Estimation of Phylogeny Using a General Markov Model

The non-homogeneous model of nucleotide substitution proposed by Barry and Hartigan ( Stat Sci , 2: 191–210) is the most general model of DNA evolution assuming an independent and identical process at each site. We present a computational solution for this model, and use it to analyse two data sets, each violating one or more of the assumptions of stationarity, homogeneity, and reversibility. The log likelihood values returned by programs based on the F84 model ( J Mol Evol , 29: 170–179), the general time reversible model ( J Mol Evol , 20: 86–93), and Barry and Hartigan's model are compared to determine the validity of the assumptions made by the first two models. In addition, we present a method for assessing whether sequences have evolved under reversible conditions and discover that this is not so for the two data sets. Finally, we determine the most likely tree under the three models of DNA evolution and compare these with the one favoured by the tests for symmetry.