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

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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 (\(n \ge 4\)); 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.

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Acknowledgments

The authors would like to thank the referees for very useful comments to improve the manuscript.

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Authors and Affiliations

  1. Department of Mathematics, North Carolina State University, 2108 SAS Hall, 2311 Stinson Drive, Raleigh, NC, 27695, USA

    Jing Xi

  2. Statistics Department, University of Kentucky, Multidisplinary Science Building, Lexington, KY, 40506-0082, USA

    Jin Xie

  3. Statistics Department, University of Kentucky, 325D Multidisplinary Science Building, Lexington, KY, 40506-0082, USA

    Ruriko Yoshida

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  1. Jing Xi
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  2. Jin Xie
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  3. Ruriko Yoshida
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Correspondence to Ruriko Yoshida.

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Xi, J., Xie, J. & Yoshida, R. Distributions of topological tree metrics between a species tree and a gene tree. Ann Inst Stat Math 69, 647–671 (2017). https://doi.org/10.1007/s10463-016-0557-x

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  • DOI: https://doi.org/10.1007/s10463-016-0557-x

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