Branching Brownian motion and selection in the spatial Lambda-Fleming-Viot process

Alison Etheridge, Nic Freeman, Sarah Penington, Daniel Straulino

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3 Citations (SciVal)

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, Freeman and Straulino (The Brownian net and selection in the spatial Lambda-Fleming-Viot. Preprint). 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 reflects 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.

Original languageEnglish
Pages (from-to)2605-2645
Number of pages41
JournalAnnals of Applied Probability
Volume27
Issue number5
DOIs
Publication statusPublished - 3 Nov 2017

Keywords

  • Branching
  • Branching Brownian motion
  • Coalescing
  • Natural selection
  • Population genetics
  • Spatial Lambda-Fleming-Viot process

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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