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Equilibrium models in population biology have demonstrated that accurate predictions of species diversity can be made without reference to particular taxa. We have extended the use of equilibrium models to examine patterns of phyletic diversification in the fossil record. We assume that (1) regions become saturated with respect to the number of taxa that can coexist; and (2) after that limit is reached, rates of speciation and extinction are very similar. Using these minimal constraints, and the standard precepts of evolutionary taxonomy (monophyly), we have generated evolutionary trees by stochastic simulation and classified their lineages into clades. Random processes with minimal constraints yield phyletic trees similar to those based upon the fossil record. Of particular interest are the patterns of clade origination and extinction and of intraclade diversity. For comparison with computer simulations, we present actual clades for the Reptilia. The similarities are striking, but some patterns of the fossil record are not simulated by random processes. For example, the late Cretaceous extinction may represent a fundamentally different type of evolutionary event. The simulation program and its comparison with the real world permits a clearer separation of stochastic and deterministic elements in the evolutionary record.