Transforming phylogenetic networks: Moving beyond tree space

TL;DR

This paper introduces operations to transform unrooted phylogenetic networks, generalizing tree transformations, and establishes a framework for comparing and searching these networks using new metrics and connections to cubic graphs.

Contribution

It defines new network transformation operations, generalizes the concept of tree space to networks, and establishes foundational results for network comparison and search strategies.

Findings

Any unrooted phylogenetic network can be transformed into any other using the new operations.

Introduces new metrics for comparing unrooted phylogenetic networks.

Establishes connections between phylogenetic networks and cubic graphs.

Abstract

Phylogenetic networks are a generalization of phylogenetic trees that are used to represent reticulate evolution. Unrooted phylogenetic networks form a special class of such networks, which naturally generalize unrooted phylogenetic trees. In this paper we define two operations on unrooted phylogenetic networks, one of which is a generalization of the well-known nearest-neighbor interchange (NNI) operation on phylogenetic trees. We show that any unrooted phylogenetic network can be transformed into any other such network using only these operations. This generalizes the well-known fact that any phylogenetic tree can be transformed into any other such tree using only NNI operations. It also allows us to define a generalization of tree space and to define some new metrics on unrooted phylogenetic networks. To prove our main results, we employ some fascinating new connections between phylogenetic networks and cubic graphs that we have recently discovered. Our results should be useful in developing new strategies to search for optimal phylogenetic networks, a topic that has recently generated some interest in the literature, as well as for providing new ways to compare networks.