Inconsistency of Maximum Parsimony Revisited

Felsenstein (1978, Syst. Zool. 27:401-410) showed that the method of maximum parsimony can be inconsistent, i.e., lead to an incorrect result with an infinite amount of data. The situation in which this inconsistency occurs is often called the "Felsenstein zone," the phenomenon also known as "long-branch attraction." Felsenstein derived a sufficient inconsistency condition from a model for four taxa with only two different parameters for the probability of change on the five branches connecting the four taxa. In the present paper, his approach is used to derive the inconsistency condition of maximum parsimony from the most general model for four taxa, i.e., with five different parameters for the probabilities of change on the five branches and, for the first time, for characters with k states (k = 2, 3, 4, 5, 6, ...) This is used to determine the factors that can cause the inconsistency of maximum parsimony. It is shown that the probability of change on all five branches and the number of character states play a role in causing inconsistency.