Table of Contents
ISRN Biomathematics
Volume 2012, Article ID 384275, 8 pages
http://dx.doi.org/10.5402/2012/384275
Research Article

The Ancestry of Genetic Segments

Department of Mathematics, University of Northern Iowa, Cedar Falls, IA 50614-0506, USA

Received 21 November 2011; Accepted 4 January 2012

Academic Editor: O. François

Copyright © 2012 R. B. Campbell. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Recombination within a DNA segment during the neutral fixation process is studied to determine the number of individuals in previous generations which carry genetic material ancestral to that region in the present generation. If 𝑁 π‘Ÿ β‰ͺ 1 , where 𝑁 is the population size and π‘Ÿ is the probability of a recombination event within that region per individual in a generation, the ancestors of all the base pairs in that segment were probably in the same individual in an arbitrary generation in the asymptotic past (prior to the most recent common ancestor) and all the base pairs in that segment share a common coalescent. If 𝑁 π‘Ÿ ≫ 1 , the ancestors of the base pairs in a segment are probably spread among several individuals in asymptotic generations; hence, there is not an ancestral individual, but an ancestral pool, and the coalescents of base pairs do not coincide. The overlap of the ancestral pools of unlinked genetic segments is less than 2 𝑝 π‘ž where 𝑝 and π‘ž are the relative frequencies of the two ancestral pools, which provides that the size of the ancestral pool for the human genome is close to the .80 upper bound which ensues from the Poisson progeny distribution.