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2013 The impact of selection in the $\Lambda$-Wright-Fisher model
Clément Foucart
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Electron. Commun. Probab. 18: 1-10 (2013). DOI: 10.1214/ECP.v18-2838


The purpose of this article is to study some asymptotic properties of the $\Lambda$-Wright-Fisher process with selection. This process represents the frequency of a disadvantaged allele. The resampling mechanism is governed by a finite measure $\Lambda$ on $[0,1]$ and selection by a parameter $\alpha$. When the measure $\Lambda$ obeys $\int_{0}^{1}-\log(1-x)x^{-2}\Lambda(dx)<\infty$, some particular behaviour in the frequency of the allele can occur. The selection coefficient $\alpha$ may be large enough to override the random genetic drift. In other words, for certain selection pressure, the disadvantaged allele will vanish asymptotically with probability one. This phenomenon cannot occur in the classical Wright-Fisher diffusion. We study the dual process of the $\Lambda$-Wright-Fisher process with selection and prove this result through martingale arguments.

There is an Erratum in ECP volume 19 paper 15 (2014).


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Clément Foucart. "The impact of selection in the $\Lambda$-Wright-Fisher model." Electron. Commun. Probab. 18 1 - 10, 2013.


Accepted: 24 August 2013; Published: 2013
First available in Project Euclid: 7 June 2016

zbMATH: 1337.60179
MathSciNet: MR3101637
Digital Object Identifier: 10.1214/ECP.v18-2838


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