The numerical response: rate of increase and food limitation in herbivores and predators

Two types of numerical response function have evolved since Solomon first introduced the term to generalize features of Lotka-Volterra predator-prey models: (i) the demographic numerical response, which links change in consumer demographic rates to food availability; and (ii) the isocline numerical response, which links consumer abundance per se to food availability. These numerical responses are interchangeable because both recognize negative feedback loops between consumer and food abundance resulting in population regulation. We review how demographic and isocline numerical responses have been used to enhance our understanding of population regulation of kangaroos and possums, and argue that their utility may be increased by explicitly accounting for non-equilibrium dynamics (due to environmental variability and/or biological interactions) and the existence of multiple limiting factors. Interferential numerical response functions may help bridge three major historical dichotomies in population ecology (equilibrium versus non-equilibrium dynamics, extrinsic versus intrinsic regulation and demographic versus isocline numerical responses).