Maximum likelihood estimates of pairwise rearrangement distances

Abstract

Accurate estimation of evolutionary distances between taxa is important for many phylogenetic reconstruction methods. Distances can be estimated using a range of different evolutionary models, from single nucleotide polymorphisms to large-scale genome rearrangements. Corresponding corrections for genome rearrangement distances fall into 3 categories: Empirical computational studies, Bayesian/MCMC approaches, and combinatorial approaches. Here, we introduce a maximum likelihood estimator for the inversion distance between a pair of genomes, using a group-theoretic approach to modelling inversions introduced recently. This MLE functions as a corrected distance: in particular, we show that because of the way sequences of inversions interact with each other, it is quite possible for minimal distance and MLE distance to differently order the distances of two genomes from a third. The second aspect tackles the problem of accounting for the symmetries of circular arrangements. While, generally, a frame of reference is locked, and all computation made accordingly, this work incorporates the action of the dihedral group so that distance estimates are free from any a priori frame of reference. The philosophy of accounting for symmetries can be applied to any existing correction method, for which examples are offered.

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

“…This provides a minimal distance between two genomes that is very easy to calculate but has the disadvantage of not being closely aligned to a specific model of genome rearrangement. Using simulation, an empirically-derived correction to the breakpoint distance was presented in [36], and in [32] we explored the importance of specifying a stochastic model of rearrangements, explicitly showing there are cases where the maximum likelihood estimate of time elapsed and the minimal distance produce contradictory answers.…”

A Preliminary Metagenome Analysis Based on a Combination of Protein Domains

“…Supplementary Figure S3 shows the phylogenetic tree that was created for the genome DNA sequences of DNA gyrase subunit B for using MEGA 7. Pairwise distances were also calculated for combinations of two species out of 296 species ( 296 C 2 = 43,660 patterns) [24].…”

Position and Content Paradigms in Genome Rearrangements: The Wild and Crazy World of Permutations in Genomics

“…In fact this symmetry needs to be accounted for while determining rearrangement distance between a pair of circular chromosomes. This was done for example by Watterson et al (1982) and more recently by Egri-Nagy et al (2014b) and Serdoz et al (2016), who also consider the symmetry between a circular permutation and its mirror images.…”