Bacterial phylogeny in the Cayley graph

TL;DR

This paper explores the use of Cayley graphs and Steiner trees to improve bacterial phylogeny reconstruction by leveraging the full structure of genome rearrangement groups, beyond minimal distance methods.

Contribution

It introduces a novel approach to phylogeny using Cayley graph intervals and Steiner trees, expanding the analysis beyond traditional minimal distance methods.

Findings

Describes genome rearrangement as walks on Cayley graphs.

Proposes using Steiner trees to represent phylogenetic relationships.

Explores the group-theoretic properties of genome arrangements.

Abstract

Many models of genome rearrangement involve operations (e.g. inversions and translocations) that are self-inverse, and hence generate a group acting on the space of genomes. This gives a correspondence between genome arrangements and the elements of a group, and consequently, between evolutionary paths and walks on the Cayley graph. Many common methods for phylogeny reconstruction rely on calculating the minimal distance between two genomes; this omits much of the other information available from the Cayley graph. In this paper we begin an exploration of some of this additional information, in particular describing the phylogeny as a Steiner tree within the Cayley graph, and exploring the "interval" between two genomes. While motivated by problems in systematic biology, many of these ideas are of independent group-theoretic interest.