INVARIANTS OF SOME PROBABILITY-MODELS USED IN PHYLOGENETIC INFERENCE

The so-called method of invariants is a technique in the field of mole cular evolution for inferring phylogenetic relations among a number of species on the basis of nucleotide sequence data. An invariant is a p olynomial function of the probability distribution defined by a stocha stic model for the observed nucleotide sequence. This function has the special property that it is identically zero for one possible phyloge ny and typically nonzero for another possible phylogeny. Thus it is po ssible to discriminate statistically between two competing phylogenies using an estimate of the invariant. The advantage of this technique i s that it enables such inferences to be made without the need for esti mating nuisance parameters that are related to the specific mechanisms by which the molecular evolution occurs. For a wide class of models f ound in the literature, we present a simple algebraic formalism for re cognising whether or not a function is an invariant and for generating all possible invariants. Our work is based on recognising an underlyi ng group structure and using discrete Fourier analysis.