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The impact of selection in the $\Lambda$-Wright-Fisher model


 
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1. Title Title of document The impact of selection in the $\Lambda$-Wright-Fisher model
 
2. Creator Author's name, affiliation, country Clément Foucart; Humboldt-Universität zu Berlin; Germany
 
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4. Description Abstract

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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7. Date (YYYY-MM-DD) 2013-08-24
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/2838
 
10. Identifier Digital Object Identifier 10.1214/ECP.v18-2838
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 18
 
12. Language English=en en
 
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