Mathematical models of cladogenesis

The evolutionary pattern of speciation and extinction in any biologic group may be described by a variety of mathematical models. These models provide a framework for describing the history of taxonomic diversity (clade shape) and other aspects of larger evolutionary patterns. The simplest model assumes time homogeneity: that is, speciation and extinction probabilities are constant through time and within taxonomic groups. In some cases the homogeneous model provides a good fit to real world paleontological data, but in other cases the model serves only as a null hypothesis that must be rejected before more complex models can be applied. In cases where the homogeneous model does not fit the data, time-inhomogeneous models can be formulated that specify change, regular or episodic, in speciation and extinction probabilities. An appendix provides a list of the most useful equations based on the homogeneous model.