Consequences of variation in foraging success among predators on numerical response

The relationship between foraging success and reproduction is commonly assumed to be linear in theoretical investigations. Although the exact relationship (e.g., linear or nonlinear) does not influence qualitative conclusions of models under some assumptions, an inclusion of individual behavioral variation can make it otherwise due to Jensen's inequality. In particular, a mechanism that stabilizes food web dynamics is generated when two conditions are satisfied: (1) the reproduction of predators experiences diminishing returns from foraging success (i.e., concave down relationship between foraging success and reproduction) and (2) foraging success variation among predator individuals increases with the predator density. However, empirical results that confirm these conditions are scarce. This study describes the mechanism as a hypothesis for stability and discusses some important considerations for empirical verifications of the mechanism.