A global envelope test to detect early and late bursts of trait evolution

Abstract

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. Disparity through time (DTT) is a popular method that estimates the relative trait disparity within and between subclades at each time point, and compares this to the null hypothesis that trait values follow an uncorrelated random walk along the time calibrated phylogenetic tree. A simulation envelope is normally created by calculating, at every time point, the 95% minimum and 95% maximum disparity values from multiple simulations of the null model on the phylogenetic tree. 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. However, this method of envelope construction leads to multiple testing and a poor, uncontrolled, false positive rate. As a consequence it cannot be recommended. A recently developed method in spatial statistics is introduced that constructs a confidence envelope by giving each DTT curve a single ranking value based upon its most extreme disparity value. This method avoids the pitfalls of multiple testing whilst retaining a visual interpretation. Results using simulated data show this new test has desirable type 1 properties and is at least as powerful in correctly rejecting the null hypothesis as the morphological disparity index and node height test that lack a visual interpretation. Three example datasets are reanalyzed to show how the new test may lead to different inferences being drawn. Overall the results suggest the new rank envelope test should be used in null model testing for DTT analyses, and that there is no need to combine the envelope test with other tests such as has been done previously. Moreover, the rank envelope method can easily be adopted into recently developed posterior predictive simulation methods. More generally, the rank envelope test should be adopted when-ever a null model produces a vector of correlated values and the user wants to determine where the empirical data is different to the null model.