{
  "id": "2306.03539",
  "version": "v1",
  "published": "2023-06-06T09:37:17.000Z",
  "updated": "2023-06-06T09:37:17.000Z",
  "title": "Bernoulli factories and duality in Wright-Fisher and Allen-Cahn models of population genetics",
  "authors": [
    "Jere Koskela",
    "Krzysztof Łatuszyński",
    "Dario Spanò"
  ],
  "comment": "10 pages",
  "categories": [
    "math.PR",
    "q-bio.PE"
  ],
  "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 forward in time, and the latter describes the genetic ancestry of randomly sampled individuals from the population backward in time. As well as providing a richer description than either model in isolation, duality often yields equations satisfied by unknown 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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-06-06T09:37:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35C99",
      "60J70",
      "60J90",
      "92D10"
    ],
    "keywords": [
      "bernoulli factory",
      "population genetics",
      "allen-cahn models",
      "wright-fisher diffusion",
      "duality relation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}