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The non-equilibrium allele frequency spectrum in a Poisson random field framework
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
Uppsala University, Disciplinary Domain of Science and Technology, Biology, Department of Ecology and Genetics, Evolutionary Biology.
2016 (English)In: Theoretical Population Biology, ISSN 0040-5809, E-ISSN 1096-0325, Vol. 111, 51-64 p.Article in journal (Refereed) Published
Abstract [en]

In population genetic studies, the allele frequency spectrum (AFS) efficiently summarizes genome-wide polymorphism data and shapes a variety of allele frequency-based summary statistics. While existing theory typically features equilibrium conditions, emerging methodology requires an analytical understanding of the build-up of the allele frequencies over time. In this work, we use the framework of Poisson random fields to derive new representations of the non-equilibrium AFS for the case of a Wright-Fisher population model with selection. In our approach, the AFS is a scaling-limit of the expectation of a Poisson stochastic integral and the representation of the non-equilibrium AFS arises in terms of a fixation time probability distribution. The known duality between the Wright-Fisher diffusion process and a birth and death process generalizing Kingman's coalescent yields an additional representation. The results carry over to the setting of a random sample drawn from the population and provide the non-equilibrium behavior of sample statistics. Our findings are consistent with and extend a previous approach where the non-equilibrium AFS solves a partial differential forward equation with a non-traditional boundary condition. Moreover, we provide a bridge to previous coalescent-based work, and hence tie several frameworks together. Since frequency-based summary statistics are widely used in population genetics, for example, to identify candidate loci of adaptive evolution, to infer the demographic history of a population, or to improve our understanding of the underlying mechanics of speciation events, the presented results are potentially useful for a broad range of topics.

Place, publisher, year, edition, pages
2016. Vol. 111, 51-64 p.
Keyword [en]
Population genetics; Non-equilibrium allele frequency spectrum; Poisson random field; Coalescent theory; Duality relation; Natural selection
National Category
Evolutionary Biology
Identifiers
URN: urn:nbn:se:uu:diva-300226DOI: 10.1016/j.tpb.2016.06.003ISI: 000383923400006PubMedID: 27378747OAI: oai:DiVA.org:uu-300226DiVA: diva2:951143
Available from: 2016-08-06 Created: 2016-08-06 Last updated: 2016-10-18Bibliographically approved

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