Alternative Methods of Phylogenetic Inference and their Interrelationship

A probabilistic model of evolution in a character is presented. It involves two character states, 0 and 1. The population may have a third state, 01, in which there is polymorphism for both character states. There are three evolutionary events in the model: origination of state 1, reversion from state 1, and loss of polymorphism, plus an event corresponding to total misinterpretation of the character by the taxonomist. The maximum likelihood method of estimating the phylogeny is described. When the probabilities of the four events are taken to be extreme, then depending on their relative sizes under different circumstances four different phylogenetic inference methods emerge as maximum likelihood methods. Three are known: the Camin-Sokal parsimony method, Farris's Dollo parsimony method, and the Estabrook-Johnson-McMorris compatibility method. A new method, the polymorphism parsimony method, also emerges. It explains parallelism and convergence by persistence of character-state polymorphism after a unique origin of the derived character state, and attempts to find that evolutionary tree which requires the least extent of polymorphism. Details of implementation of the polymorphism parsimony method are given. Some variants of the evolutionary model are discussed, involving unrooted character state trees. The use of the model to resolve a paradox which arises when we attempt to apply the Dollo parsimony method to multiple-state characters is briefly considered.