Advances in Applied Probability

Recent common ancestors of all present-day individuals

Joseph T. Chang

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

Previous study of the time to a common ancestor of all present-day individuals has focused on models in which each individual has just one parent in the previous generation. For example, `mitochondrial Eve' is the most recent common ancestor (MRCA) when ancestry is defined only through maternal lines. In the standard Wright-Fisher model with population size n, the expected number of generations to the MRCA is about 2n, and the standard deviation of this time is also of order n. Here we study a two-parent analog of the Wright-Fisher model that defines ancestry using both parents. In this model, if the population size n is large, the number of generations, 𝒯n, back to a MRCA has a distribution that is concentrated around lgn (where lg denotes base-2 logarithm), in the sense that the ratio 𝒯n(lgn) converges in probability to 1 as n→∞. Also, continuing to trace back further into the past, at about 1.77 lgn generations before the present, all partial ancestry of the current population ends, in the following sense: with high probability for large n, in each generation at least 1.77lgn generations before the present, all individuals who have any descendants among the present-day individuals are actually ancestors of all present-day individuals.

Article information

Source
Adv. in Appl. Probab. Volume 31, Number 4 (1999), 1002-1026.

Dates
First available in Project Euclid: 21 August 2002

Permanent link to this document
https://projecteuclid.org/euclid.aap/1029955256

Digital Object Identifier
doi:10.1239/aap/1029955256

Mathematical Reviews number (MathSciNet)
MR1747454

Zentralblatt MATH identifier
0979.92027

Subjects
Primary: 92D25: Population dynamics (general)
Secondary: 60J85: Applications of branching processes [See also 92Dxx]

Keywords
Coalescent Wright-Fisher model Galton-Watson process genealogical models population genetics

Citation

Chang, Joseph T. Recent common ancestors of all present-day individuals. Adv. in Appl. Probab. 31 (1999), no. 4, 1002--1026. doi:10.1239/aap/1029955256. https://projecteuclid.org/euclid.aap/1029955256.


Export citation

See also

  • Invited discussion: Peter Donnelly, Carsten Wiuf, Jotun Hein, Montgomery Slatkin, W. J. Ewens, J. F. C. Kingman. Adv. Appl. Prob. 31 (1999), pp. 1027-1035.
  • Reply to discussants: Adv. Appl. Prob. 31 (1999), pp. 1036-1038.