Statistical Properties of Genealogical Trees

Bernard Derrida, Susanna C. Manrubia, and Damián H. Zanette
Phys. Rev. Lett. 82, 1987 – Published 1 March 1999
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Abstract

We analyze the statistical properties of genealogical trees in a neutral model of a closed population with sexual reproduction and nonoverlapping generations. By reconstructing the genealogy of an individual from the population evolution, we measure the distribution of ancestors appearing more than once in a given tree. After a transient time, the probability of repetition follows, up to a rescaling, a stationary distribution which we calculate both numerically and analytically. This distribution exhibits a universal shape with a nontrivial power law which can be understood by an exact, though simple, renormalization calculation. Some real data on human genealogy illustrate the problem, which is relevant to the study of the real degree of diversity in closed interbreeding communities.

  • Received 14 October 1998

DOI:https://doi.org/10.1103/PhysRevLett.82.1987

©1999 American Physical Society

Authors & Affiliations

Bernard Derrida1, Susanna C. Manrubia2, and Damián H. Zanette3

  • 1Laboratoire de Physique Statistique de l'École Normale Supérieure, 24 rue Lhomond, F-75231 Paris 05 Cedex, France
  • 2Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, 14195 Berlin, Germany
  • 3Consejo Nacional de Investigaciones Científicas y Técnicas, Centro Atómico Bariloche e Instituto Balseiro, 8400 S.C. de Bariloche, Río Negro, Argentina

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Vol. 82, Iss. 9 — 1 March 1999

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