A Space of Phylogenetic Networks

TL;DR

This paper introduces a geometric space for phylogenetic networks, extending tree space to include circular split networks, and explores its properties and connections to moduli space.

Contribution

It defines a new geometric space for phylogenetic networks, generalizing tree space and linking it to moduli space of curves.

Findings

Introduces a geometric space for circular split networks.

Shows embedding of moduli space within the network space.

Analyzes properties of the new network space.

Abstract

A classic problem in computational biology is constructing a phylogenetic tree given a set of distances between n species. In most cases, a tree structure is too constraining. We consider a circular split network, a generalization of a tree in which multiple parallel edges signify divergence. A geometric space of such networks is introduced, forming a natural extension of the work by Billera, Holmes, and Vogtmann on tree space. We explore properties of this space, and show a natural embedding of the compactification of the real moduli space of curves within it.