  Species richness varies widely across the tree of life, and there is great
interest in identifying ecological, geographic, and other factors that affect
rates of species proliferation. Recent methods for explicitly modeling the
relationships among character states, speciation rates, and extinction rates on
phylogenetic trees- BiSSE, QuaSSE, GeoSSE, and related models - have been
widely used to test hypotheses about character state-dependent diversification
rates. Here, we document the disconcerting ease with which neutral traits are
inferred to have statistically significant associations with speciation rate.
We first demonstrate this unfortunate effect for a known model assumption
violation: shifts in speciation rate associated with a character not included
in the model. We further show that for many empirical phylogenies, characters
simulated in the absence of state-dependent diversification exhibit an even
higher Type I error rate, indicating that the method is susceptible to
additional, unknown model inadequacies. For traits that evolve slowly, the root
cause appears to be a statistical framework that does not require replicated
shifts in character state and diversification. However, spurious associations
between character state and speciation rate arise even for traits that lack
phylogenetic signal, suggesting that phylogenetic pseudoreplication alone
cannot fully explain the problem. The surprising severity of this phenomenon
suggests that many trait-diversification relationships reported in the
literature may not be real. More generally, we highlight the need for
diagnosing and understanding the consequences of model inadequacy in
phylogenetic comparative methods.
