Standard sister clade comparison fails when testing derived character states

Comparing species richness in sister clades that differ in a character is one of the ways to study factors influencing diversification. While most of its applications focused on traits that increase diversification, some were used to study the association of a trait with less species richness, e.g. the occurrence of dioecy in flowering plants. We show here, using simulations and an analytical model, that the null expectation of equal species richness that is generally used in sister clade comparisons is wrong in the case of a derived trait occurring independently from speciation: one should expect less species in the clade with the derived character when there is no difference in diversification rates. This is due to the waiting time for the derived state to appear, which causes it to occur more often on longer branches. This has the important implication that the probability for a clade to possess the derived state depends on the tree geometry, and thus on species richness: less species-rich clades are more likely to possess the derived state. A test for differences in species richness should be based upon observed tree imbalance. We present a method to do this, and find that we cannot confirm earlier work that concluded that dioecy decreases diversification; on the contrary, it seems to be associated to higher species richness than expected.