Classifying and counting linear phylogenetic invariants for the Jukes Cantor model
Degree GrantorUniversity of Canterbury
Degree NameResearch report
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.
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