A global envelope test to detect non-random bursts of trait evolution

1. The joint analysis of species' evolutionary relatedness and their morphological evolution has offered much promise in understanding the processes that underpin the generation of biological diversity. 2. Disparity through time (DTT) is a popular method that estimates the relative trait disparity within and between subclades, and compares this to the null hypothesis that trait values follow Brownian evolution along the time-calibrated phylogenetic tree. To visualise the differences a confidence envelope is normally created by calculating, at every time point, the 97.5% minimum and 97.5% maximum disparity values from multiple simulations of the null model. The null hypothesis is rejected whenever the empirical DTT curve falls outside of this envelope, and these time periods may then be linked to events that may have sparked non-random trait evolution. 3. Here, simulated data are used to show this pointwise (ranking at each time point) method of envelope construction suffers from multiple testing and a poor, uncontrolled, false-positive rate. As a consequence it cannot be recommended. Instead, each DTT curve can be given a single rank based upon their most extreme disparity value, relative to all other curves, and across all time points. Ordering curves this way leads to a test that avoids multiple testing, but still allows construction of a confidence envelope. The null hypothesis is rejected if the empirical DTT curve is ranked within the most extreme 5% ranked curves from the null model. Comparison of the rank envelope curve to the Morphological Disparity Index and Node Height tests shows it to have generally higher power to detect non-Brownian trait evolution. An extension to allow simultaneous testing over multiple traits is also detailed. 4. Overall the results suggest the new rank envelope test should be used in null model testing for DTT analyses. The rank envelope method can easily be adapted into recently developed posterior predictive simulation methods used in model selection analyses. More generally, the rank envelope test should be adopted whenever a null model produces a vector of correlated values and the user wants to determine where the empirical data are different to the null model.