The agreement distance of rooted phylogenetic networks

TL;DR

This paper introduces maximum agreement graphs to measure differences between rooted phylogenetic networks, establishing a new metric called agreement distance that generalizes existing concepts from phylogenetic trees.

Contribution

It generalizes maximum agreement forests to maximum agreement graphs for phylogenetic networks and proves that the resulting agreement distance bounds other network transformation distances.

Findings

Introduces maximum agreement graphs as a new representation.

Defines the agreement distance as a metric on phylogenetic networks.

Shows the agreement distance bounds SNPR and related distances with constant factors.

Abstract

The minimal number of rooted subtree prune and regraft (rSPR) operations needed to transform one phylogenetic tree into another one induces a metric on phylogenetic trees - the rSPR-distance. The rSPR-distance between two phylogenetic trees $T$ and $T'$ can be characterised by a maximum agreement forest; a forest with a minimum number of components that covers both $T$ and $T'$. The rSPR operation has recently been generalised to phylogenetic networks with, among others, the subnetwork prune and regraft (SNPR) operation. Here, we introduce maximum agreement graphs as an explicit representations of differences of two phylogenetic networks, thus generalising maximum agreement forests. We show that maximum agreement graphs induce a metric on phylogenetic networks - the agreement distance. While this metric does not characterise the distances induced by SNPR and other generalisations of rSPR, we prove that it still bounds these distances with constant factors.