Characterising rooted and unrooted tree-child networks

TL;DR

This paper introduces a new way to characterize tree-child phylogenetic networks using cherry-picking sequences, extending the concept to unrooted networks and addressing their computational complexity.

Contribution

It provides a novel characterization of rooted tree-child networks via cherry-picking sequences and extends this approach to unrooted networks, offering insights into their orientation complexity.

Findings

Characterization of rooted tree-child networks using cherry-picking sequences.

Extension of the characterization to unrooted tree-child networks.

New approach to determine the orientation complexity of unrooted networks.

Abstract

Rooted phylogenetic networks are used by biologists to infer and represent complex evolutionary relationships between species that cannot be accurately explained by a phylogenetic tree. Tree-child networks are a particular class of rooted phylogenetic networks that has been extensively investigated in recent years. In this paper, we give a novel characterisation of a tree-child network $\mathcal{R}$ in terms of cherry-picking sequences that are sequences on the leaves of $\mathcal{R}$ and reduce it to a single vertex by repeatedly applying one of two reductions to its leaves. We show that our characterisation extends to unrooted tree-child networks which are mostly unexplored in the literature and, in turn, also offers a new approach to settling the computational complexity of deciding if an unrooted phylogenetic network can be oriented as a rooted tree-child network.