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  Statistical properties of pairwise distances between leaves on a random Yule tree

Sheinman, M., Massip, F., & Arndt, P. F. (2015). Statistical properties of pairwise distances between leaves on a random Yule tree. PLoS One, 10(3): e0120206. doi:10.1371/journal.pone.0120206.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-002A-392A-7 Version Permalink: http://hdl.handle.net/11858/00-001M-0000-002A-392B-5
Genre: Journal Article

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© 2015 Sheinman et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

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 Creators:
Sheinman, Michel1, Author              
Massip, Florian1, 2, Author              
Arndt, Peter F.1, Author              
Affiliations:
1Evolutionary Genomics (Peter Arndt), Dept. of Computational Molecular Biology (Head: Martin Vingron), Max Planck Institute for Molecular Genetics, Max Planck Society, ou_1479638              
2INRA, UR1077 Unite Mathematique Informatique et Genome, Jouy-en-Josas, France , ou_persistent22              

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 Abstract: A Yule tree is the result of a branching process with constant birth and death rates. Such a process serves as an instructive null model of many empirical systems, for instance, the evolution of species leading to a phylogenetic tree. However, often in phylogeny the only available information is the pairwise distances between a small fraction of extant species representing the leaves of the tree. In this article we study statistical properties of the pairwise distances in a Yule tree. Using a method based on a recursion, we derive an exact, analytic and compact formula for the expected number of pairs separated by a certain time distance. This number turns out to follow a increasing exponential function. This property of a Yule tree can serve as a simple test for empirical data to be well described by a Yule process. We further use this recursive method to calculate the expected number of the n-most closely related pairs of leaves and the number of cherries separated by a certain time distance. To make our results more useful for realistic scenarios, we explicitly take into account that the leaves of a tree may be incompletely sampled and derive a criterion for poorly sampled phylogenies. We show that our result can account for empirical data, using two families of birds species.

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Language(s): eng - English
 Dates: 2015-03-31
 Publication Status: Published online
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 Identifiers: DOI: 10.1371/journal.pone.0120206
ISSN: 1932-6203 (Electronic)
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Title: PLoS One
  Alternative Title : PloS one
Source Genre: Journal
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Publ. Info: Public Library of Science
Pages: - Volume / Issue: 10 (3) Sequence Number: e0120206 Start / End Page: - Identifier: -