Theoretical Basis of Likelihood Methods in Molecular Phylogenetic Inference

Phylogenetic inference for molecular data by the maximum-likelihood approach has been attacked from a theoretical point of view, because the likelihood functions take different forms for different trees, so that optimised likelihood values for different trees do not appear directly comparable (Nei, 1987). Here, a new "super-tree" perspective is introduced to refute these criticisms. A super-tree likelihood expression is constructed which is a function of all possible bipartition lengths; it reduces to the individual tree likelihood functions when bipartitions not in a given tree are set to zero. From this perspective, the problem of phylogeny inference is seen to be a classical statistical problem involving selection between composite hypotheses. In particular, the usual ML procedure is welljustified, and, moreover, the likelihood ratio between two trees does indeed indicate the posterior odds of the trees. This "literal" interpretation of the likelihood values shown by simulation to provide a more intuitive indication of tree selection accuracy than the "integrated" likelihood posterior probabilities of Rannala and Yang (1996) and bootstrap supports. Thus, the likelihood framework for phylogenetic inference for molecular phylogenetic inference has a good theoretical basis -provided that an adequately realistic model of molecular mutation is used to fit the data. To test the adequacy of such molecular mutation models, a set of straightforward "consistency checks", based on likelihood ratio statistics, are also presented. Predicted distributions of these statistics are shown to agree with simulation. These consistency checks as well as a likelihood-based tree selection procedure have been applied to several data sets: mtDNA from five primates, α and β globin genes from five mammals, mtDNA and wingless genes from sixty Heliconiiini butterflies, and mtDNA from forty mimicking races of Heliconius melpomene and Heliconius erato butteflies. These consistency checks, as well as the presence of internal contradictions, reject the commonly used HKY85+Γ model when applied to many of these data sets. It is concluded that while maximum likelihood is rigorous in principle (and clearly preferable to theoretically unjustified methods like maximum parsimony), it should be considered a heuristic procedure for phylogenetic inference until the complex biological processes influencing molecular mutation are fully understood. This dissertation does not exceed 18,000 words in length, exclusive of tables, figure captions, appendices, and references.