2022/07/06 by Wu, Yufeng, Zhang, Louxin
#05C30 #FOS: Biological sciences #J.3 #Populations and Evolution (q-bio.PE)
paper · doi:10.48550/arxiv.2207.02629
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.