Ecologists and anthropologists have had a long-standing interest in the settlement and evolution of isolated islands, particularly Easter Island. The open access model is often used to describe the evolution of a human population and its resource base. Unfortunately, an open access model, with spiral convergence to a steady state, is inappropriate for island dynamics where the human population peaks and then goes into permanent decline. We develop more appropriate two-state and three-state models. The nonautonomous version of the three-state model, which collapses to the stable two-state model, produces dynamics that are more consistent with the history of Easter Island.