Optimal Giving-Up Times and the Marginal Value Theorem

The Marginal Value Theorem (Charnov 1976) is a special case of the results presented here, which deals with properties of an optimal RT strategy, which all strategies of this class will share many of the same properties.

Abstract

Krebs et al. (1974) predicted that an optimal forager in a patchy habitat should apply the same giving-up time (GUT) to all patches, even if they differ in quality. This prediction has repeatedly appeared in the literature. However, it is based on a model which is not designed to predict GUT's. When an analogous model is derived which is designed to predict optimal GUT's, it is found that larger GUT's should be used in better quality patches. This result suggests a forager should be more persistent in patches it knows are good than in ones it knows are poor. Under the proposed definition of "better quality," it also follows that, on the average, more time will be spent in better quality patches, and a greater yield will be obtained. Increasing the mean interpatch travel time increases the optimal GUT's, as well as the mean patch yields and residence times. The theoretical development employed to predict optimal GUT's is not restricted to this strategy. Rather, by simply renaming certain quantities which appear in the formulas used, it can be applied to a broad class of strategies, to which the residence time (RT) strategy of Charnov (1976), Krebs et al. (1974), and others belongs. Thus, the Marginal Value Theorem (Charnov 1976), which deals with properties of an optimal RT strategy, is a special case of the results presented here. All strategies of this class will share many of the same properties. Numerical examples show that neither an optimal GUT strategy nor an optimal RT strategy is consistently superior to the other when their performances in the same habitat are compared between habitats. Further, other strategies of the same class, such as hunting by expectation (Gibb 1962), can be superior to both. Thus, even within this class of strategies, one should not treat "optimal foraging strategy" and "optimal RT strategy" as synonyms.