Unrooted non-binary tree-based phylogenetic networks

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 tree-based networks, i.e. networks that can be constructed from a phylogenetic tree, called the 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 binary tree-based networks to unrooted 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.