Effects of spatial grouping on the functional response of predators

A unified mechanistic approach is given for the derivation of various forms of functional response in predator-prey models. The derivation is based on the principle of mass action but with the crucial refinement that the nature of the spatial distribution of predators and/or opportunities for predation are taken into account in an implicit way. If the predators are assumed to have a homogeneous spatial distribution, then the derived functional response is prey-dependent. If the predators are assumed to form a dense colony or school in a single (possibly moving) location, or if the region where predators can encounter prey is assumed to be of limited size, then the functional response depends on both predator and prey densities in a manner that reflects feeding interference between predators. Depending on the specific assumptions, the resulting functional response may be of Beddington-DeAngelis type, of Hassell-Varley type, or ratio-dependent.