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2 results

  • Estimating the frequency of the oldest allele: a bayesian approach

  • Paul Joyce
  • Journal:
    Advances in Applied Probability / Volume 23 / Issue 3 / September 1991
    Published online by Cambridge University Press:
    01 July 2016, pp. 456-475
    Print publication:
    September 1991

  • In this paper we calculate posterior distributions associated with a version of the Poisson–Dirichlet distribution called the GEM. The GEM has been shown (by several authors) to be the limiting stationary distribution for allele frequencies listed in age order associated with the neutral infinite alleles model. In view of this result, we use our posterior distributions to calculate Bayes estimators for the frequency of the oldest allele given a sample.

  • On the genealogy of nested subsamples from a haploid population

  • Ian W. Saunders, Simon Tavaré, G. A. Watterson
  • Journal:
    Advances in Applied Probability / Volume 16 / Issue 3 / September 1984
    Published online by Cambridge University Press:
    01 July 2016, pp. 471-491
    Print publication:
    September 1984

  • For the haploid genetic model of Moran, the joint distribution of the numbers of distinct ancestors of a collection of nested subsamples is derived. These results are shown to apply to the diffusion approximations of a wide variety of other genetic models, including the Wright–Fisher process. The results allow us to relate the ancestries of populations sampled at different times. Analogous results for a line-of-descent process that incorporates the effect of mutation are given. Some results about the ages of alleles in an infinite-alleles model are described.