Skip to main content
×
Home
    • Aa
    • Aa

Recent common ancestors of all present-day individuals

  • Joseph T. Chang (a1)
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, 𝒯 n , back to a MRCA has a distribution that is concentrated around lgn (where lg denotes base-2 logarithm), in the sense that the ratio 𝒯 n (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.

Copyright
Corresponding author
Postal address: Statistics Department, Yale University, Box 208290, New Haven, CT 06520, USA. Email address: joseph.chang@yale.edu
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

and (). . , . M. Abramowitz I. A. Stegun 1992 Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables DoverNew York

and (). . , –. C. Berg C. Vignat 2008 Linearization coefficients of Bessel polynomials and properties of Student t-distributions Constr. Approx. 27 1532

(). . , –. A. Di Crescenzo 2001 On random motions with velocities alternating at Erlang-distributed random times Adv. Appl. Prob. 33 690701

(). . , –. A. Di Crescenzo 2002 Exact transient analysis of a planar random motion with three directions Stoch. Stoch. Reports 72 175189

and (). . , –. A. Di Crescenzo B. Martinucci 2010 A damped telegraph random process with logistic stationary distribution J. Appl. Prob. 47 8496

and (). . , –. A. Di Crescenzo F. Pellerey 2002 On prices' evolutions based on geometric telegrapher's process Appl. Stoch. Models Business Industry 18 171184

, and (). . In , eds and , , pp. –. A. Di Crescenzo B. Martinucci S. Zacks 2011 On the damped geometric telegrapher's process Mathematical and Statistical Methods for Actuarial Sciences and Finance C. Perna M. Sibillo Springer175182

and (). . , –. I. Di Matteo E. Orsingher 1997 Detailed probabilistic analysis of the integrated three-valued telegraph signal J. Appl. Prob. 34 671684

(). . , –. A. Lachal 2006 Cyclic random motions in {R}-space with n directionsd ESAIM Prob. Statist. 10 277316

(). . , –. E. Orsingher 1990 Probability law, flow function, maximum distribution of wave-governed random motions and their connections with Kirchhoff's laws Stoch. Process. Appl. 34 4966

(). . , –. E. Orsingher 1990 Random motions governed by third-order equations Adv. Appl. Prob. 22 915928

(). . In (Miramare-Trieste, 1982; Biomath. 17), eds and , , , pp. –. L. M. Ricciardi 1986 Stochastic population theory: birth and death processes Mathematical Ecology T. G. Hallam S. A. Levin SpringerBerlin155190

and (). . , –. W. Stadje S. Zacks 2004 Telegraph processes with random velocities J. Appl. Prob. 41 665678

S. Zacks (2004). Generalized integrated telegraph processes and the distribution of related stopping times. J. Appl. Prob. 41, 497507.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Advances in Applied Probability
  • ISSN: 0001-8678
  • EISSN: 1475-6064
  • URL: /core/journals/advances-in-applied-probability
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Keywords:

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 7 *
Loading metrics...

Abstract views

Total abstract views: 148 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 21st September 2017. This data will be updated every 24 hours.