Help Privacy Policy Disclaimer
  Advanced SearchBrowse




Journal Article

Distribution of repetitions of ancestors in genealogical trees


Manrubia,  Susanna C.
Physical Chemistry, Fritz Haber Institute, Max Planck Society;

External Resource
No external resources are shared
Fulltext (restricted access)
There are currently no full texts shared for your IP range.
Fulltext (public)
There are no public fulltexts stored in PuRe
Supplementary Material (public)
There is no public supplementary material available

Derrida, B., Manrubia, S. C., & Zanette, D. H. (2000). Distribution of repetitions of ancestors in genealogical trees. Physica A: Statistical Mechanics and its Applications, 281(1-4), 1-16. doi:10.1016/S0378-4371(00)00031-5.

Cite as: https://hdl.handle.net/21.11116/0000-0009-3ED5-2
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.