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Bernoulli factories and duality in Wright-Fisher and Allen-Cahn models of population genetics
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Koskela, Jere, Łatuszyński, Krzysztof and Spanò, Dario (2024) Bernoulli factories and duality in Wright-Fisher and Allen-Cahn models of population genetics. Journal of Theoretical Biology, 156 . pp. 40-45. doi:10.1016/j.tpb.2024.01.002 ISSN 0022-5193.
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Official URL: http://doi.org/10.1016/j.tpb.2024.01.002
Abstract
Mathematical models of genetic evolution often come in pairs, connected by a so-called duality relation. The most seminal example are the Wright-Fisher diffusion and the Kingman coalescent, where the former describes the stochastic evolution of neutral allele frequencies in a large population forwards in time, and the latter describes the genetic ancestry of randomly sampled individuals from the population backwards in time. As well as providing a richer description than either model in isolation, duality often yields equations satisfied by quantities of interest. We employ the so-called Bernoulli factory - a celebrated tool in simulation-based computing - to derive duality relations for broad classes of genetics models. As concrete examples, we present Wright-Fisher diffusions with general drift functions, and Allen-Cahn equations with general, nonlinear forcing terms. The drift and forcing functions can be interpreted as the action of frequency-dependent selection. To our knowledge, this work is the first time a connection has been drawn between Bernoulli factories and duality in models of population genetics.
Item Type: | Journal Article | |||||||||
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Subjects: | Q Science > QA Mathematics | |||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | |||||||||
Library of Congress Subject Headings (LCSH): | Differential equations, Partial , Brownian motion processes, Diffusion processes , Genetic algebras, Bernoulli numbers, Mathematical statistics | |||||||||
Journal or Publication Title: | Journal of Theoretical Biology | |||||||||
Publisher: | Elsevier | |||||||||
ISSN: | 0022-5193 | |||||||||
Official Date: | April 2024 | |||||||||
Dates: |
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Volume: | 156 | |||||||||
Page Range: | pp. 40-45 | |||||||||
DOI: | 10.1016/j.tpb.2024.01.002 | |||||||||
Status: | Peer Reviewed | |||||||||
Publication Status: | Published | |||||||||
Access rights to Published version: | Open Access (Creative Commons) | |||||||||
Date of first compliant deposit: | 30 January 2024 | |||||||||
Date of first compliant Open Access: | 7 March 2024 | |||||||||
RIOXX Funder/Project Grant: |
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