© 1991 International Society for Behavioral Ecology
research-article |
Optimal patch residence time of a sit-and-wait forager
Institute of Biological Sciences, University of Tsukuba, Ibaraki 305, Japan
ABSTRACT
This paper addresses optimal giving-up time of a sit-and-wait forager by a rate maximization model. It was assumed that a forager takes at most only one prey item in a patch in one trial, that is, the forager leaves a patch with a prey item (if it attacks it) or without prey (if it gives up). Some kinds of sit-and-wait foragers, like owls, hunt in this manner. The following assumptions were made: (1) A forager recognizes the habitat type of patches (e.g., forest type or grassland type). (2) Spatial or temporal heterogeneity generates the uncertainty of the environment in each habitat type. It was assumed that in a patch (in habitat type i), prey encounter rate (X) is fixed during the trial and encounter with prey depends on a Poisson process. However, prey encounter rate varies across trials within each habitat type according to 
i-(
). Thus the forager does not know the prey encounter rate that is assigned to each patch in the type, but it knows the probability density function, i-(). (3) The forager encounters each habitat type randomly in the environment. The patch residence time for each habitat type was considered as the only decision parameter. Considering stochastic change of prey encounter rate in patches of a habitat type, information limitation for the foraging animal can be treated. Patch residence time was influenced by the pattern of the stochasticity. When the forager knows perfectly the encounter rate of prey in each patch (i.e., no stochasticity), the optimal giving-up time is infinite or zero (reject the patch). With the limited information (stochastic environment), the condition for a finite, nonzero optimal giving-up time in patches of a habitat depends on how far the worst case is below the average among patches of the habitat and how bad the worst case is compared to the average of the whole environment. In a negatively skewed habitat, these conditions tend to hold easily. The optimal forager should perform pessimistically or doubt whether the patch contains prey, that is, set a finite giving-up time. In a positively skewed habitat, the optimal forager should perform optimistically, that is, set an infinite giving-up time. The expected gain is higher in the positively skewed habitat than in the negatively skewed habitat. When the forager must choose between the two habitats, it should choose the positively skewed habitat. [Behav Ecol 1991;2:283–294]