Fearnhead, Paul, Jenkins, Paul and Song, Yun S. (2015) Tractable diffusion and coalescent processes for weakly correlated loci. Electronic Journal of Probability, Volume 20 . pp. 1-26. Article number 58. doi:10.1214/EJP.v20-3564 ISSN 1083-6489.

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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.

Item Type:	Journal Article
Subjects:	Q Science > QH Natural history > QH426 Genetics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Statistics
Library of Congress Subject Headings (LCSH):	Population genetics -- Mathematical models
Journal or Publication Title:	Electronic Journal of Probability
Publisher:	University of Washington. Department of Mathematics
ISSN:	1083-6489
Official Date:	29 May 2015
Dates:	Date Event 29 May 2015 Published
Volume:	Volume 20
Number of Pages:	26
Page Range:	pp. 1-26
Article Number:	Article number 58
DOI:	10.1214/EJP.v20-3564
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Open Access (Creative Commons)
Date of first compliant deposit:	29 December 2015
Date of first compliant Open Access:	29 December 2015
Funder:	Engineering and Physical Sciences Research Council (EPSRC), National Institutes of Health (U.S.) (NIH), David & Lucile Packard Foundation
Grant number:	EP/L018497/1 (EPSRC), EP/K014463 (EPSRC), R01-GM094402 (NIH)
Related URLs:	Publisher

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