Regular Article
On the Genealogy of a Population of Biparental Individuals

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Abstract

If one goes backward in time, the number of ancestors of an individual doubles at each generation. This exponential growth very quickly exceeds the population size, when this size is finite. As a consequence, the ancestors of a given individual cannot be all different and most remote ancestors are repeated many times in any genealogical tree. The statistical properties of these repetitions in genealogical trees of individuals for a panmictic closed population of constant size N can be calculated. We show that the distribution of the repetitions of ancestors reaches a stationary shape after a small numberGc ∝log N of generations in the past, that only about 80% of the ancestral population belongs to the tree (due to coalescence of branches), and that two trees for individuals in the same population become identical after Gcgenerations have elapsed. Our analysis is easy to extend to the case of exponentially growing population.

References (27)

  • R.R. HUDSON

    Properties of the neutral allele model with intergenic recombination

    Theor. Pop. Biol.

    (1983)
  • J.F.C. KINGMAN

    The coalescent

    Stochast. Proc. Appl.

    (1982)
  • F. AUSTERLITZ et al.

    Social transmission of reproductive behavior increases frequency of inherited disorders in a young-expanding population

    Proc. Nat. Acad. Sci. U.S.A.

    (1998)
  • L.L. CAVALLI-SFORZA et al.

    Analisi della fluttuazione di frequenze geniche nella popolazione della Val Parma

    Atti Assoc. Genet. Ital.

    (1960)
  • S.N. COPPERSMITH et al.

    Model for force fluctuations in bead packs

    Phys. Rev. E

    (1996)
  • B. DERRIDA et al.

    The genealogical tree of a chromosome

    J. Stat. Phys.

    (1999)
  • B. DERRIDA et al.

    Statistical properties of genealogical trees

    Phys. Rev. Lett.

    (1999)
  • A.K. DEWDNEY

    Computer recreations: Branching phylogenies of the Paleozoic and the fortunes of English family names

    Scientific American

    (1986)
  • P. DIACONIS

    The cutoff phenomenon in finite Markov chains

    Proc. Nat. Acad. Sci. U.S.A.

    (1996)
  • P. DONNELLY et al.

    Coalescents and genealogical structure under neutrality

    Annu. Rev. Genet.

    (1995)
  • R.A. FISHER

    On the dominance ratio

    Proc. Roy. Soc. Edin.

    (1922)
  • R.A. FISHER

    The Genetical Theory of Natural Selection

    (1930)
  • J.S. GALE

    Theoretical Population Genetics

    (1990)
  • Cited by (0)

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