A representation-theoretic approach to the calculation of evolutionary distance in bacteria

TL;DR

This paper introduces a representation-theoretic method leveraging eigenvalue estimation to efficiently compute bacterial evolutionary distances, bypassing complex combinatorial calculations.

Contribution

It applies group representation theory to bacterial evolution models, simplifying maximum likelihood inference through elementary matrix algebra.

Findings

Eigenvalue-based approach reduces computational complexity.

Method applicable to general models of genome rearrangement.

Enables practical inference of bacterial evolutionary history.

Abstract

In the context of bacteria and models of their evolution under genome rearrangement, we explore a novel application of group representation theory to the inference of evolutionary history. Our contribution is to show, in a very general maximum likelihood setting, how to use elementary matrix algebra to sidestep intractable combinatorial computations and convert the problem into one of eigenvalue estimation amenable to standard numerical approximation techniques.