  A number of methods have been developed to infer differential rates of
species diversification through time and among clades using time-calibrated
phylogenetic trees. However, we lack a general framework that can delineate and
quantify heterogeneous mixtures of dynamic processes within single phylogenies.
I developed a method that can identify arbitrary numbers of time-varying
diversification processes on phylogenies without specifying their locations in
advance. The method uses reversible-jump Markov Chain Monte Carlo to move
between model subspaces that vary in the number of distinct diversification
regimes. The model assumes that changes in evolutionary regimes occur across
the branches of phylogenetic trees under a compound Poisson process and
explicitly accounts for rate variation through time and among lineages. Using
simulated datasets, I demonstrate that the method can be used to quantify
complex mixtures of time-dependent, diversity-dependent, and constant-rate
diversification processes. I compared the performance of the method to the
MEDUSA model of rate variation among lineages. As an empirical example, I
analyzed the history of speciation and extinction during the radiation of
modern whales. The method described here will greatly facilitate the
exploration of macroevolutionary dynamics across large phylogenetic trees,
which may have been shaped by heterogeneous mixtures of distinct evolutionary
processes.
