Constraints in Optimal Foraging Models

Traditionally, the kinds of constraints assumed in optimal foraging models have been simple physical constraints, such as the impossibility of simultaneously handling one prey item while searching for another, or the reduction in the rate of prey acquisition as the forager's bill fills up with prey. In general, potential psychological constraints imposed by limitations of an animal's information-processing capacities have received much less attention from optimal foraging theorists. There are several reasons for this neglect. First, theoreticians usually seek to keep models as simple and as general as possible. Second, foraging theorists justify neglecting psychological constraints on the grounds that natural selection should have provided animals with near-perfect psychological mechanisms if these mechanisms have a measurable impact on optimal performance. Finally, due to the lack of integration of the psychological and ecological literatures, behavioral ecologists are often simply unaware of the wealth of data that is available regarding animals' information-processing capacities.

The ignorance of behavioral ecologists of the psychological literature has resulted in some misguided early attempts by them to introduce psychological constraints, such as imperfect timing, into optimal foraging models. For example, Yoccoz et al. (1993) presented a general theoretical framework for understanding the effects of perceptual error on optimal foraging decisions. In order to do this, they assumed explicit relationships between the real energy content and handling time of each food item and what the forager estimates these quantities to be. They incorporated these assumptions into a model of optimal diet choice (Engen and Stenseth, 1984), which is based on the assumption that animals maximize their long-term rate of energy intake, and investigated the effects of adding perceptual error on the optimal solution to the model. In their model, Yoccoz et al. (1993) represent the actual energetic gains and times as random variables G and T, and the animal's perception of these random variables as X and Y respectively. They construct X and Y from G and T by adding unbiased normally distributed errors such that X = G +

Eg and Y = T + ep where eg and et are the errors in gain and time respectivdy. This general strategy is completely sound; however, Yoccoz et al. (1993) assume that the variances of the errors EG and ET are independent of the actual gains and times, G and T. This latter assumption flies in the face of over a century's worth of psychophysics showing that the error in the perception of the magnitude of a stimulus is not independent of its magnitude, but rather increases with stimulus magnitude (Bateson and Kacelnik, 1995a), a relationship known as Weber's law (see Figure 5.1).

The value of Yoccoz et al.'s (1993) model is that it demonstrates that introducing perceptual error can result in constrained rate-maximizing solutions that differ substantially from naïve, unconstrained treatments of the same problem. However, if such models are to be of use in understanding the behavior of real animals, then they need to include more realistic assumptions regarding the nature of perceptual constraints.

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