# Arboreal networks and their underlying trees

## TL;DR

This paper explores arboreal networks to better understand horizontal gene transfer in bacteria, by studying how these networks can be encoded and constructed.

## Contribution

The paper introduces a method to encode arboreal networks using their underlying trees, extending encoding techniques from single-rooted networks.

## Key findings

- Arboreal networks can be encoded using their underlying trees and additional arcs.
- Triplets, trinets, and quarnets are extended to encode arboreal networks.
- This approach helps in understanding and constructing phylogenetic networks with multiple roots.

## Abstract

Horizontal gene transfer (HGT) is an important process in bacterial evolution. Current phylogeny-based approaches to capture it cannot however appropriately account for the fact that HGT can occur between bacteria living in different ecological niches. Due to the fact that arboreal networks are a type of multiple-rooted phylogenetic network that can be thought of as a forest of rooted phylogenetic trees along with a set of additional arcs each joining two different trees in the forest, understanding the combinatorial structure of such networks might therefore pave the way to extending current phylogeny-based HGT-inference methods in this direction. A central question in this context is, how can we construct an arboreal network? Answering this question is strongly informed by finding ways to encode an arboreal network, that is, breaking up the network into simpler combinatorial structures that, in a well defined sense uniquely determine the network. In the form of triplets, trinets and quarnets such encodings are known for certain types of single-rooted phylogenetic networks. By studying the underlying tree of an arboreal network, we complement them here with an answer for arboreal networks.