Directional evolution has played an important role in shaping the morphological, ecological, and molecular diversity of life. However, standard substitution models assume stationarity of the evolutionary process over the time scale examined, thus impeding the study of directionality. Here we explore a simple, nonstationary model of evolution for discrete data, which assumes that the state frequencies at the root differ from the equilibrium frequencies of the homogeneous evolutionary process along the rest of the tree (i.e., the process is nonstationary, nonreversible, but homogeneous). Within this framework, we develop a Bayesian approach for testing directional versus stationary evolution using a reversible-jump algorithm. Simulations show that when only data from extant taxa are available, the success in inferring directionality is strongly dependent on the evolutionary rate, the shape of the tree, the relative branch lengths, and the number of taxa. Given suitable evolutionary rates (0.1–0.5 expected substitutions between root and tips), accounting for directionality improves tree inference and often allows correct rooting of the tree without the use of an outgroup. As an empirical test, we apply our method to study directional evolution in hymenopteran morphology. We focus on three character systems: wing veins, muscles, and sclerites. We find strong support for a trend toward loss of wing veins and muscles, while stationarity cannot be ruled out for sclerites. Adding fossil and time information in a total-evidence dating approach, we show that accounting for directionality results in more precise estimates not only of the ancestral state at the root of the tree, but also of the divergence times. Our model relaxes the assumption of stationarity and reversibility by adding a minimum of additional parameters, and is thus well suited to studying the nature of the evolutionary process in data sets of limited size, such as morphology and ecology.

Supplementary Table S1: Characters PartitionsMorphological character matrix with numbers from this and the previous publication (Ronquist et al. 2012), partition assignment, and descriptions of character states.Supplementary_Table_S1_Characters_Partitions.xlsxSupplementary Files S2: Scripts SimulationsArchive containing a bash script and several R scripts used for simulating and analyzing the data from the simulation study.Supplementary_Files_S2_Scripts_Simulations.rarSupplementary Files S3: Results SimulationsPdf files containing all graphs produced in the simulation study (see ReadMe.txt for details).Supplementary_Files_S3_Results_Simulations.rarSupplementary File S4: Tracing the High-Rates ArtefactDetailed explanation of the occurrence of false positives when analyzing random or highly saturated data, and of the impact of the branch length prior.Supplementary_File_S4_Tracing_the_High-Rates_Artefact.pdf