Cases in which Parsimony or Compatibility Methods will be Positively Misleading

Felsenstein, J. (Department of Genetics, University of Washington, Seattle, WA 98195) 1978. Cases in which parsimony or compatibility methods will be positively misleading. Syst. Zool. 27:401-410. -For some simple threeand four-species cases involving a character with two states, it is determined under what conditions several methods of phylogenetic inference will fail to converge to the true phylogeny as mo,re and more data are accumulated. The methods are the Camin-Sokal parsimony method, the compatibility method, and Farris's unrooted Wagner tree parsimony method. In all cases the conditions for this failure (which is the failure to be statistically consistent) are essentially that parallel changes exceed informative, nonparallel changes. It is possible for these methods to be inconsistent even when change is improbable a priori, provided that evolutionary rates in different lineages are sufficiently unequal. It is by extension of this approach that we may provide a sound methodology for evaluating methods of phylogenetic inference. [Numerical cladistics; phylogenetic inference; maximum likelihood estimation; parsimony; compatibility. ] Parsimony or minimum evolution methods were first introduced into phylogenetic inference by Camin and Sokal (1965). This class of methods for inferring an evolutionary tree from discrete-character data involves making a reconstruction of the changes in a given set of characters on a given tree, counting the smallest number of times that a given kind of event need have happened, and using this as the measure of the adequacy of the evolutionary tree. (Alternatively, one can compute the weighted sum of the numbers of times several different kinds of events have occurred.) One attempts to find that evolutionary tree which requires the fewest of these evolutionary events to explain the observed data. Camin and Sokal treated the case of irreversible changes along a character state tree, minimizing the number of changes I This report was prepared as an account of work sponsored by the United States Government. Neither the United States nor the United States Department of Energy, nor any of their employees, nor any of their contractors, subcontractors, or their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness or usefulness of any information, apparatus, product or process disclosed, or represents that its use would not infringe privatelyowned rights. of character states required. A number of other parsimony methods have since appeared in the systematic literature (Kluge and Farris, 1969; Farris, 1969, 1970, 1972, 1977; Farris, Kluge, and Eckhardt, 1970) and parsimony methods have also found widespread use in studies of molecular evolution (Fitch and Margoliash, 1967, 1970; Dayhoff and Eck, 1968; see also Fitch, 1973). Cavalli-Sforza and Edwards (1967; Edwards and Cavalli-Sforza, 1964) earlier formulated a minimum evolution method for continuous-character data. An alternative methodology for phylogenetic inference is the compatibility method, introduced by Le Quesne (1969, 1972). He suggested that phylogenetic inference be based on finding the largest possible set of characters -which could simultaneously have all states be uniquely derived -on the same ftree. The estimate of the phylogeny is then takento be that tree. -While Le Quesne's specific suggestions as to how this might be done have been criticized by Farris (1969), his general approach, which is based on Camin and Sokal's (1965) concept of the compatibility of two characters, has been made rigorous and extended in a series of papers by G. F. Estabrook, C. S. Johnson, Jr., and F. R. McMorris (Estabrook,