Two rival models of evolution in multispecies systems are tested against empirical species-level data. The two models are the Red Queen model of Van Valen as reformulated by Stenseth and Maynard Smith, which assumes that evolution is driven principally by biotic interactions, and the Stationary model of Stenseth and Maynard Smith, which assumes that evolution is propelled primarily by abiotic factors and will cease in the absence of changes in abiotic parameters. Testing refers to the models' predictions regarding the behavior of extinction and origination rates, and assumptions regarding equilibrium diversity and a constant effective environment. The data set includes the dates of origination and extinction for all coccolith, planktic foraminifer, and radiolarian species recorded in the Oligocene through Holocene, and all planktic diatom and silicoflagellate and ebridian species recorded in the Middle Miocene through Holocene in 111 DSDP sites of the low- to mid-latitude Pacific Ocean.