Common intervals and symmetric difference in a model-free phylogenomics, with an application to streptophyte evolution

Authors:
Zaky Adam;Monique Turmel;Claude Lemieux;David Sankoff
Affiliations:
School of Information Technology and Engineering, and Department of Mathematics and Statistics, University of Ottawa, Ottawa, Canada;Département de biochimie et de microbiologie, Université Laval, Québec, Canada;Département de biochimie et de microbiologie, Université Laval, Québec, Canada;School of Information Technology and Engineering, and Department of Mathematics and Statistics, University of Ottawa, Ottawa, Canada
Venue:
RCG'06 Proceedings of the RECOMB 2006 international conference on Comparative Genomics
Year:
2006

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Abstract

The common intervals of two permutations on n elements are the subsets of terms contiguous in both permutations. They constitute the most basic representation of conserved local order. We use d, the size of the symmetric difference (the complement of the common intervals) of the two subsets of 2{ 1,⋯,n} thus determined by two permutations, as an evolutionary distance between the gene orders represented by the permutations. We consider the Steiner Tree problem in the space (2{ 1,⋯,n},d) as the basis for constructing phylogenetic trees, including ancestral gene orders. We extend this to genomes with unequal gene content and to genomes containing gene families. Applied to streptophyte phylogeny, our method does not support the positioning of the complex algae Charales as a sister group to the land plants.