Multiple time scales in consumer-resource interactions

Arguments regarding the appropriate form for the rate at which consumers extract biomass from resource populations hinge on relative time scales of underlying processes. Some ecologists argue that, because differential equation models imply instantaneous rates of change, time scale arguments do not hold. Here we point out that this reasoning is fallacious. We define three natural time scales for consumer-resource interactions and demonstrate, using asymptotic methods of analysis, how relative differences in these scales lead to the formulation of models with qualitatively distinct dynamics. Further, we identify time scale and resource heterogeneity assumptions that constrain the R* competition rule (i.e., the competitor that suppresses the resource to the lowest density excludes all other competitors), as well as clarify the dichotomy between Schoener’s models of competition for overlapping and for partitioned resources.