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

Author

Listed:
  • Jing Xi

    (North Carolina State University)

  • Jin Xie

    (University of Kentucky)

  • Ruriko Yoshida

    (University of Kentucky)

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.

Suggested Citation

  • Jing Xi & Jin Xie & Ruriko Yoshida, 2017. "Distributions of topological tree metrics between a species tree and a gene tree," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(3), pages 647-671, June.
    • Handle: RePEc:spr:aistmt:v:69:y:2017:i:3:d:10.1007_s10463-016-0557-x
    DOI: 10.1007/s10463-016-0557-x
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