Fast likelihood calculations for automatic identification of macroevolutionary rate heterogeneity in continuous and discrete traits

Understanding phenotypic disparity across the tree of life requires
identifying where and when evolutionary rates change on phylogeny. A
primary methodological challenge in macroevolution is therefore to develop
methods for accurate inference of among-lineage variation in rates of
phenotypic evolution. Here, we describe a method for inferring
among-lineage evolutionary rate heterogeneity in both continuous and
discrete traits. The method assumes that the present-day distribution of a
trait is shaped by a variable-rate process arising from a mixture of
constant-rate processes and uses a single-pass tree traversal algorithm to
estimate branch-specific evolutionary rates. By employing dynamic
programming optimization techniques and approximate maximum likelihood
estimators where appropriate, our method permits rapid exploration of the
tempo and mode of phenotypic evolution. Simulations indicate that the
method reconstructs rates of trait evolution with high accuracy.
Application of the method to datasets on squamate reptile reproduction and
turtle body size recovers patterns of rate heterogeneity identified by
previous studies but with computational costs reduced by many orders of
magnitude. Our results expand the set of tools available for detecting
macroevolutionary rate heterogeneity and point to the utility of fast,
approximate methods for studying large scale biodiversity dynamics.