INDIVIDUAL DECISIONS AND THE DISTRIBUTION OF PREDATORS IN A PATCHY ENVIRONMENT .2. THE INFLUENCE OF TRAVEL COSTS AND STRUCTURE OF THE ENVIRONMENT

(1) We investigate properties of a model of predator distribution in relation to prey abundance, when the predation process is subject to: (i) non-negligible handling time and mutual interference; (ii) predator learning; (iii) intake rate maximization by individual predators. The model is a development of that of Bernstein, Kacelnik & Krebs (1988). (2) The independent variables are between-patch travel cost and structure of the environment. The outcome of the model is described in relation to the predictions of the ideal free distribution (IFD). We consider both the numerical distribution of predators and the mortality rate imposed on the prey population. (3) When travel cost is small, prey depletion is slow and interference is moderate, predators conform to the predictions of the IFD and prey mortality is density-dependent. (4) As travel cost is increased, rate-maximizing predators become more sedentary and the population settles at distributions far from the IFD. In common with all other disturbances of the predation process that impair the correlation between prey and predator densities, this causes mortality to approach density independence and later negative density dependence. (5) In semi-continuous environments where prey density is correlated between neighbouring patches, the slower the spatial rate of variation in prey density (the coarser the environmental grain), the poorer is the adjustment to the IFD. This effect is due to the predators' need for learning: when the environmental sample experienced within the reach of each individual predator is unrepresentative of the global average prey density (as it happens when the environmental grain is very coarse relative to migration range of predators), the predators cannot learn the global distribution of foraging opportunities and fail to take the policy that optimizes individual intake rate. (6) We discuss how these findings might account for observed patterns of mortality in real insects populations.