Distributions of topological tree metrics between a species tree and a gene tree. (English) Zbl 1400.62296
Summary: 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 (\(n \geq 4\)); 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.
MSC:
| 62P10 | Applications of statistics to biology and medical sciences; meta analysis |
| 62H30 | Classification and discrimination; cluster analysis (statistical aspects) |
| 05C90 | Applications of graph theory |
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