Genetic Phase Angle Distance (GPAD)

It is hypothesized that a mapping of the biochemical properties of genetic nucleotides into the three dimensional ℝ3 Clifford algebra will yield a novel and meaningful evolutionary distance measure. The nucleotides A,T,C,G are mapped according to three biochemical properties (amino/keto, purine/pyrimidine, weak/strong), resulting in four base-vectors. A weighted linear combination of the base-vectors as codon triplets results in a "Tetrahedral Genetic Code " (TGC), where all 64 codons map to 64 unique codon-vectors in the space. Phase distance θ is measured as the angle between sequentially neighboring codon-vectors, and a sequence of codons is measured as the total path length in radians of the vector as it traverses the TGC. Angular difference Δθ is computed as the absolute value of the difference in phase θ between sequences, at homologous loci. The Genetic Phase Angle Distance (GPAD) is computed as the Δθ mean. GPAD is computed on a sample sequence matrix for 11 different species and compared side by side to the Equal-input distance and phylogenetic tree computed on that sam