Fig. 1

Three examples of rooted phylogenetic networks. Reticulation nodes are those with two incoming edges. a A temporal network with reticulation number 1 and level 1. Timestamps are shown as labels on the internal nodes; observe that the parents of the single reticulation node have the same timestamp. b A tree-child, non-temporal network with two disjoint reticulate regions, both containing one reticulation. It has reticulation number 2 and level 1. c A network that is not tree-child, because both child nodes (in red) of the green node are reticulations. It has reticulation number 2 and level 2; it is level 2 because the cycles induced by the reticulation nodes overlap