Quantifying the risk of hemiplasy in phylogenetic inference

Convergent evolution-the appearance of the same character state in apparently unrelated organisms-is often inferred when a trait is incongruent with the species tree. However, trait incongruence can also arise from changes that occur on discordant gene trees, a process referred to as hemiplasy. Hemiplasy is rarely taken into account in studies of convergent evolution, despite the fact that phylogenomic studies have revealed rampant discordance. Here, we study the relative probabilities of homoplasy (including convergence and reversal) and hemiplasy for an incongruent trait. We derive expressions for the probabilities of the two events, showing that they depend on many of the same parameters. We find that hemiplasy is as likely-or more likely-than homoplasy for a wide range of conditions, even when levels of discordance are low. We also present a method to calculate the ratio of these two probabilities (the "hemiplasy risk factor") along the branches of a phylogeny of arbitrary length. Such calculations can be applied to any tree to identify when and where incongruent traits may be due to hemiplasy.