The seasonality hypothesis states that climates characterized by large annual cycles select for large body sizes. In order to study the effects of seasonality on the evolution of body size, we use a model that is based on physiological rules and first principles. At the ecological time scale, our model results show that both larger productivity and seasonality may lead to larger body sizes. Our model is the first dynamic and process-based model to support the seasonality hypothesis and hence demonstrates the importance of basing models on physiological processes. We focus not only on variability at the ecological time scale, but also on the temporal variations in seasonality existing at geological time scales. A particularly strong forcing of seasonality exists on the scale of 20,000-400,000 years, the scale of Milankovitch cycles. Therefore, we simulated the evolutionary response of body size to a Milankovitch-type of forcing of climate and food density. Results illustrate that for a given level of investment in reserves body size may track climatic cycles, and that below a certain seasonality threshold the body size will decrease rapidly, leading to extinction.