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Distribution of repetitions of ancestors in genealogical trees

Author

Listed:
  • Derrida, Bernard
  • Manrubia, Susanna C.
  • Zanette, Damián H.

Abstract

We calculate the probability distribution of repetitions of ancestors in a genealogical tree for simple neutral models of a closed population with sexual reproduction and non-overlapping generations. Each ancestor at generation g in the past has a weight w which is (up to a normalization) the number of times this ancestor appears in the genealogical tree of an individual at present. The distribution Pg(w) of these weights reaches a stationary shape P∞(w), for large g, i.e., for a large number of generations back in the past. For small w,P∞(w) is a power law (P∞(w)∼wβ), with a non-trivial exponent β which can be computed exactly using a standard procedure of the renormalization group approach. Some extensions of the model are discussed and the effect of these variants on the shape of P∞(w) are analysed.

Suggested Citation

  • Derrida, Bernard & Manrubia, Susanna C. & Zanette, Damián H., 2000. "Distribution of repetitions of ancestors in genealogical trees," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 281(1), pages 1-16.
    • Handle: RePEc:eee:phsmap:v:281:y:2000:i:1:p:1-16
    DOI: 10.1016/S0378-4371(00)00031-5
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    Citations

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    Cited by:

    1. Gravel, Simon & Steel, Mike, 2015. "The existence and abundance of ghost ancestors in biparental populations," Theoretical Population Biology, Elsevier, vol. 101(C), pages 47-53.
    2. Neves, Armando G.M. & Moreira, Carlos H.C., 2006. "Applications of the Galton–Watson process to human DNA evolution and demography," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 368(1), pages 132-146.
    3. Matsen, Frederick A. & Evans, Steven N., 2008. "To what extent does genealogical ancestry imply genetic ancestry?," Theoretical Population Biology, Elsevier, vol. 74(2), pages 182-190.

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