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.
Description
[cond-mat/9912059] Distribution of repetitions of ancestors in genealogical trees
%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
}