Does Cladistic Information Affect Inferences about Branching Rates?

Abstract

Despite long-standing interest in reconstructing rates of branching in the history of groups and recent attempts to use cladistic information to make inferences about such rates, the conditions under which genealogy affects rate reconstruction have not been demonstrated because studies of branching rates rely on methods that either ignore genealogy (and focus on changes in species richness through time) or do not reconstruct absolute rates. We consider stochastic and deterministic approaches that associate branching rates with branches of a phy? logeny, allowing the influence of genealogy to be directly assessed. Both approaches assume that the phylogeny is known. The stochastic approach uses maximum likelihood to estimate one or more parameters of a Yule model in which individual lineages branch according to a Poisson process. In a model with only one rate parameter over the entire tree, genealogy affects the estimation of rate whenever some taxa are not extant (i.e., are known only from fossils) or are direct descendants of fossils of known age. In more complex multiparameter models, the esti? mated rates always depend on genealogy regardless of when the taxa are observed in time. The deterministic model uses nonlinear optimization methods to reconstruct local branching rates in a tree. This procedure minimizes the transformation in local rate required by the data on topology and times of occurrence. A uniform tree need not entail any transformation in local rate, but a nonuniform tree does. Genealogy therefore affects reconstructed branching rates in both deterministic and stochastic approaches. The approaches are illustrated using Vrba's phy? logeny of fossil and extant African bovids. (Cladogenesis; branching rate; phylogeny; maximum likelihood; optimization.)