Constructing and Counting Phylogenetic Invariants

Abstract. The method of invariants is an approach to the problem of reconstructing the phylogenetic tree of a collection of m taxa using nucleotide sequence data. Models for the respective probabilities of the 4m possible vectors of bases at a given site will have unknown parameters that describe the random mechanism by which substitution occurs along the branches of a putative phylogenetic tree. An invariant is a polynomial in these probabilities that, for a given phylogeny, is zero for all choices of the substitution mechanismparameters. If theinvariantistypicallynon zerofor anotherphylogenetic tree, then estimates of the invariant can be used as evidence to support one phylogeny over another. Previous work of Evans and Speed showed that, for certain commonlyused substitution models, the problem of nding a minimal generating set for the ideal of invariants can be reduced to the linear algebra problem of nding a basis for a certain lattice that is, a free Z-module. They also conject...

• Type: Journal
• Year: 1998
• Where: JCB
• Authors: Steven N. Evans, Xiaowen Zhou
• Keywords: Generating Set, JCB 1998, Nucleotide Sequence Data, Phylogenetic Tree