Classifying and counting linear phylogenetic invariants for the Jukes Cantor model

Type of content
Discussion / Working Papers
Publisher's DOI/URI
Thesis discipline
Degree name
Research Report
Publisher
University of Canterbury. Dept. of Mathematics
Journal Title
Journal ISSN
Volume Title
Language
Date
1994
Authors
Steel, M. A.
Fu, Y. X.
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.

Description
Citation
Keywords
Phylogenetic invariants, trees, forests, Hadamard matrix, Jukes-Cantor model
Ngā upoko tukutuku/Māori subject headings
ANZSRC fields of research
Field of Research::01 - Mathematical Sciences
Rights
Copyright M. A. Steel