%0 Generic %1 derrida1999distribution %A Derrida, B. %A Manrubia, S. C. %A Zanette, D. H. %D 1999 %K common_ancestors genealogies pedigrees %R 10.1016/S0378-4371(00)00031-5 %T Distribution of repetitions of ancestors in genealogical trees %U http://arxiv.org/abs/cond-mat/9912059 %X 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_ınfty(w) for large g, i.e. for a large number of generations back in the past. For small w, P_ınfty(w) is a power law with a non-trivial exponent 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_ınfty(w) are analysed.

@misc{derrida1999distribution, 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_\infty(w) for large g, i.e. for a large number of generations back in the past. For small w, P_\infty(w) is a power law with a non-trivial exponent 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_\infty(w) are analysed.}, added-at = {2012-04-23T01:34:40.000+0200}, author = {Derrida, B. and Manrubia, S. C. and Zanette, D. H.}, biburl = {https://www.bibsonomy.org/bibtex/234d575cf4d816f2e2144feb017330f21/peter.ralph}, description = {[cond-mat/9912059] Distribution of repetitions of ancestors in genealogical trees}, doi = {10.1016/S0378-4371(00)00031-5}, interhash = {5e7c3d206573c2e1f0cc62abf451b76e}, intrahash = {34d575cf4d816f2e2144feb017330f21}, keywords = {common_ancestors genealogies pedigrees}, note = {cite arxiv:cond-mat/9912059Comment: 20 pages, 5 figures included, to appear in Physica A}, timestamp = {2012-04-23T01:34:40.000+0200}, title = {Distribution of repetitions of ancestors in genealogical trees}, url = {http://arxiv.org/abs/cond-mat/9912059}, year = 1999 }