Unique Solvability of Certain Hybrid Networks from Their Distances

Abstract

Phylogenetic relationships among taxa have usually been represented by rooted trees in which the leaves correspond to extant taxa and interior vertices correspond to extinct ancestral taxa. Recently, more general graphs than trees have been investigated in order to be able to represent hybridization, lateral gene transfer, and recombination events. A model is presented in which the genome at a vertex is represented by a binary string. In the presence of hybridization and the absence of convergent evolution and homoplasies, the evolution is modeled by an acyclic digraph. It is shown how distances are most naturally related to the vertices rather than to the edges. Indeed, distances are computed in terms of the “originating weights” at vertices. It is shown that some distances may not in fact correspond to the sum of branch lengths on any path in the graph. In typical applications, direct measurements can be made only on the leaves, including the root. A study is made of how to infer the originating weights at interior vertices from such information.