Unrooted non-binary tree-based phylogenetic networks

TL;DR

This paper investigates unrooted non-binary phylogenetic networks, revealing that unlike binary networks, non-binary networks are only guaranteed to be tree-based up to level 3, highlighting differences in their structural properties.

Contribution

It extends the understanding of tree-based properties from binary to non-binary unrooted phylogenetic networks, identifying a key difference at level 3.

Findings

Up to level 4, all unrooted binary networks are tree-based.

Non-binary networks are only guaranteed to be tree-based up to level 3.

The study clarifies the structural limitations of non-binary networks.

Abstract

Phylogenetic networks are a generalization of phylogenetic trees allowing for the representation of non-treelike evolutionary events such as hybridization. Typically, such networks have been analyzed based on their `level', i.e. based on the complexity of their 2-edge-connected components. However, recently the question of how `treelike' a phylogenetic network is has become the center of attention in various studies. This led to the introduction of \emph{tree-based networks}, i.e. networks that can be constructed from a phylogenetic tree, called the \emph{base tree}, by adding additional edges. While the concept of tree-basedness was originally introduced for rooted phylogenetic networks, it has recently also been considered for unrooted networks. In the present study, we compare and contrast findings obtained for unrooted \emph{binary} tree-based networks to unrooted \emph{non-binary} networks. In particular, while it is known that up to level 4 all unrooted binary networks are tree-based, we show that in the case of non-binary networks, this result only holds up to level 3.