Electronic Journal of Probability

Tractable diffusion and coalescent processes for weakly correlated loci

Paul Fearnhead, Paul Jenkins, and Yun Song

Full-text: Open access

Abstract

Widely used models in genetics include the Wright-Fisher diffusion and its moment dual, Kingman's coalescent. Each has a multilocus extension but under neither extension is the sampling distribution available in closed-form, and their computation is extremely difficult. In this paper we derive two new multilocus population genetic models, one a diffusion and the other a coalescent process, which are much simpler than the standard models, but which capture their key properties for large recombination rates. The diffusion model is based on a central limit theorem for density dependent population processes, and we show that the sampling distribution is a linear combination of moments of Gaussian distributions and hence available in closed-form. The coalescent process is based on a probabilistic coupling of the ancestral recombination graph to a simpler genealogical process which exposes the leading dynamics of the former. We further demonstrate that when we consider the sampling distribution as an asymptotic expansion in inverse powers of the recombination parameter, the sampling distributions of the new models agree with the standard ones up to the first two orders.

Article information

Source
Electron. J. Probab., Volume 20 (2015), paper no. 58, 25 pp.

Dates
Accepted: 29 May 2015
First available in Project Euclid: 4 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1465067164

Digital Object Identifier
doi:10.1214/EJP.v20-3564

Mathematical Reviews number (MathSciNet)
MR3354618

Zentralblatt MATH identifier
1332.92041

Subjects
Primary: 92D15: Problems related to evolution

Keywords
diffusion sampling distribution coupling population genetics recombination

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Fearnhead, Paul; Jenkins, Paul; Song, Yun. Tractable diffusion and coalescent processes for weakly correlated loci. Electron. J. Probab. 20 (2015), paper no. 58, 25 pp. doi:10.1214/EJP.v20-3564. https://projecteuclid.org/euclid.ejp/1465067164


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