Nonbinary tree-based phylogenetic networks

Rooted phylogenetic networks are used to describe evolutionary histories that contain non-treelike evolutionary events such as hybridization and horizontal gene transfer. In some cases, such histories can be described by a phylogenetic base-tree with additional linking arcs, which can for example represent gene transfer events. Such phylogenetic networks are called tree-based. Here, we consider two possible generalizations of this concept to nonbinary networks, which we call tree-based and strictly-tree-based nonbinary phylogenetic networks. We give simple graph-theoretic characterizations of tree-based and strictly-tree-based nonbinary phylogenetic networks. Moreover, we show for each of these two classes that it can be decided in polynomial time whether a given network is contained in the class. Our approach also provides a new view on tree-based binary phylogenetic networks. Finally, we discuss two examples of nonbinary phylogenetic networks in biology and show how our results can be applied to them.