Phylogenetic networks form partial trees

TL;DR

This paper introduces novel closure rules, including the $Y$-closure rule, to construct phylogenetic networks from partial trees, addressing conflicts and overlapping taxa sets, and explores their theoretical properties and applications.

Contribution

It proposes the $Y$-closure rule for building phylogenetic networks from partial trees, enhancing existing methods and analyzing their theoretical properties and applications.

Findings

The $Y$-closure rule has desirable theoretical properties.

Combination of $Y$- and $M$-rules improves network construction.

Reconstruction of the 'ring of life' from subtrees is demonstrated.

Abstract

A contemporary and fundamental problem faced by many evolutionary biologists is how to puzzle together a collection $\mathcal P$ 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 $\mathcal P$. This already difficult problem is complicated by the fact that the trees in $\mathcal P$ 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 $Q$-imputation 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.