Scott Schmidler Duke University Statistics and Decision Sciences We examine limits on inferring evolutionary divergence times using sequence evolution models arising as a consequence of the probabilistic “cutoff phenomenon”, in which a Markov chain remains far equilibrium for an extended period, followed by a rapid transition into equilibrium. We show that evolutionary sequence models exhibit a cutoff, which relates directly to increased uncertainty in evolutionary distance inferences. We derive the cutoff explicitly for symmetric models, and demonstrate empirically the behavior in models routinely used in the literature. We also show how to locate cutoffs for specific models and sequences. Finally, we show that the cutoff explains several previously reported problems with common default priors for Bayesian phylogenetic analysis, and we suggest a new class of priors to address these problems.