Classifying and counting linear phylogenetic invariants for the Jukes Cantor model
dc.contributor.author | Steel, M. A. | |
dc.contributor.author | Fu, Y. X. | |
dc.date.accessioned | 2015-11-24T01:31:06Z | |
dc.date.available | 2015-11-24T01:31:06Z | |
dc.date.issued | 1994 | en |
dc.description.abstract | Linear invariants are useful tools for testing phylogenetic hypotheses from aligned DNA/RNA sequences, particularly when the sites evolve at different rates. Here we give a simple, graph theoretic classification, for each phylogenetic tree T, of its associated vector space I(T) of linear invariants under the Jukes-Cantor one parameter model of nucleotide substitution. We also provide an easilydescribed basis for I(T), and show that if T is a binary (fully resolved) phylogenetic tree with n sequences at its leaves then : dim[I(T)] = 4ⁿ - F2n-2 where F n is the n-th Fibonacci number. Our method applies a recently-developed Hadamard-matrix based technique to describe elements of I(T) in terms of edge-disjoint packings of subtrees in T, and thereby complements earlier more algebraic treatments. | en |
dc.identifier.issn | 1172-8531 | |
dc.identifier.uri | http://hdl.handle.net/10092/11405 | |
dc.language.iso | en | |
dc.publisher | University of Canterbury. Dept. of Mathematics | en |
dc.relation.isreferencedby | NZCU | |
dc.rights | Copyright M. A. Steel | en |
dc.rights.uri | https://canterbury.libguides.com/rights/theses | |
dc.subject | Phylogenetic invariants | en |
dc.subject | trees | en |
dc.subject | forests | en |
dc.subject | Hadamard matrix | en |
dc.subject | Jukes-Cantor model | en |
dc.subject.anzsrc | Field of Research::01 - Mathematical Sciences | en |
dc.title | Classifying and counting linear phylogenetic invariants for the Jukes Cantor model | en |
dc.type | Discussion / Working Papers | |
thesis.degree.grantor | University of Canterbury | |
thesis.degree.level | Research Report | en |
thesis.degree.name | Research Report | en |
uc.bibnumber | 433489 | |
uc.college | Faculty of Engineering |
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