{
  "id": "1906.02668",
  "version": "v1",
  "published": "2019-06-06T16:10:34.000Z",
  "updated": "2019-06-06T16:10:34.000Z",
  "title": "A dual process for the coupled Wright-Fisher diffusion",
  "authors": [
    "Martina Favero",
    "Henrik Hult",
    "Timo Koski"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "The coupled Wright-Fisher diffusion is a multi-dimensional Wright-Fisher diffusion for multi-locus and multi-allelic genetic frequencies, expressed as the strong solution to a system of stochastic differential equations that are coupled in the drift, where the pairwise interaction among loci is modelled by an inter-locus selection. In this paper, a dual process to the coupled Wright-Fisher diffusion is derived, which contains transition rates corresponding to coalescence and mutation as well as single-locus selection and double-locus selection. The coalescence and mutation rates correspond to the typical transition rates of Kingman's coalescent process. The single-locus selection rate not only contains the single-locus selection parameters in a form that generalises the rates for an ancestral selection graph, but it also contains the double-selection parameters to include the effect of the pairwise interaction on the single locus. The double-locus selection rate reflects the particular structure of pairwise interactions of the coupled Wright-Fisher diffusion. Moreover, in the special case of two loci, two alleles, with selection and parent independent mutation, the stationary density for the coupled Wright-Fisher diffusion and the transition rates of the dual process are obtained in an explicit form.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-06T16:10:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J70",
      "92D25",
      "60J60",
      "92D10"
    ],
    "keywords": [
      "coupled wright-fisher diffusion",
      "dual process",
      "single-locus selection",
      "pairwise interaction",
      "double-locus selection rate reflects"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}