Bernoulli factories and duality in Wright-Fisher and Allen-Cahn models of population genetics
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866913218003206144 |
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| author | Koskela, Jere Łatuszyński, Krzysztof Spanò, Dario |
| author_facet | Koskela, Jere Łatuszyński, Krzysztof Spanò, Dario |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_03539 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Bernoulli factories and duality in Wright-Fisher and Allen-Cahn models of population genetics Koskela, Jere Łatuszyński, Krzysztof Spanò, Dario Probability Populations and Evolution 35C99, 60J70, 60J90, 92D10 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. |
| title | Bernoulli factories and duality in Wright-Fisher and Allen-Cahn models of population genetics |
| topic | Probability Populations and Evolution 35C99, 60J70, 60J90, 92D10 |
| url | https://arxiv.org/abs/2306.03539 |