Reconstruction of Evolutionary Trees from Pairwise Distributions on Current Species

Suppose that the evolution of a character possessed by a number of current species is modelled as a Markov random eld on an evolutionary tree. Suppose that for each pair of current species we know the joint probability distribution of the pair of characters possessed by that pair of species. We give conditions under which the evolutionary tree can be reconstructed from knowledge of these pairwise joint distributions, that is, conditions under which there is only one evolutionary tree topology consistent with the given pairwise distributions. In this way we establish consistency of a method for reconstructing evolutionary trees using pairwise distributions estimated from observed homologous DNA sequences.