The agreement distance of unrooted phylogenetic networks

TL;DR

This paper introduces maximum agreement graphs as a new way to measure differences between unrooted phylogenetic networks, providing bounds on existing rearrangement distances and extending concepts from trees to networks.

Contribution

It generalizes maximum agreement forests to maximum agreement graphs for networks, offering new bounds on TBR- and PR-distances.

Findings

Maximum agreement graphs provide constant-factor bounds on TBR-distance.

Agreement graphs extend agreement forests from trees to networks.

Results apply to both TBR and PR rearrangement operations.

Abstract

A rearrangement operation makes a small graph-theoretical change to a phylogenetic network to transform it into another one. For unrooted phylogenetic trees and networks, popular rearrangement operations are tree bisection and reconnection (TBR) and prune and regraft (PR) (called subtree prune and regraft (SPR) on trees). Each of these operations induces a metric on the sets of phylogenetic trees and networks. The TBR-distance between two unrooted phylogenetic trees $T$ and $T'$ can be characterised by a maximum agreement forest, that is, a forest with a minimum number of components that covers both $T$ and $T'$ in a certain way. This characterisation has facilitated the development of fixed-parameter tractable algorithms and approximation algorithms. Here, we introduce maximum agreement graphs as a generalisations of maximum agreement forests for phylogenetic networks. While the agreement distance -- the metric induced by maximum agreement graphs -- does not characterise the TBR-distance of two networks, we show that it still provides constant-factor bounds on the TBR-distance. We find similar results for PR in terms of maximum endpoint agreement graphs.