Distributions of topological tree metrics between a species tree and a gene tree

Jing Xi (), Jin Xie () and Ruriko Yoshida ()
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Jing Xi: North Carolina State University
Jin Xie: University of Kentucky
Ruriko Yoshida: University of Kentucky

Annals of the Institute of Statistical Mathematics, 2017, vol. 69, issue 3, No 7, 647-671

Abstract: Abstract In order to conduct a statistical analysis on a given set of phylogenetic gene trees, we often use a distance measure between two trees. In a statistical distance-based method to analyze discordance between gene trees, it is a key to decide “biologically meaningful” and “statistically well-distributed” distance between trees. Thus, in this paper, we study the distributions of the three tree distance metrics: the edge difference, the path difference, and the precise K interval cospeciation distance, between two trees: First, we focus on distributions of the three tree distances between two random unrooted trees with n leaves ( $$n \ge 4$$ n ≥ 4 ); and then we focus on the distributions the three tree distances between a fixed rooted species tree with n leaves and a random gene tree with n leaves generated under the coalescent process with the given species tree. We show some theoretical results as well as simulation study on these distributions.

Keywords: Coalescent; Phylogenetics; Tree metrics; Tree topologies (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s10463-016-0557-x

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