Vivek Jayaswal¹, Lars S. Jermiin², John Robinson³

¹School of Mathematics and Statistics, University of Sydney, NSW 2006, Australia; Sydney University Biological Informatics and Technology Centre, University of Sydney, NSW 2006, Australia. ²School of Biological Sciences, University of Sydney, NSW 2006, Australia; Sydney University Biological Informatics and Technology Centre, University of Sydney, NSW 2006, Australia. Unité de Biologie Moléculaire de Gène chez les Extrêmophiles, Institut Pasteur, 75724 Paris Cedex 15, France. ³School of Mathematics and Statistics, University of Sydney, NSW 2006, Australia.

Abstract: 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.