Measuring rates of phenotypic evolution and the inseparability of tempo and mode

Rates of phenotypic evolution are central to many issues in paleontology, but traditional rate metrics such as darwins or haldanes are seldom used because of their strong dependence on interval length. In this paper, I argue that rates are usefully thought of as model parameters that relate magnitudes of evolutionary divergence to elapsed time. Starting with models of directional evolution, random walks, and stasis, T derive for each a reasonable rate metric. These metrics can be linked to existing approaches in evolutionary biology, and simulations show that they can be estimated accurately at any temporal resolution via maximum likelihood, but only when that metric's underlying model is true. The estimation of generational rates of a random walk under realistic paleontological conditions is compared with simulations to that of a prominent alternative approach, Gingerich's LRI (log-rate, log-interval) method. Generational rates are estimated poorly by LRI; they often reflect sampling error more than the actual pace of change. Further simulations show that under some realistic conditions, it is simply not possible to infer generational rates from coarsely sampled populations. These modeling results indicate a complex dependence between evolutionary mode and the measurement of evolutionary rates, and that there is unlikely to be a rate metric that works well for all traits and time scales. Compilations of paleontological and phylogenetic data indicate that all of the three rate metrics derived here show some relationship with interval length. Although there is no perfect rate metric, at present the most practical choices derive from the parameters of the stasis and random walk models. The latter, called the step variance, is particularly promising as a rate metric in paleontology and comparative biology.