Vol. 9, No. 1, 2016

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Using ciliate operations to construct chromosome phylogenies

Jacob L. Herlin, Anna Nelson and Marion Scheepers

Vol. 9 (2016), No. 1, 1–26
Abstract

Whole genome sequencing has revealed several examples where genomes of different species are related by permutation. The number of certain types of rearrangements needed to transform one permuted list into another can measure the distance between such lists. Using an algorithm based on three basic DNA editing operations suggested by a model for ciliate micronuclear decryption, this study defines the distance between two permutations to be the number of ciliate operations the algorithm performs during such a transformation. Combining well-known clustering methods with this distance function enables one to construct corresponding phylogenies. These ideas are illustrated by exploring the phylogenetic relationships among the chromosomes of eight fruit fly (Drosophila) species, using the well-known UPGMA algorithm on the distance function provided by the ciliate operations.

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Keywords
permutations, reversals, block interchanges, fruit fly, ciliate, phylogeny
Mathematical Subject Classification 2010
Primary: 05E15, 20B99, 92-08, 92D15, 92D99
Milestones
Received: 23 January 2013
Revised: 11 December 2014
Accepted: 21 December 2014
Published: 17 December 2015

Communicated by Joseph A. Gallian
Authors
Jacob L. Herlin
Department of Mathematics
Indiana University
Rawles Hall
831 East 3rd Street
Bloomington, IN 47405
United States
Anna Nelson
Department of Mathematics
University of Utah
155 S 1400 E
Room 233
Salt Lake City, UT 84112-0090
United States
Marion Scheepers
Department of Mathematics
Boise State University
Boise, ID 83725
United States