The Ideal Free Distribution of Unequal Competitors: Predictions from a Behaviour-Based Functional Response

Abstract

1. The spatial distribution of foraging predators differing in foraging traits was investigated theoretically. Three types of individual differences were investigated: dominance that determines the outcomes in fights for food, searching efficiency and prey handling efficiency. The basic assumptions were: (i) predators search for prey; (ii) encountered prey takes time to handle; (iii) the handling process may be interrupted by a searching competitor initiating a conflict about the prey; (iv) conflicts take an expected time to settle; and (v) the winner resumes handling and the loser resumes searching. 2. Stable equilibrium distributions were found in all cases, in the sense that no competitor could achieve a higher intake rate from switching patch. 3. When it was assumed that each of the predators was different from the others, the ideal free distributions of the dominance model and the handling efficiency model resembled one another. A boundary phenotype existed with more dominant/efficient competitors only occurring in the high prey density patch and less dominant/efficient ones occurring mixed across patches. This was labelled semitruncated distribution. In the search efficiency model, the distribution was truncated, i.e. competitors less efficient than the boundary phenotype only occurred in the high prey density patch whereas the more efficient competitors occurred in the low prey density patch. 4. The models were also analysed with the predators classified into two types. As the density of competitors increased, the solution approached a set of neutral equilibria where a few predators of the more efficient type could be exchanged for a larger number of the less efficient type to reach a new equilibrium. 5. The density of predators may be negatively correlated with patch productivity and prey density when predators differ in handling efficiency. Prey-searching efficiency of predators was negatively correlated with predator density, patch productivity and prey density. Its consequences for the conservation of species are discussed