Aggregation of Predators and Insect Parasites and its Effect on Stability

Searching animals, such as predators and insect parasites,t usually spend more time where their requisites are more plentiful, a behaviour that has an obvious selective advantage. Despite this, it is only from relatively recent work that aggregative responses to uneven prey distributions have been adequately quantified in terms of predator numbers, or the time spent by a predator, per unit areas of different prey density. This in turn is reflected in the relatively few predator-prey models that have allowed for such aggregative behaviour (Royama 1971; Hassell & Rogers 1972; Hassell & May 1973; Murdoch & Oaten 1974). These are in contrast to the many models (e.g. Lotka 1925; Volterra 1928; Thompson 1924; Nicholson & Bailey 1935; Watt 1959; Hassell & Varley 1969) where search is random, which effectively implies an even distribution of predators throughout the whole prey area and makes the particular types of prey distribution irrelevant to the model outcome. In an attempt to show how predator aggregation could affect stability, Hassell & May (1973) considered a simple modification of the Nicholson-Bailey model in which the prey survival was given by