We tested the ability of six quantitative genetic models to explain the evolution of phenotypic means using an extensive database compiled by Gingerich. Our approach differs from past efforts in that we use explicit models of evolutionary process, with parameters estimated from contemporary populations, to analyze a large sample of divergence data on many different timescales. We show that one quantitative genetic model yields a good fit to data on phenotypic divergence across timescales ranging from a few generations to 10 million generations. The key feature of this model is a fitness optimum that moves within fixed limits. Conversely, a model of neutral evolution, models with a stationary optimum that undergoes Brownian or white noise motion, a model with a moving optimum, and a peak shift model all fail to account for the data on most or all timescales. We discuss our results within the framework of Simpson's concept of adaptive landscapes and zones. Our analysis suggests that the underlying process causing phenotypic stasis is adaptation to an optimum that moves within an adaptive zone with stable boundaries. We discuss the implication of our results for comparative studies and phylogeny inference based on phenotypic characters.