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 LambdaFlemingViot. 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 language  English 

Pages (fromto)  26052645 
Number of pages  41 
Journal  Annals of Applied Probability 
Volume  27 
Issue number  5 
DOIs  
Publication status  Published  3 Nov 2017 
Keywords
 Branching
 Branching Brownian motion
 Coalescing
 Natural selection
 Population genetics
 Spatial LambdaFlemingViot process
ASJC Scopus subject areas
 Statistics and Probability
 Statistics, Probability and Uncertainty
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Sarah Penington
 Department of Mathematical Sciences  Lecturer & Royal Society Research Fellow
 Probability Laboratory at Bath
 EPSRC Centre for Doctoral Training in Statistical Applied Mathematics (SAMBa)
Person: Research & Teaching, Researcher