Distribution of repetitions of ancestors in genealogical trees

Bernard Derrida, Susanna C. Manrubia and Damián H. Zanette

Physica A: Statistical Mechanics and its Applications, 2000, vol. 281, issue 1, 1-16

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 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.

Keywords: Genealogy; Critical phenomena; Renormalization group (search for similar items in EconPapers)
Date: 2000
References: View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437100000315
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:281:y:2000:i:1:p:1-16

DOI: 10.1016/S0378-4371(00)00031-5

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().