Maximum Likelihood Estimates of Rearrangement Distance: Implementing a Representation-Theoretic Approach. 2019

Venta Terauds, and Jeremy Sumner
Discipline of Mathematics, School of Natural Sciences, University of Tasmania, Private Bag 37, Sandy Bay, Tasmania, 7001, Australia. venta.terauds@utas.edu.au.

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.

UI MeSH Term Description Entries
D008957 Models, Genetic Theoretical representations that simulate the behavior or activity of genetic processes or phenomena. They include the use of mathematical equations, computers, and other electronic equipment. Genetic Models,Genetic Model,Model, Genetic
D010802 Phylogeny The relationships of groups of organisms as reflected by their genetic makeup. Community Phylogenetics,Molecular Phylogenetics,Phylogenetic Analyses,Phylogenetic Analysis,Phylogenetic Clustering,Phylogenetic Comparative Analysis,Phylogenetic Comparative Methods,Phylogenetic Distance,Phylogenetic Generalized Least Squares,Phylogenetic Groups,Phylogenetic Incongruence,Phylogenetic Inference,Phylogenetic Networks,Phylogenetic Reconstruction,Phylogenetic Relatedness,Phylogenetic Relationships,Phylogenetic Signal,Phylogenetic Structure,Phylogenetic Tree,Phylogenetic Trees,Phylogenomics,Analyse, Phylogenetic,Analysis, Phylogenetic,Analysis, Phylogenetic Comparative,Clustering, Phylogenetic,Community Phylogenetic,Comparative Analysis, Phylogenetic,Comparative Method, Phylogenetic,Distance, Phylogenetic,Group, Phylogenetic,Incongruence, Phylogenetic,Inference, Phylogenetic,Method, Phylogenetic Comparative,Molecular Phylogenetic,Network, Phylogenetic,Phylogenetic Analyse,Phylogenetic Clusterings,Phylogenetic Comparative Analyses,Phylogenetic Comparative Method,Phylogenetic Distances,Phylogenetic Group,Phylogenetic Incongruences,Phylogenetic Inferences,Phylogenetic Network,Phylogenetic Reconstructions,Phylogenetic Relatednesses,Phylogenetic Relationship,Phylogenetic Signals,Phylogenetic Structures,Phylogenetic, Community,Phylogenetic, Molecular,Phylogenies,Phylogenomic,Reconstruction, Phylogenetic,Relatedness, Phylogenetic,Relationship, Phylogenetic,Signal, Phylogenetic,Structure, Phylogenetic,Tree, Phylogenetic
D011336 Probability The study of chance processes or the relative frequency characterizing a chance process. Probabilities
D000465 Algorithms A procedure consisting of a sequence of algebraic formulas and/or logical steps to calculate or determine a given task. Algorithm
D000818 Animals Unicellular or multicellular, heterotrophic organisms, that have sensation and the power of voluntary movement. Under the older five kingdom paradigm, Animalia was one of the kingdoms. Under the modern three domain model, Animalia represents one of the many groups in the domain EUKARYOTA. Animal,Metazoa,Animalia
D015233 Models, Statistical Statistical formulations or analyses which, when applied to data and found to fit the data, are then used to verify the assumptions and parameters used in the analysis. Examples of statistical models are the linear model, binomial model, polynomial model, two-parameter model, etc. Probabilistic Models,Statistical Models,Two-Parameter Models,Model, Statistical,Models, Binomial,Models, Polynomial,Statistical Model,Binomial Model,Binomial Models,Model, Binomial,Model, Polynomial,Model, Probabilistic,Model, Two-Parameter,Models, Probabilistic,Models, Two-Parameter,Polynomial Model,Polynomial Models,Probabilistic Model,Two Parameter Models,Two-Parameter Model
D015321 Gene Rearrangement The ordered rearrangement of gene regions by DNA recombination such as that which occurs normally during development. DNA Rearrangement,DNA Rearrangements,Gene Rearrangements,Rearrangement, DNA,Rearrangement, Gene,Rearrangements, DNA,Rearrangements, Gene
D016013 Likelihood Functions Functions constructed from a statistical model and a set of observed data which give the probability of that data for various values of the unknown model parameters. Those parameter values that maximize the probability are the maximum likelihood estimates of the parameters. Likelihood Ratio Test,Maximum Likelihood Estimates,Estimate, Maximum Likelihood,Estimates, Maximum Likelihood,Function, Likelihood,Functions, Likelihood,Likelihood Function,Maximum Likelihood Estimate,Test, Likelihood Ratio
D016678 Genome The genetic complement of an organism, including all of its GENES, as represented in its DNA, or in some cases, its RNA. Genomes
D055641 Mathematical Concepts Numeric or quantitative entities, descriptions, properties, relationships, operations, and events. Concept, Mathematical,Concepts, Mathematical,Mathematical Concept

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