Parsimony, likelihood, and the role of models in molecular phylogenetics

Methods such as maximum parsimony (MP) are frequently criticized as being statistically unsound and not being based on any "model." On the other hand, advocates of MP claim that maximum likelihood (ML) has some fundamental problems. Here, we explore the connection between the different versions of MP and ML methods, particularly in light of recent theoretical results. We describe links between the two methods - for example, we describe how MP can be regarded as an ML method when there is no common mechanism between sites (such as might occur with morphological data and certain forms of molecular data). In the process, we clarify certain historical points of disagreement between proponents of the two methodologies, including a discussion of several forms of the ML optimality criterion. We also describe some additional results that shed light on how much needs to be assumed about underling models of sequence evolution in order to successfully reconstruct evolutionary trees.