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#### Distribution of repetitions of ancestors in genealogical trees

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##### Citation

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

##### 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 P

_{g}(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)∼w^{β}), 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.