{
  "id": "math/0511743",
  "version": "v2",
  "published": "2005-11-30T16:10:16.000Z",
  "updated": "2006-04-17T20:05:20.000Z",
  "title": "The process of most recent common ancestors in an evolving coalescent",
  "authors": [
    "P. Pfaffelhuber",
    "A. Wakolbinger"
  ],
  "categories": [
    "math.PR",
    "q-bio.PE"
  ],
  "abstract": "Consider a haploid population which has evolved through an exchangeable reproduction dynamics, and in which all individuals alive at time $t$ have a most recent common ancestor (MRCA) who lived at time $A_t$, say. As time goes on, not only the population but also its genealogy evolves: some families will get lost from the population and eventually a new MRCA will be established. For a time-stationary situation and in the limit of infinite population size $N$ with time measured in $N$ generations, i.e. in the scaling of population genetics which leads to Fisher-Wright diffusions and Kingman's coalescent, we study the process $\\mathcal A = (A_t)$ whose jumps form the point process of time pairs $(E,B)$ when new MRCAs are established and when they lived. By representing these pairs as the entrance and exit time of particles whose trajectories are embedded in the look-down graph of Donnelly and Kurtz (1999) we can show by exchangeability arguments that the times $E$ as well as the times $B$ from a Poisson process. Furthermore, the particle representation helps to compute various features of the MRCA process, such as the distribution of the coalescent at the instant when a new MRCA is established, and the distribution of the number of MRCAs to come that live in today's past.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-04-17T20:05:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35"
    ],
    "keywords": [
      "common ancestor",
      "evolving coalescent",
      "particle representation helps",
      "mrca process",
      "reproduction dynamics"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math.....11743P"
    }
  }
}