Maximum Likelihood Inference of Phylogenetic Trees, with Special Reference to a Poisson Process Model of DNA Substitution and to Parsimony Analyses

Maximum likelihood inference is discussed, and some of its advantages and disadvantages are noted. The application of maximum likelihood inference to phylogenetics is examined, and a simple Poisson process model of DNA substitution is used as one example. Further examples follow from the clarification of implicit models underlying traditional "parsimony" and "compatibility" analyses. From the elucidation of these models and analyses, it is seen that Poisson process analysis gives a statistically consistent estimate of phylogeny, and that parsimony methods do indeed have a maximum likelihood foundation but give potentially incorrect estimates of phylogeny. The maximum likelihood formulation provides a common framework within which these analyses are discussed and compared.