{
  "id": "0910.4009",
  "version": "v1",
  "published": "2009-10-21T07:38:56.000Z",
  "updated": "2009-10-21T07:38:56.000Z",
  "title": "Spatially explicit non-Mendelian diploid model",
  "authors": [
    "N. Lanchier",
    "C. Neuhauser"
  ],
  "comment": "Published in at http://dx.doi.org/10.1214/09-AAP598 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Annals of Applied Probability 2009, Vol. 19, No. 5, 1880-1920",
  "doi": "10.1214/09-AAP598",
  "categories": [
    "math.PR"
  ],
  "abstract": "We introduce a spatially explicit model for the competition between type $a$ and type $b$ alleles. Each vertex of the $d$-dimensional integer lattice is occupied by a diploid individual, which is in one of three possible states or genotypes: $aa$, $ab$ or $bb$. We are interested in the long-term behavior of the gene frequencies when Mendel's law of segregation does not hold. This results in a voter type model depending on four parameters; each of these parameters measures the strength of competition between genes during meiosis. We prove that with or without a spatial structure, type $a$ and type $b$ alleles coexist at equilibrium when homozygotes are poor competitors. The inclusion of a spatial structure, however, reduces the parameter region where coexistence occurs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-10-21T07:38:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "82C22",
      "92D25"
    ],
    "keywords": [
      "spatially explicit non-mendelian diploid model",
      "spatial structure",
      "dimensional integer lattice",
      "voter type model",
      "coexistence occurs"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0910.4009L"
    }
  }
}