A Mechanistic Approach for Modeling Temperature‐Dependent Consumer‐Resource Dynamics

Abstract

Paramount to our ability to manage and protect biological communities from impending changes in the environment is an understanding of how communities will respond. General mathematical models of community dynamics are often too simplistic to accurately describe this response, partly to retain mathematical tractability and partly for the lack of biologically pleasing functions representing the model/environment interface. We address these problems of tractability and plausibility in community/environment models by incorporating the Boltzmann factor (temperature dependence) in a bioenergetic consumer-resource framework. Our analysis leads to three predictions for the response of consumer-resource systems to increasing mean temperature (warming). First, mathematical extinctions do not occur with warming; however, stable systems may transition into an unstable (cycling) state. Second, there is a decrease in the biomass density of resources with warming. The biomass density of consumers may increase or decrease depending on their proximity to the feasibility (extinction) boundary. Third, consumer biomass density is more sensitive to warming than resource biomass density (with some exceptions). These predictions are in line with many current observations and experiments. The model presented and analyzed here provides an advancement in the testing framework for global change scenarios and hypotheses of latitudinal and elevational species distributions.