Reconstructing phylogenies from nucleotide pattern probabilities: A survey and some new results Original Research Article

The variations between homologous nucleotide sequences representative of various species are, in part, a consequence of the evolutionary history of these species. Determining the evolutionary tree from patterns in the sequences depends on inverting the stochastic processes governing the substitutions from their ancestral sequence. We present a number of recent (and some new) results which allow for a tree to be reconstructed from the expected frequencies of patterns in its leaf colorations generated under various Markov models. We summarize recent work using Hadamard conjugation, which provides an analytic relation between the parameters of Kimuraʹs 3ST model on a phylogenetic tree and the sequence patterns produced. We give two applications of the theory by describing new properties of the popular “maximum parsimony” method for tree reconstruction.