Optimal foraging: the importance of environmental stochasticity and accuracy in parameter estimation

The Engen and Stenseth theorem is applied to a situation where the expected energy content and handling time of encountered food items are estimated with some stochastic error. We extended the Engen-Stenseth approach by incorporating in the model an explicit relationship between what the forager actually observes and what the situation actually is like. By such a formulation, we are able to evaluate the changes in the optimal foraging tactic and the cost of incomplete information; this cost is defined as the reduction in the optimal reward rate that results from the incomplete knowledge about the environmental situation. The approach presented in this article is general and makes it possible to study the problem of incomplete information in a variety of situations. In this article, however, we give some numerical examples that provide insights into the effect of incomplete information. For instance, we demonstrate that the optimal reward rate may attain a minimum for intermediate values of environmental uncertainty. However, since the location of this minimum depends on other parameters of the model, an increase in environmental uncertainty cannot in general be concluded to be favorable to the forager. In order to draw such conclusions, a thorough knowledge of both the environmental features entering the calculation of the optimal reward rate and also the intrinsic properties of the food items (measured by the energy content and the handling time) is necessary. We suggest how results like those derived in this article can be evaluated experimentally.