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Genealogies of two linked neutral loci after a selective sweep in a large population of stochastically varying size

Part of: Markov processes Limit theorems

Published online by Cambridge University Press:  17 March 2017

Rebekka Brink-Spalink  and
Charline Smadi
Rebekka Brink-Spalink*
Affiliation:
Georg-August-Universität Göttingen
Charline Smadi*
Affiliation:
LISC and University of Oxford
*
* Postal address: Institute for Mathematical Stochastics, Georg-August-Universität Göttingen, Goldschmidtstr. 7, 37077 Göttingen, Germany.
** Current address: Institut des Systèmes Complexes Paris Île-de-France, 113 rue Nationale, 75013 Paris, France. Email address: [email protected]
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Abstract

We study the impact of a hard selective sweep on the genealogy of partially linked neutral loci in the vicinity of the positively selected allele. We consider a sexual population of stochastically varying size and, focusing on two neighboring loci, derive an approximate formula for the neutral genealogy of a sample of individuals taken at the end of the sweep. Individuals are characterized by ecological parameters depending on their genetic type, and governing their growth rate and interactions with other individuals (competition). As a consequence, the `fitness' of an individual depends on the population state and is not an intrinsic characteristic of individuals. We provide a deep insight into the dynamics of the mutant and wild-type populations during the different stages of a selective sweep.

Keywords

Birth-and-death processcoalescentcouplingeco-evolutiongenetic hitchhikingselective sweep

MSC classification

Primary: 92D25: Population dynamics (general) 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 60J27: Continuous-time Markov processes on discrete state spaces 92D15: Problems related to evolution
Secondary: 60F15: Strong theorems
Type
Research Article
Information
Advances in Applied Probability , Volume 49 , Issue 1 , March 2017 , pp. 279 - 326
Copyright
Copyright © Applied Probability Trust 2017 

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