Modeling pulsed evolution and time-independent variation improves the confidence level of ancestral and hidden state predictions in continuous traits

Ancestral state reconstruction is a fundamental tool for studying trait evolution. It is also very useful for predicting the unknown trait values (hidden states) of extant species. A well-known problem in ancestral and hidden state predictions is that the uncertainty associated with predictions can be so large that predictions themselves are of little use. Therefore, for meaningful interpretation of predicted traits and hypothesis testing, it is prudent to accurately assess the uncertainty of the predictions. Commonly used Brownian motion (BM) model fails to capture the complexity of tempo and mode of trait evolution in nature, making predictions under the BM model vulnerable to lack-of-fit errors from model misspecification. Using simulations and empirical data (bacterial genomic traits and vertebrate body size), we show that the presence of pulsed evolution and time-independent variation significantly undermines the confidence level of continuous traits predicted under the BM model. The residual Z-scores are neither homoscedastic nor normally distributed. Consequently, the 95% confidence intervals of predicted traits are so unreliable that the actual coverage probability ranges from 29% (strongly permissive) to 100% (strongly conservative). To remedy the model misspecification problem, we develop RasperGade that accounts for both pulsed evolution and time-independent variation. When applied to simulated and empirical data, RasperGade outperforms commonly used tools such as ape. It restores the normality and homoscedasticity of the Z-score distributions. Accordingly, RasperGade greatly improves the reliability of confidence intervals of predictions and reduces the deviation of their actual coverage probabilities from the 95% expectation by as much as 99%.