We develop a decision tree based game-theoretical approach for constructing functional responses in multi-prey/multi-patch environments and for finding the corresponding optimal foraging strategies. Decision trees provide a way to describe details of predator foraging behavior, based on the predator's sequence of choices at different decision points, that facilitates writing down the corresponding functional response. It is shown that the optimal foraging behavior that maximizes predator energy intake per unit time is a Nash equilibrium of the underlying optimal foraging game. We apply these game-theoretical methods to three scenarios: the classical diet choice model with two types of prey and sequential prey encounters, the diet choice model with simultaneous prey encounters, and a model in which the predator requires a positive recognition time to identify the type of prey encountered. For both diet choice models, it is shown that every Nash equilibrium yields optimal foraging behavior. Although suboptimal Nash equilibrium outcomes may exist when prey recognition time is included, only optimal foraging behavior is stable under evolutionary learning processes.

Department of Biological Sciences University of Illinois at Chicago Chicago United States of America

Department of Mathematics Wilfrid Laurier University Waterloo Ontario Canada

Institute of Entomology Biology Centre Academy of Sciences of the Czech Republic and Faculty of Science University of South Bohemia České Budějovice Czech Republic

MTA ELTE Theoretical Biology and Evolutionary Ecology Research Group and Department of Plant Systematics Ecology and Theoretical Biology Eötvös Loránd University Budapest Hungary

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