Skip to Main content Skip to Navigation
Journal articles

Statistical Properties of Pairwise Distances between Leaves on a Random Yule Tree

M. Sheinman F. Massip 1 P. F. Arndt 
1 Statistique en grande dimension pour la génomique
PEGASE - Département PEGASE [LBBE]
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.
Document type :
Journal articles
Complete list of metadata

Cited literature [33 references]  Display  Hide  Download
Contributor : Lauriane Pillet Connect in order to contact the contributor
Submitted on : Thursday, May 28, 2020 - 12:17:48 AM
Last modification on : Tuesday, July 20, 2021 - 5:20:05 PM


Publisher files allowed on an open archive


Distributed under a Creative Commons Attribution 4.0 International License




M. Sheinman, F. Massip, P. F. Arndt. Statistical Properties of Pairwise Distances between Leaves on a Random Yule Tree. PLoS ONE, Public Library of Science, 2015, 10 (3), pp.e0120206. ⟨10.1371/journal.pone.0120206⟩. ⟨hal-02018975⟩



Record views


Files downloads