Phylogenetic inference: how much evolutionary history is knowable?

In order to reconstruct phylogenetic trees from extremely dissimilar sequences it is necessary to estimate accurately the extent of sequence divergence. In this paper a new method of sequence analysis, Markov triple analysis, is developed for determining the relative frequencies of nucleotide substitutions within the three branches of a three-taxon dendrogram. Assuming that nucleotide sites are independently and identically distributed and assuming a Markov model for nucleotide (or protein) evolution, it is shown that the unique Markov matrices can be reconstructed given only the joint probability distribution relating three taxa. (In the much simpler case involving only two taxa and two character states, Markov matrices can also be reconstructed, provided symmetry assumptions are placed on the elements of the matrices.) The method is illustrated using sequence data from the combined first and second codon positions derived from complete human, mouse, and cow mitochondrial sequences.