Evolutionary inferences about quantitative traits are affected by underlying genealogical discordance
Modern phylogenetic methods used to study how traits evolve often require a single species tree as input, and do not take underlying gene tree discordance into account. Such approaches may lead to errors in phylogenetic inference because of hemiplasy -- the process by which single changes on discordant trees appear to be homoplastic when analyzed on a fixed species tree. Hemiplasy has been shown to affect inferences about discrete traits, but it is still unclear whether complications arise when quantitative traits are analyzed. In order to address this question and to characterize the effect of hemiplasy on traits controlled by a large number of loci, we present a multispecies coalescent model for quantitative traits evolving along a species tree. We demonstrate theoretically and through simulations that hemiplasy decreases the expected covariances in trait values between more closely related species relative to the covariances between more distantly related species. This effect leads to an overestimation of a traits evolutionary rate parameter, to a decrease of the traits phylogenetic signal, and to increased false positive rates in comparative methods such as the phylogenetic ANOVA. We also show that hemiplasy affects discrete, threshold traits that have an underlying continuous liability, leading to false inferences of convergent evolution. The number of loci controlling a quantitative trait appears to be irrelevant to the trends reported, for all analyses. Our results demonstrate that gene tree discordance and hemiplasy are a problem for all types of traits, across a wide range of methods. Our analyses also point to the conditions under which hemiplasy is most likely to be a factor, and suggest future approaches that may mitigate its effects.