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Minimal clade size and external branch length under the neutral coalescent

Minimal clade size and external branch length under the neutral coalescent Given a sample of genes taken from a large population, we consider the neutral coalescent genealogy and study the theoretical and empirical distributions of the size of the smallest clade containing a fixed gene. We show that the theoretical distribution is strongly related to a Yule distribution of parameter 2, and that the empirical count statistics are asymptotically Gaussian as the number of genes grows to infinity. Then we consider external branches of the coalescent tree, and describe their lengths. Using the infinitely many sites model of mutation, we also describe the conditional distribution of the external branch lengths, given the number of pairwise differences between a reference DNA sequence and the sequence of one closest relative in the sample. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Advances in Applied Probability Cambridge University Press

Minimal clade size and external branch length under the neutral coalescent

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Publisher
Cambridge University Press
Copyright
Copyright © Applied Probability Trust 2005 
ISSN
1475-6064
eISSN
0001-8678
DOI
10.1239/aap/1127483740
Publisher site
See Article on Publisher Site

Abstract

Given a sample of genes taken from a large population, we consider the neutral coalescent genealogy and study the theoretical and empirical distributions of the size of the smallest clade containing a fixed gene. We show that the theoretical distribution is strongly related to a Yule distribution of parameter 2, and that the empirical count statistics are asymptotically Gaussian as the number of genes grows to infinity. Then we consider external branches of the coalescent tree, and describe their lengths. Using the infinitely many sites model of mutation, we also describe the conditional distribution of the external branch lengths, given the number of pairwise differences between a reference DNA sequence and the sequence of one closest relative in the sample.

Journal

Advances in Applied ProbabilityCambridge University Press

Published: Jul 1, 2016

Keywords: Coalescent genealogies; tree shape statistics; statistical genetics; 92D10; 92D20; 60J70

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