On the genealogy of a population of biparental individuals

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dc.creatorDerrida, B.
dc.creatorManrubia, S. C.
dc.creatorZanette, D. H.
dc.date2000-03-07
dc.date.accessioned2026-07-07T05:43:50Z
dc.date.available2026-07-07T05:43:50Z
dc.descriptionIf one goes backward in time, the number of ancestors of an individual doubles at each generation. This exponential growth very quickly exceeds the population size, when this size is finite. As a consequence, the ancestors of a given individual cannot be all different and most remote ancestors are repeated many times in any genealogical tree. The statistical properties of these repetitions in genealogical trees of individuals for a panmictic closed population of constant size N can be calculated. We show that the distribution of the repetitions of ancestors reaches a stationary shape after a small number Gc ~ log N of generations in the past, that only about 80% of the ancestral population belongs to the tree (due to coalescence of branches), and that two trees for individuals in the same population become identical after Gc generations have elapsed. Our analysis is easy to extend to the case of exponentially growing population.
dc.description14 pages, 7 figures, to appear in the Journal of Theoretical Biology
dc.identifierhttps://arxiv.org/abs/physics/0003016
dc.identifierhttp://arxiv.org/abs/physics/0003016
dc.identifierJour. theor. Biol. 203 (2000) 303.
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/83405
dc.subjectBiological Physics
dc.subjectCondensed Matter
dc.subjectQuantitative Biology
dc.titleOn the genealogy of a population of biparental individuals
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