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The genealogy of branching processes and the age of our most recent common ancestor

Part of: Markov processes

Published online by Cambridge University Press:  01 July 2016

Neil O'Connell
Neil O'Connell*
Affiliation:
Dublin Institute for Advanced Studies
*
* Postal address: DIAS, 10 Burlington Road, Dublin 4, Ireland.
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Abstract

We obtain a weak approximation for the reduced family tree in a near-critical Markov branching process when the time interval considered is long; we also extend Yaglom's theorem and the exponential law to this case. These results are then applied to the problem of estimating the age of our most recent common female ancestor, using mitochondrial DNA sequences taken from a sample of contemporary humans.

Keywords

REDUCED BRANCHING PROCESS'NEAR-CRITICALYAGLOM'S THEOREMEXPONENTIAL LIMIT LAWMITOCHONDRIAL DNAEVEEVOLUTIONMUTATION

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60J85: Applications of branching processes
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 27 , Issue 2 , June 1995 , pp. 418 - 442
Copyright
Copyright © Applied Probability Trust 1995 

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Footnotes

This work constitutes part of the author's Ph.D. thesis, completed at the University of California at Berkeley, and was supported in part by NSF grants MCS90-01710 and DMS91-58583.

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