Tree-metrizable HGT networks

TL;DR

This paper investigates the properties of HGT networks that can display tree metrics, revealing that such networks can contain many reticulations, unlike simpler cases with fewer reticulations.

Contribution

It extends the understanding of tree-metrized networks by showing that HGT networks can be complex with multiple reticulations while still displaying a tree metric.

Findings

HGT networks can be tree-metrized with many reticulations.

Characterization of tree-metrized networks with multiple reticulations.

Extension of previous results on single reticulation networks.

Abstract

Phylogenetic trees are often constructed by using a metric on the set of taxa that label the leaves of the tree. While there are a number of methods for constructing a tree using a given metric, such trees will only display the metric if it satisfies the so-called "four point condition", established by Buneman in 1971. While this condition guarantees that a unique tree will display the metric, meaning that the distance between any two leaves can be found by adding the distances on arcs in the path between the leaves, it doesn't exclude the possibility that a phylogenetic network might also display the metric. This possibility was recently pointed out and "tree-metrized" networks --- that display a tree metric --- with a single reticulation were characterized. In this paper, we show that in the case of HGT (horizontal gene transfer) networks, in fact there are tree-metrized networks containing many reticulations.