Abstract
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.
Highlights
The functional response [1,2] considers the number of prey consumed by a single predator as influenced by prey abundance
Foraging with simultaneous resource encounters we again assume that there are two resource types but, unlike section Decision trees and the functional response for two prey types, some microhabitats can contain a mixture of both types
We develop a game-theoretic approach for constructing functional responses in multi-prey environments and for finding optimal foraging strategies based on these functional responses [9,20]
Summary
The functional response [1,2] considers the number of prey (or resource items) consumed by a single predator (or forager) as influenced by prey abundance. Short-term apparent competition [6,7] results if the presence of the second prey encourages the predator to spend more time or effort searching for and capturing prey. This happens when foragers bias their efforts towards areas rich in resources. Regardless, the two-food functional response is central to understanding diets, optimal foraging for multiple resources, predator mediated indirect effects between prey, and population dynamics within food webs
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