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

Ancestral state reconstruction is not only a fundamental tool for studying
trait evolution, but 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 constant-rate 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 empirical data (mammalian body
size and bacterial genome size), we show that the distribution of residual
Z-scores under the BM model is neither homoscedastic nor normal as
expected. Consequently, the 95% confidence intervals (CIs) of predicted
traits are so unreliable that the actual coverage probability ranges from
33% (strongly permissive) to 100% (strongly conservative). Alternative
methods such as BayesTraits and StableTraits that allow variable rates in
evolution improve the predictions but are computationally expensive. Here
we develop RasperGade, a method of ancestral and hidden state prediction
that uses the Levy process to explicitly model gradual evolution, pulsed
evolution and time-independent variation. Using the same empirical data,
we show that RasperGade outperforms both BayesTraits and StableTraits and
is orders-of-magnitude faster. Our results suggest that, when predicting
the ancestral and hidden states of continuous traits, the tempo and mode
of evolution should always be assessed and the quality of confidence
estimates should always be examined.