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On the genealogy of nested subsamples from a haploid population

Published online by Cambridge University Press:  01 July 2016

Ian W. Saunders ,
Simon Tavaré  and
G. A. Watterson
Ian W. Saunders*
Affiliation:
CSIRO Division of Mathematics and Statistics
Simon Tavaré*
Affiliation:
Colorado State University
G. A. Watterson*
Affiliation:
Monash University
*
∗Postal address: CSIRO Division of Mathematics and Statistics, Private Bag 10, Clayton, VIC 3168, Australia.
∗∗ Postal address: Department of Statistics, Colorado State University, Fort Collins, CO 80532, USA.
∗∗∗Postal address: Department of Mathematics, Monash University, Clayton, VIC 3168, Australia.
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Abstract

For the haploid genetic model of Moran, the joint distribution of the numbers of distinct ancestors of a collection of nested subsamples is derived. These results are shown to apply to the diffusion approximations of a wide variety of other genetic models, including the Wright–Fisher process. The results allow us to relate the ancestries of populations sampled at different times. Analogous results for a line-of-descent process that incorporates the effect of mutation are given. Some results about the ages of alleles in an infinite-alleles model are described.

Keywords

MORAN MODELWRIGHT–FISHER MODELINFINITE ALLELESAGE OF ALLELESLINES OF DESCENTDIFFUSION APPROXIMATION
Type
Research Article
Information
Advances in Applied Probability , Volume 16 , Issue 3 , September 1984 , pp. 471 - 491
Copyright
Copyright © Applied Probability Trust 1984 

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