A rate-independent technique for analysis of nucleic acid sequences: evolutionary parsimony

The method of evolutionary parsimony--or operator invariants--is atechnique of nucleic acid sequence analysis related to parsimony analysisand explicitly designed for determining evolutionary relationships amongfour distantly related taxa. The method is independent of substitutionrates because it is derived from consideration of the group properties ofsubstitution operators rather than from an analysis of the probabilities ofsubstitution in branches of a tree. In both parsimony and evolutionaryparsimony, three patterns of nucleotide substitution are associatedone-to-one with the three topologically linked trees for four taxa. Inevolutionary parsimony, the three quantities are operator invariants. Theseinvariants are the remnants of substitutions that have occurred in theinterior branch of the tree and are analogous to the substitutions assignedto the central branch by parsimony. The two invariants associated with theincorrect trees must equal zero (statistically), whereas only the correcttree can have a nonzero invariant. The chi 2-test is used to ascertain thenonzero invariant and the statistically favored tree. Examples, obtainedusing data calculated with evolutionary rates and branchings designed tocamouflage the true tree, show that the method accurately predicts thetree, even when substitution rates differ greatly in neighboring peripheralbranches (conditions under which parsimony will consistently fail). As thenumber of substitutions in peripheral branches becomes fewer, the parsimonyand the evolutionary-parsimony solutions converge. The method is robust andeasy to use.