Establishing Existence of Paths between Ranked Phylogenetic Networks

Abstract

In the study of phylogenetic trees and -networks, it is frequently desirable to have a measure
of the distance between them. A potentially useful definition of this distance is the length (in
steps) of the shortest path from one to the other, where this path consists of single rearrangement moves of certain types. While there have recently been developments in methods for finding the shortest path between ranked phylogenetic trees, we will instead be inspecting paths between ranked phylogenetic networks in this work. The primary difference between trees and networks here is in the presence of reticulations in the latter, which are moments where different "branches" come together. More specifically, we work out an algorithm that will provide a path between any two binary, level-1, phylogenetic networks with some restrictions, so as to lay the groundwork for work to find shortest paths within this space