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Hadamard Conjugation for the Kimura 3ST Model: Formal Proof

Hadamard conjugation is an analytic description of the relationship between the probabilities of expected site patterns of nucleotides from a set of homologous nucleotide sequences, and the parameters of some simple, yet powerful and popular models of sequence evolution on a proposed phylogeny T . An important application of these relations is to give a theoretical tool to analyse properties of phylogenetic inference, such as the methods of maximum likelihood and maximum parsimony, as well as being a tool for generating simulated data, and direct phylogenetic inference.