Can Multiple Phylogenetic Trees Be Displayed in a Tree-Child Network Simultaneously?

Yufeng Wu; Louxin Zhang

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arXiv · 2207.02629

Can Multiple Phylogenetic Trees Be Displayed in a Tree-Child Network Simultaneously?

Yufeng Wu·Louxin Zhang

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Abstract

A binary phylogenetic network on a taxon set $X$ is a rooted acyclic digraph in which the degree of each nonleaf node is three and its leaves (i.e.degree-one nodes) are uniquely labeled with the taxa of $X$. It is tree-child if each nonleaf node has at least one child of indegree one. A set of binary phylogenetic trees may or may not be simultaneously displayed in a binary tree-child network. Necessary conditions for multiple phylogenetic trees being simultaneously displayed in a tree-child network are given here. In particular, it is proved that any two phylogenetic trees can always simultaneously be displayed in some tree-child network on the same taxa set. It is also proved that any set of multiple binary phylogenetic trees can always simultaneously be displayed in some non-binary tree-child network on the same taxa set, where each nonleaf node is of either indegree one and outdegree two or indegree at least two and outdegree out.

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Yufeng Wu, Louxin Zhang. 2022-07-06. Can Multiple Phylogenetic Trees Be Displayed in a Tree-Child Network Simultaneously?. https://arxiv.org/abs/2207.02629

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