect Of a Barrier In Two Dimensionsmentioning

confidence: 99%

“…In this paper, I extend previous results to the two-dimensional case, and show that because fluctuations are localized, barriers have effects which can be detected more readily than in a linear habitat. The existence of local fluctuations in two dimensions complicates the mathematical formulation, since the diffusion approximation breaks down over small scales (Nagylaki, 1978;Barton et al, 2002). In the first part of the paper, I ignore this difficulty, and derive analytic results which apply over all but the shortest scales.…”

Section: Introductionmentioning

confidence: 99%

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The effect of a barrier to gene flow on patterns of geographic variation

Barton

2008

Genet. Res.

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SummaryExplicit formulae are given for the effects of a barrier to gene flow on random fluctuations in allele frequency; these formulae can also be seen as generating functions for the distribution of coalescence times. The formulae are derived using a continuous diffusion approximation, which is accurate over all but very small spatial scales. The continuous approximation is confirmed by comparison with the exact solution to the stepping stone model. In both one and two spatial dimensions, the variance of fluctuations in allele frequencies increases near the barrier; when the barrier is very strong, the variance doubles. However, the effect on fluctuations close to the barrier is much greater when the population is spread over two spatial dimensions than when it occupies a linear, one-dimensional habitat : barriers of strength comparable with the dispersal range (B s) can have an appreciable effect in two dimensions, whereas only barriers with strength comparable with the characteristic scale (B L=s= ffiffiffiffiffi ffi 2m p ) are significant in one dimension (m is the rate of mutation or long-range dispersal). Thus, in a two-dimensional population, barriers to gene flow can be detected through their effect on the spatial pattern of genetic marker alleles.

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“…Similar analyses by Lee and Hastings (personal communication) have also found little effect of clumping. Recently, Barton et al (2002) examined the effects of clumping on identity in state for a general densitydependent survival model (of Bolker and Pacala, 1997) that uses two parameters (r and a) to represent the effects of local density on mortality. They gave an example for specific values of r and a, and found virtually no effect on spatial genetic structure.…”

Section: Bk Eppersonmentioning

confidence: 99%

Estimating dispersal from short distance spatial autocorrelation

Epperson

2005

Heredity

124

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A series of theoretical studies has formed a strong connection between spatial statistics observed in populations and summary measures of the amount of dispersal. Synthesized, these developments allow dispersal to be indirectly estimated from standing spatial patterns of genetic variation under a range of conditions broad enough to be likely met in most populations of either plants or animals. The spatial correlations at the shortest distances are particularly robust to range of conditions and have disproportionately high statistical power. This review integrates theoretical results in a way that maximizes robustness and flexibility in the use of short distance autocorrelation to estimate Wright's neighborhood size, or the total variance in dispersal distances. Empirical guidelines are developed that are meant to be as practical and broad as possible. The guidelines focus on Moran's I-statistics for diploid genotypes converted to allele frequencies, but are also extended to or compared with several other approaches. Heredity (2005) 95, 7-15.

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Neutral Evolution in Spatially Continuous Populations

Cited by 145 publications

References 13 publications

Genetic hitchhiking in spatially extended populations

Genetic hitchhiking in spatially extended populations

The effect of a barrier to gene flow on patterns of geographic variation

Estimating dispersal from short distance spatial autocorrelation

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