A global envelope test to detect non‐random 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, 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. 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. 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.

Adaptive evolution shapes the present-day distribution of the thermal sensitivity of population growth rate

“…To understand why thermal sensitivity has an intermediate phylogenetic heritability, we 200 examined how clades throughout the phylogeny explore the parameter space. For this, 201 we used a disparity-through-time analysis [38,39]. At each branching point of the 202 phylogeny, mean subclade disparity is calculated as the average squared Euclidean 203 distance among trait values within the subclades, normalised to the disparity of trait 204 values across the entire tree.…”

“…We performed disparity-through-time analyses for ln(E) and ln(W op ), using the rank 214 envelope method [39] to generate a confidence envelope from 10,000 simulations of 215 random evolution. As it is not straightforward to incorporate multiple measurements 216 per species with this method, we selected the ln(E) or ln(W op ) estimate of the 217 Sharpe-Schoolfield fit with the highest R 2 value per species.…”

Contrasting trajectories of morphological diversification on continents and islands in the Afrotropical white‐eye radiation

“…To test if morphological evolution shows a departure from the null model of Brownian motion, we used Disparity‐through‐time (DTT) analyses (Harmon et al., 2003). We employed the recently developed rank envelope method to compare the empirical data to the null model simulations, following Murrell (2018). Here, the DTT curves from the null model simulations are ordered according to their most extreme relative disparity value, and the empirical DTT curve is then ranked to see if it falls within the most extreme 5% of curves in which case the null hypothesis of Brownian evolution is rejected.…”

A Total-Evidence Dated Phylogeny of Echinoids and the Evolution of Body Size across Adaptive Landscape

“…We analyzed the phylogenetic signal of the trait using Pagel’s λ (Pagel 1999) and the temporal dynamics of disparity using disparity-through-time (DTT) plots (Harmon et al 2003). The empirical DTT trajectory was compared with 10,000 replicates of character evolution under Brownian motion (BM), and deviations were evaluated using the rank envelope test (Murrell 2018).…”