Etheridge, A., Freeman, N.P., Penington, S. et al. (1 more author) (2017) Branching Brownian motion and Selection in the Spatial Lambda-Fleming-Viot Process. Annals of Applied Probability, 27 (5). pp. 2605-2645. ISSN 1050-5164
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 $\log(1/\mu)$ where $\mu$ 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 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.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © Institute of Mathematical Statistics. This is an author-produced version of a paper accepted for publication in Annals of Applied Probability. Uploaded in accordance with the publisher's self-archiving policy. |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 17 May 2017 14:26 |
Last Modified: | 02 Feb 2018 11:10 |
Published Version: | https://doi.org/10.1214/16-AAP1245 |
Status: | Published |
Publisher: | Institute of Mathematical Statistics (IMS) |
Refereed: | Yes |
Identification Number: | 10.1214/16-AAP1245 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:99155 |