MAXIMUM-LIKELIHOOD WITH MULTIPARAMETER MODELS OF SUBSTITUTION

Maximum-likelihood approaches to phylogenetic estimation have the pote ntial of great flexibility, even though current implementations are hi ghly constrained. One such constraint has been the limitation to one-p arameter models of substitution. A general implementation of Newton's maximization procedure was developed that allows the maximum likelihoo d method to be used with multiparameter models. The Estimate and Maxim ize (EM) algorithm was also used to obtain a good approximation to the maximum likelihood for a certain class of multiparameter models. The condition for which a multiparameter model will only have a single max imum on the likelihood surface was identified. Two-and three-parameter models of substitution in base-paired regions of RNA sequences were u sed as examples for computer simulations to show that these implementa tions of the maximum likelihood method are not substantially slower th an one-parameter models. Newton's method is much faster than the EM me thod but may be subject to divergence in some circumstances. In these cases the EM method can be used to restore convergence.