Considering the effects of temperature × nutrient interactions on the thermal response curve of carrying capacity

Climate warming will likely destabilize populations or drive consumers locally extinct. These predictions arise from consumer-resource models incorporating temperature-dependent parameters, and the accuracy of these predictions hinges on the validity of temperature scalings for each parameter. Among all parameters, carrying capacity (K) is the most ill-defined and the temperature scaling of this parameter has no empirically verified foundation. Most studies assume that K declines exponentially with warming, but others have assumed a positive or no relationship between K and temperature. Here, I developed a theoretical foundation for a temperature scaling of K based on physiological principles of temperature and nutrient limitation of phytoplankton growth. The trade-off between thermodynamics and nutrient uptake yields a unimodal thermal response curve for K, and this prediction is supported by empirical data on both phytoplankton and insects. Analyses of consumer-resource models demonstrate the primacy of K in determining predictions of coexistence and stability. Since K exerts a dominant influence on model predictions, ecologists should carefully consider the temperature scaling of K for the species and region in question to ensure accurate estimates of population stability and extinction risk.