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Aggregation of Predators and Insect Parasites and its Effect on Stability

M. P. Hassell and R. M. May
Journal of Animal Ecology
Vol. 43, No. 2 (Jun., 1974), pp. 567-594
DOI: 10.2307/3384
Stable URL: http://www.jstor.org/stable/3384
Page Count: 28
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Aggregation of Predators and Insect Parasites and its Effect on Stability
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Abstract

(1) Some examples are illustrated where predators have been shown to concentrate their searching activities in regions of high prey density. (2) A model, based on the changes in turning behaviour seen in many predators after feeding (or parasites after parasitism), is developed to show the expected form of aggregative responses resulting from this behaviour alone. The responses tend to be sigmoid in form when expressed as the time spent by a predator in unit areas of different prey density. (3) A further model is discussed in which predators remain in a unit area of prey provided that a prey is encountered within a critical threshold time. This model also generates responses which are more-or-less sigmoid in form. (4) On the basis of these examples (from observation, experiment and models) a general aggregative response may be characterized by three components: an upper plateau where approximately the same (maximum) time is spent in unit areas of relatively high prey densities; similarly, a lower plateau at relatively low prey densities where a constant minimum time is spent in each area and, thirdly, a transitional region where there is a marked increase in time spent per unit area as prey density increases. (5) The stability properties of models including different types of aggregative response are discussed. These responses vary from simple linear relationships between time spent per unit area and prey density, to more complex responses containing the three components of a general response listed in (4) above. In the first place, the prey are assumed to have an effective rate of increase of approximately unity and to have a strongly clumped distribution (k of negative binomial <<1). These constraints enable a full analytic treatment to be presented. However, the basic findings are also shown to apply when the prey are not so strongly clumped (k = 1) and for the general case where prey reproductive rate can taken any value. (6) Stability is increased when (a) there is a marked difference between the maximum and minimum time spent per unit area, (b) the average prey density falls in the neighbourhood of the transition region where the response to prey density is most marked, (c) the time spent travelling between unit areas of prey is high, (d) the effective prey reproductive rate is reduced and (e) the prey distribution becomes more clumped.

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