If culture is defined as variation acquired and maintained by social learning, then culture is common in nature. However, cumulative cultural evolution resulting in behaviors that no individual could invent on their own is limited to humans, song birds, and perhaps chimpanzees. Circumstantial evidence suggests that cumulative cultural evolution requires the capacity for observational learning. Here, we analyze two models the evolution of psychological capacities that allow cumulative cultural evolution. Both models suggest that the conditions which allow the evolution of (...) such capacities when rare are much more stringent than the conditions which allow the maintenance of the capacities when common. This result follows from the fact that the assumed benefit of the capacities, cumulative cultural adaptation, cannot occur when the capacities are rare. These results suggest why such capacities may be rare in nature. (shrink)