Classifying and counting linear phylogenetic invariants for the Jukes Cantor model

Steel, M. A.; Fu, Y. X.

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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