Electronic Communications in Probability

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

Clément Foucart

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).

Article information

Source
Electron. Commun. Probab., Volume 18 (2013), paper no. 72, 10 pp.

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

https://projecteuclid.org/euclid.ecp/1465315611

Digital Object Identifier
doi:10.1214/ECP.v18-2838

Mathematical Reviews number (MathSciNet)
MR3101637

Zentralblatt MATH identifier
1337.60179

Rights

Citation

Foucart, Clément. The impact of selection in the $\Lambda$-Wright-Fisher model. Electron. Commun. Probab. 18 (2013), paper no. 72, 10 pp. doi:10.1214/ECP.v18-2838. https://projecteuclid.org/euclid.ecp/1465315611

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