Parsimony, likelihood, and simplicity

The latest charge against parsimony in phylogenetic inference is that it involves estimating too many parameters. The charge is derived from the fact that, when each character is allowed a branch length vector of its own (instead of the homogeneous branch lengths assumed in current likelihood models), the results for likelihood and parsimony are identical. Parsimony, however, can also be derived from simpler models, involving fewer parameters. Therefore, parsimony provides (as many authors had argued before) the simplest explanation of the data, or the most realistic, depending on one s views. If (as argued by likelihoodists) phylogenetic inference is to use the simplest model that provides sufficient explanation of the data, the starting point of phylogenetic analyses should be parsimony, not maximum likelihood. If the addition of new parameters (which increase the likelihood) to a parsimony estimation is seen as desirable, this may lead to a preference for results based on current likelihood models. If the addition of parameters is continued, however, the results will eventually come back to the same place where they had started, since allowing each character a branch length of its own also produces parsimony. Parsimony can be justified by very different types of models— either very complex or very simple. This suggests that parsimony does have a unique place among methods of phylogenetic estimation. 2003 The Willi Hennig Society. Published by Elsevier Science (USA). All rights reserved. The two most widely used criteria for phylogenetic inference are parsimony and maximum likelihood. Usually, parsimony is defended by recourse to realism, generality, and economy of assumptions, while maximum likelihood is defended by its explicit use of evolutionary models and the idea that phylogenetic inference must be viewed exclusively as a problem in statistical inference. Parsimony, under some specific models, is also a maximum likelihood estimator; as noted by Farris (1986, p. 24), the ‘‘method of maximumlikelihood is not a technique for estimating anything in particular, but a way of deriving estimation procedures from models.’’ The most widely used maximum likelihood methods are now the ones based on the work of Felsenstein (1973, 1981), reviewed in Swofford et al. (1996), which assume stochastic, Markovian models of evolution, where all the sites have the same probability of change along a branch (a limited amount of rate variation is allowed in some models; see Yang, 1993, 1994). This probability depends on the ‘‘length’’ of the branch (time and mutation rates combined). These models are derived from neutral theories of evolution, which assume that only time and mutation rate are the forces behind most of molecular evolution. Throughout this paper, the term ‘‘likelihood’’ (or ‘‘likelihoodist’’) is used to denote this type of method (or the people espousing its use). Parsimony was not originally justified by means of an explicit probabilistic model. In the belief that only methods based on explicit probabilistic models are defensible, the likelihoodists have tried to discover (starting with Felsenstein, 1978) ‘‘the model’’ implicit in parsimony; the resulting findings have been used to criticize the assumptions supposedly required to justify parsimony. Some authors have defended parsimony from a philosophical perspective (Kluge, 1997, 2001; Siddall, 1997, 2002), but most likelihoodists (with few exceptions, such as de Queiroz and Poe, 2001) have ignored these philosophical issues. The purpose of the present paper is to revise some aspects of the parsimony vs likelihood controversy, from a more statistical perspective. Recent criticisms of parsimony accuse it of relying Cladistics 19 (2003) 91–103 www.elsevier.com/locate/yclad Cladistics E-mail address: [email protected]. 0748-3007/03/$ see front matter 2003 The Willi Hennig Society. Published by Elsevier Science (USA). All rights reserved. doi:10.1016/S0748-3007(03)00017-3 on an implicit model that is too complex and therefore over-fits the data (this charge has now replaced earlier criticisms that accused it of being too simplistic—e.g., Felsenstein, 1982, p. 388; Felsenstein, 1988, p. 535). My main conclusion is that, since most parsimonious trees are maximum likelihood estimates under different models (either very simple or very complex), parsimony can be seen as providing either the simplest explanation of the data or the most realistic. Current likelihood methods lie in between. More importantly, the fact that parsimony can be derived under very different types of models also casts doubt on the notion that one can evaluate a method justified on logical grounds by simply evaluating statistical models that happen to produce similar results.