A Counterexample to Fitch’s Method for Maximum Parsimony Trees

Abstract

A major goal in numerical taxonomy over the past decade has been to discover a rapid method for finding the ancestral tree, or dendrogram, requiring the minimum number of evolutionary steps or changes, given an initial set of contemporary Operational Taxonomic Units (OTUs) for which the character states are known. Short of searching all possible dendrograms and all possible ancestral configurations for each dendrogram, the problem has never been solved in the general case. FARRIS (1970) has suggested a variety of intriguing approaches but has not proved them mathematically. ESTABROOK (1968) has solved the problem mathematically for the special case in which the CAMIN-SOKAL (1965) hypothesis is satisfied, but this special case has rather limited applications (MOORE, GOODMAN, and BARNABAS, 1973). FITCH (1971) has focused his attention on the less spectacular but more attainable goal of finding maximum parsimony ancestral character states when both the contemporary character states and the dendrogram are known. Although his method may, in many cases, find a maximum parsimony solution, it is relatively easy to demonstrate that it will not always do so.