Author
Etheridge, A
Freeman, N
Penington, S
Straulino, D
Journal title
Annals of Applied Probability
DOI
10.1214/16-AAP1245
Issue
5
Volume
27
Last updated
2024-03-27T22:02:29.937+00:00
Page
2605-2645
Abstract
We ask the question "when will natural selection on a gene in a spatially structured population cause a detectable trace in the patterns of genetic variation observed in the contemporary population?". We focus on the situation in which `neighbourhood size', that is the effective local population density, is small. The genealogy relating individuals in a sample from the population is embedded in a spatial version of the ancestral selection graph and through applying a diffusive scaling to this object we show that whereas in dimensions at least three, selection is barely impeded by the spatial structure, in the most relevant dimension, d = 2, selection must be stronger (by a factor of log(1=μ) where μ is the neutral mutation rate) if we are to have a chance of detecting it. The case d = 1 was handled in Etheridge et al. (2015). The mathematical interest is that although the system of branching and coalescing lineages that forms the ancestral selection graph converges to a branching Brownian motion, this re ects a delicate balance of a branching rate that grows to infinity and the instant annullation of almost all branches through coalescence caused by the strong local competition in the population.
Symplectic ID
644223
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Publication type
Journal Article
Publication date
03 Nov 2017
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