Optimal Foraging and the Form of the Predator Isocline

I explore the relation between optimal foraging and the geometrical character of the predator isocline. Two basic models are discussed. The first is a multispecies generalization of Holling's "disc" equation. If a predator can rapidly discriminate among prey types, it is argued that its isoclines should not have positive slopes. Isoclines with positive slopes may occur if the predator must invest time discriminating between prey of unequal value, and there is a high absolute abundance of the better quality prey species. For a food-limited predator, however, selection should moderate the degree of rightward slope. In the second model, encounter and capture rates vary directly with relative prey abundance because of switching behavior. A number of published switching models are shown to produce isoclines with partially positive slopes. If the attack rates on each of two prey species are functionally related, it is argued that an optimally foraging predator will either have rectangular isoclines or isoclines with negative slope. This suggests that existing switching models are not completely satisfactory representations of switching behavior. A few examples of predators with isoclines of positive slope have been observed. Some possible mechanisms for generating such isoclines are discussed briefly. Several central ideas in community theory would founder were predators often to have isoclines with positive slopes.