Coexistence: How to identify trophic trade-offs.

Analyses of growth response to resource availability are the basis for interpreting whether trophic trade-offs contributes to diversity. If different species respond most to resources that are limiting at different times, then those differences may trade off with other trophic or life-history traits that, together, help to maintain diversity. The statistical models used to infer trophic differences do not accommodate uncertainty in resources and variability in how individuals use resources. We provide hierarchical models for resource-growth responses that accommodate stochasticity in parameters and in data, despite the fact causes are typically unknown. A complex joint posterior distribution taken over >102 parameters is redily integrated to provide a comprehensive accounting of uncertainty in the growth response, together with a small number of hyperparameters that summarize the population response. An application involving seedling growth response to light availability shows that large trophic differences among species suggested by traditional models can be an artifact of the assumption that all individuals respond identically. The hierarchical analysis indicates broad trophic overlap, with the implication that slow dynamics play a more important role in preserving diversity than is widely believed.