Phylogenetic Networks from Partial Trees

A contemporary and fundamental problem faced by many evolutionary biologists is how to puzzle together a collection P of partial trees (leaf-labelled trees whose leaves are bijectively labelled by species or, more generally, taxa, each supported by e. g. a gene) into an overall parental structure that displays all trees in P . This already difficult problem is complicated by the fact that the trees in P regularly support conflicting phylogenetic relationships and are not on the same but only overlapping taxa sets. A desirable requirement on the sought after parental structure therefore is that it can accommodate the observed conflicts. Phylogenetic networks are a popular tool capable of doing precisely this. However, not much is known about how to construct such networks from partial trees, a notable exception being the Z-closure super-network approach and the recently introduced Qimputation approach. Here, we propose the usage of closure rules to obtain such a network. In particular, we introduce the novel Y -closure rule and show that this rule on its own or in combination with one of Meacham’s closure rules (which we call the M -rule) has some very desirable theoretical properties. In addition, we use the M and Y -rule to explore the dependency of Rivera et al.’s “ring of life” on the fact that the underpinning phylogenetic trees are all on the same data set. Our analysis culminates in the presentation of a collection of induced subtrees from which this ring can be reconstructed.