Swarms of predators exhibit "preytaxis" if individual predators use area-restricted search

TLDR: It is shown how short-term observations of individual predators can lead to a complete macroscopic description of predator-prey interactions in a spatially distributed environment and how this model might be used to evaluate the effectiveness of different predators as biological control agents.

Abstract: We show that if individual predators restrict the area of their search following an encounter with prey, then this behavior translates into populations of predators flowing toward regions of high prey density. This result requires only that predators move at a constant speed but change their direction of movement more often when their stomachs are full and that increases in prey density increase the feeding rate and stomach fullness of predators. The partial differential equation that is derived by assuming such behavior includes terms representing both random motion and taxis on the part of the predator. The form and magnitude of these terms can be estimated by quantifying how prey density influences the frequency of directional changes in a foraging predator and by obtaining functional-response curves for predators that have been starved for different lengths of time. In general, the strength of a predator's taxis or aggregation response depends on its average velocity of search and on the sensitivity o...