SPECTRAL-ANALYSIS OF PHYLOGENETIC DATA

The spectral analysis of sequence and distance data is a new approach to phylogenetic analysis. For two-state character sequences, the chara cter values at a given site split the set of taxa into two subsets, a bipartition of the taxa set. The vector which counts the relative numb ers of each of these bipartitions over all sites is called a sequence spectrum. Applying a transformation called a Hadamard conjugation, the sequence spectrum is transformed to the conjugate spectrum. This conj ugation corrects for unobserved changes in the data, independently fro m the choice of phylogenetic tree. For any given phylogenetic tree wit h edge weights (probabilities of state change), we define a correspond ing tree spectrum. The selection of a weighted phylogenetic tree from the given sequence data is made by matching the conjugate spectrum wit h a tree spectrum. We develop an optimality selection procedure using a least squares best fit, to find the phylogenetic tree whose tree spe ctrum most closely matches the conjugate spectrum. An inferred sequenc e spectrum can be derived from the selected tree spectrum using the in verse Hadamard conjugation to allow a comparison with the original seq uence spectrum.