Swarms of Predators Exhibit "Preytaxis" if Individual Predators Use Area-Restricted Search

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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 stomach 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 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 of its turning frequency to changes in prey density, both of which are easily measured. Thus, we show how short-term observations of individual predators can lead to a complete macroscopic description of predator-prey interactions in a spatially distributed environment. We demonstrate the use of our model by applying it to the spatial dynamics of an interaction between goldenrod aphids (Uroleucon nigrotuberculatum) and adult ladybug beetles (Coccinella septempunctata). Although in this specific case the model is limited to predictions on the order of weeks, we show how it might be used to evaluate the effectiveness of different predators as biological control agents. Our particular mechanistic model indicates that the consequences of aggregation for prey control depend on the rates of taxis relative to the rates of prey population growth; only sometimes is predator aggregation sufficient to halt an incipient prey outbreak.