Predators choosing between patches with standing crop: the influence of switching rules and input types

Where prey arriving in a patch are not consumed immediately, they will accumulate. Predators are then presented with a prey density or standing crop that increases through further input, and decreases through the consumption by predators. Firstly, I show that the switching rule of predators has a significant influence on the expected predator equilibrium distribution in such a dynamic system. Three rules are compared; for all rules, analytical solutions are calculated (where possible). To test their plausibility for natural situations, predator distributions are simulated given the assumption that each predator obtains individual patch profitability estimates by using a common learning rule. As long as prey arrive in the patches in constant numbers per time unit, the first rule leads to input matching because predators stop switching when consumption in the two patches is equal. The other two rules, where predators continue to sample both patches even in the equilibrium state, lead to predator distributions where the more profitable patch is underused. The final equilibrium depends on the exact assumptions of the switching rule; however, it is independent of interference. But if the input delivered into a patch is a function of the current prey standing crop (for example in a reproducing prey population), predator and prey distributions will not reach an equilibrium in most cases: either standing crops increase indefinitely, or they approach zero, with all predators concentrating on the better patch. Only a small number of parameter sets show intermediate crops that are reasonably stable. With this input type, only up to 54% of the simulations reach the expected distribution. In a system with competition for dynamic standing crop, it is therefore essential to know the type of input and the switching-rule used by predators to be able to predict equilibrium predator distributions. Received: 17 March 1995/Accepted after revision: 5 November 1995