Distinguishing punctuated and continuous-time models of character evolution for discrete characters and the implications for macroevolutionary theory

The recent proliferation of quantitative models for assessing anatomical character evolution all assume that character change happens continuously through time. However, the punctuated equilibrium model posits that character change should be coincide with cladogenetic events, and thus should be tied to origination rates. Rates of cladogenesis are important to quantitative phylogenetics, but typically only for establishing prior probabilities in the tree model component of phylogenetic analyses. Here, we modify existing character-likelihood models to use the local cladogenesis rates from Bayesian analyses to generate amounts of character change over time dependent on origination rates, as expected under the punctuated equilibrium model. In the case of strophomenoid brachiopods from the Ordovician, Bayesian analyses strongly favor punctuated models over continuous-time models, with elevated rates of cladogenesis early in the clade’s history inducing frequencies of change despite constant rates of change per speciation event. This corroborates prior work proposing that the early burst in strophomenoid disparity simply reflects elevated speciation rates, which in turn has implications for seemingly unrelated macroevolutionary theory about whether early bursts reflect shifts in intrinsic constraints or empty ecospace. Future development of punctuated character evolution models should account for the full durations of species, which will provide a test of continuous change rates. Ultimately, continuous change versus punctuated change should become part of phylogenetic paleobiology in the same way that we currently test other models of character evolution.