On the Subnet Prune and Regraft Distance

TL;DR

This paper introduces and analyzes the SNPR operation, a generalization of subtree prune and regraft for phylogenetic networks, providing methods to compute distances and exploring properties of shortest sequences.

Contribution

It characterizes SNPR-distance using agreement forests and investigates embedding properties of various phylogenetic network classes.

Findings

SNPR-distance can be computed via embedded trees and agreement forests.

Shortest SNPR-sequences have specific structural properties.

Certain network classes do not isometrically embed into the space of all networks under SNPR.

Abstract

Phylogenetic networks are rooted directed acyclic graphs that represent evolutionary relationships between species whose past includes reticulation events such as hybridisation and horizontal gene transfer. To search the space of phylogenetic networks, the popular tree rearrangement operation rooted subtree prune and regraft (rSPR) was recently generalised to phylogenetic networks. This new operation - called subnet prune and regraft (SNPR) - induces a metric on the space of all phylogenetic networks as well as on several widely-used network classes. In this paper, we investigate several problems that arise in the context of computing the SNPR-distance. For a phylogenetic tree $T$ and a phylogenetic network $N$, we show how this distance can be computed by considering the set of trees that are embedded in $N$ and then use this result to characterise the SNPR-distance between $T$ and $N$ in terms of agreement forests. Furthermore, we analyse properties of shortest SNPR-sequences between two phylogenetic networks $N$ and $N'$, and answer the question whether or not any of the classes of tree-child, reticulation-visible, or tree-based networks isometrically embeds into the class of all phylogenetic networks under SNPR.