{
  "id": "2003.14092",
  "version": "v1",
  "published": "2020-03-31T11:00:17.000Z",
  "updated": "2020-03-31T11:00:17.000Z",
  "title": "Moran model with strong selection and $Λ$-Wright-Fisher SDE",
  "authors": [
    "François Gaston Ged"
  ],
  "comment": "21 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We study a population model of fixed size undergoing strong selection where individuals accumulate beneficial mutations, namely the Moran model with selection. In a specific setting with strong selection, Schweinsberg showed that the genealogy of the population is described by the so-called Bolthausen-Sznitman's coalescent. In this paper we sophisticate the model by splitting the population into two adversarial subgroups, that can be interpreted as two different alleles, one of which has a selective advantage over the other. We show that the proportion of disadvantaged individuals converges to the solution of a stochastic differential equation (SDE) as the population's size goes to infinity, named the $\\Lambda$-Wright-Fisher SDE with selection. This stochastic differential equation already appeared in the $\\Lambda$-lookdown model with selection studied by Bah and Pardoux, in the case where the population's genealogy is described by Bolthausen-Sznitman's coalescent.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-31T11:00:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J80",
      "92D15",
      "92D25",
      "60H10"
    ],
    "keywords": [
      "moran model",
      "wright-fisher sde",
      "size undergoing strong selection",
      "stochastic differential equation",
      "individuals accumulate beneficial mutations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}