Scaling from optimal behavior to population dynamics and ecosystem function

While behavioral responses of individual organisms can be predicted with optimal foraging theory, the theory of how individual behavior feeds back to population and ecosystem dynamics has not been fully explored. Ecological models of trophic interactions incorporating behavior of entire populations commonly assume either that populations act as one when making decisions, that behavior is slowly varying or that non-linear effects are negligible in behavioral choices at the population scale. Here, we scale from individual optimal behavior to ecosystem structure in a classic tri-trophic chain where both prey and predators adapt their behavior in response to food availability and predation risk. Behavior is modeled as playing the field, with both consumers and predators behaving optimally at every instant basing their choices on the average population behavior. We establish uniqueness of the Nash equilibrium, and find it numerically. By modeling the interactions as playing the field, we can perform instantaneous optimization at the individual level while taking the entire population into account. We find that optimal behavior essentially removes the effect of top-down forcing at the population level, while drastically changing the behavior. Bottom-up forcing is found to increase populations at all trophic levels. These phenomena both appear to be driven by an emerging constant consumption rate, corresponding to a partial satiation. In addition, we find that a Type III functional response arises from a Type II response for both predators and consumers when their behavior follows the Nash equilibrium, showing that this is a general phenomenon. Our approach is general and computationally efficient and can be used to account for behavior in population dynamics with fast behavioral responses.