The Effects of a Limited Memory Capacity on Foraging Behavior

Abstract

We introduce a simple mathematical model to describe the behavior of a forager with a limited memory capacity in the presence of two prey types that differ in their energetic values. The model is used to analyze the effect of memory capacity on foraging behavior and on foraging energetics and it contrasts with classic optimal foraging theory, which implicitly assumes that the forager has an infinite memory capacity. Classic optimal foraging theory dictates that the low value prey type should be invariably excluded from the diet when the high value type exceeds some critical relative frequency and invariably consumed otherwise. Our model forager behaves similarly except that, as its memory capacity declines, it is increasingly predisposed to consume the low value prey when it is suboptimal to do so. Nevertheless, our analysis indicates that the energetic efficiency of a forager with an infinite memory capacity can be approximated by a forager with a memory of modest capacity, perhaps one that contains information about 5–20 previously consumed prey items. In our model, memory constraints necessarily result in so-called “partial preferences” being exercised towards the low value prey type. Thus, limited memory capacity offers a possible explanation for observed violations of the “zero–one” rule of optimal diet composition. We also find a resemblance to a sigmoidal shape in the relationship between the representation of each prey type in the diet and its relative frequency. Thus, the memory-constrained forager exhibits behavior that resembles the type III functional response. Therefore, it is possible that memory constraints such as we envisage can contribute to the explanation of both partial preferences and functional responses.