Bulletin of Mathematical Biology

, Volume 81, Issue 2, pp 535–567 | Cite as

Maximum Likelihood Estimates of Rearrangement Distance: Implementing a Representation-Theoretic Approach

  • Venta TeraudsEmail author
  • Jeremy Sumner
Special Issue: Algebraic Methods in Phylogenetics


The calculation of evolutionary distance via models of genome rearrangement has an inherent combinatorial complexity. Various algorithms and estimators have been used to address this; however, many of these set quite specific conditions for the underlying model. A recently proposed technique, applying representation theory to calculate evolutionary distance between circular genomes as a maximum likelihood estimate, reduces the computational load by converting the combinatorial problem into a numerical one. We show that the technique may be applied to models with any choice of rearrangements and relative probabilities thereof; we then investigate the symmetry of circular genome rearrangement models in general. We discuss the practical implementation of the technique and, without introducing any bona fide numerical approximations, give the results of some initial calculations for genomes with up to 11 regions.


Rearrangement models Circular genomes Maximum likelihood Evolutionary distance Group representations 

Supplementary material

11538_2018_511_MOESM1_ESM.txt (2 kb)
Supplementary material 1 (txt 2 KB)


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Copyright information

© Society for Mathematical Biology 2018

Authors and Affiliations

  1. 1.Discipline of Mathematics, School of Natural SciencesUniversity of TasmaniaSandy BayAustralia

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