{
  "id": "math/0503525",
  "version": "v1",
  "published": "2005-03-24T09:55:19.000Z",
  "updated": "2005-03-24T09:55:19.000Z",
  "title": "Mass extinctions: an alternative to the Allee effect",
  "authors": [
    "Rinaldo B. Schinazi"
  ],
  "comment": "Published at http://dx.doi.org/10.1214/105051604000000819 in 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 2005, Vol. 15, No. 1B, 984-991",
  "doi": "10.1214/105051604000000819",
  "categories": [
    "math.PR"
  ],
  "abstract": "We introduce a spatial stochastic process on the lattice Z^d to model mass extinctions. Each site of the lattice may host a flock of up to N individuals. Each individual may give birth to a new individual at the same site at rate \\phi until the maximum of N individuals has been reached at the site. Once the flock reaches N individuals, then, and only then, it starts giving birth on each of the 2d neighboring sites at rate \\lambda(N). Finally, disaster strikes at rate 1, that is, the whole flock disappears. Our model shows that, at least in theory, there is a critical maximum flock size above which a species is certain to disappear and below which it may survive.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-03-24T09:55:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "92D25"
    ],
    "keywords": [
      "allee effect",
      "individual",
      "spatial stochastic process",
      "model mass extinctions",
      "flock reaches"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......3525S"
    }
  }
}