It is possible to estimate the rate of diversification of clades from phylogenies with a temporal dimension. First, I present several methods for constructing confidence intervals for the speciation rate under the simple assumption of a pure birth process. I discuss the relationships among these methods in the hope of clarifying some fundamental theory in this area. Their performances are compared in a simulation study and one is recommended for use as a result. A variety of other questions that may, in fact, be the questions of primary interest (e.g., Has the rate of cladogenesis been declining?) are then recast as biological variants of the purely statistical question—Is the birth process model appropriate for my data? Seen in this way, a preexisting arsenal of statistical techniques is opened up for use in this area: in particular, techniques developed for the analysis of Poisson processes and the analysis of survival data. These two approaches start from different representations of the data—the branch lengths in the tree—and I explicitly relate the two. Aiming for a synoptic account of useful theory in this area, I briefly discuss some important results from the analysis of two distinct birth-death processes: the one introduced into this area by Hey (1992) is refitted with some powerful statistical tools.
Corresponding Editor: M. Whitlock