A COMPLETE FAMILY OF PHYLOGENETIC INVARIANTS FOR ANY NUMBER OF TAXA UNDER KIMURA 3ST MODEL

We describe a new family of phylogenetic invariants that arise from th e recently developed spectral analysis approach to tree reconstruction . These invariants, which are valid for Kimura's 3ST model, possess fo ur important properties-they are defined equally easily for any number of taxa, their description is tree-independent, they apply even when the distribution of the four nucleotides in the ancestral taxon is unk nown, and they can be modified to deal with sequence sites that do not mutate independently with identical distribution.