A METHOD FOR TESTING THE CORRELATED EVOLUTION OF TWO BINARY CHARACTERS: ARE GAINS OR LOSSES CONCENTRATED ON CERTAIN BRANCHES OF A PHYLOGENETIC TREE?

A method is presented for assessing whether changes in a binary character are more concentrated than expected by chance on certain branches of a phylogenetic tree. It can be used to test for correlated evolution of two characters by asking whether changes in the first character are significantly concentrated on those branches on which the second character has a specified state. Thus, one could test whether this specified state is associated with, and thus might enable or select, gains or losses in the first character. The probability of achieving a concentration as or more extreme than that observed under the null hypotheses that changes are distributed randomly on the cladogram is obtained by calculating (a) the number of ways that n gains and m losses can be distributed on the cladogram and (b) the number of ways that p gains q losses can be distributed on the branches of interest given n gains and m losses in the cladogram overall. Summing (b) for appropriate p and q then dividing by (a) yields the desired probability. Simulations suggest that biases resulting from errors in parsimony reconstructions of ancestral states are not extreme.