Trinets encode tree-child and level-2 phylogenetic networks

TL;DR

This paper proves that certain classes of rooted phylogenetic networks, specifically recoverable binary level-2 and tree-child networks, are uniquely determined by their trinets, advancing methods for reconstructing evolutionary histories.

Contribution

It extends the known classes of phylogenetic networks encoded by trinets to include recoverable binary level-2 and tree-child networks, through new decomposition theorems.

Findings

Recoverable binary level-2 networks are encoded by their trinets.

Binary tree-child networks are encoded by their trinets.

Supports the conjecture that all recoverable networks are encoded by trinets.

Abstract

Phylogenetic networks generalize evolutionary trees, and are commonly used to represent evolutionary histories of species that undergo reticulate evolutionary processes such as hybridization, recombination and lateral gene transfer. Recently, there has been great interest in trying to develop methods to construct rooted phylogenetic networks from triplets, that is rooted trees on three species. However, although triplets determine or encode rooted phylogenetic trees, they do not in general encode rooted phylogenetic networks, which is a potential issue for any such method. Motivated by this fact, Huber and Moulton recently introduced trinets as a natural extension of rooted triplets to networks. In particular, they showed that level-1 phylogenetic networks are encoded by their trinets, and also conjectured that all "recoverable" rooted phylogenetic networks are encoded by their trinets. Here we prove that recoverable binary level-2 networks and binary tree-child networks are also encoded by their trinets. To do this we prove two decomposition theorems based on trinets which hold for all recoverable binary rooted phylogenetic networks. Our results provide some additional evidence in support of the conjecture that trinets encode all recoverable rooted phylogenetic networks, and could also lead to new approaches to construct phylogenetic networks from trinets.