Print PageMathematical models of animal foraging behavior largely fall into one of two major categories: patch-use models and random search strategies. The patch-use approach focuses on patch departure criteria, such as giving-up time (GUT) and giving-up density (GUD), while the random search approach focuses on describing movement with stochastic processes like Lévy walks. We unified these disparate areas of foraging theory into a single, general modeling framework to identify optimal search strategies when resources do not occur in patches with distinct boundaries. In our model, foragers alternated between intensive and extensive modes of search with mode switching determined by GUT or GUD criteria. GUT foragers switched from intensive to extensive search mode based on time elapsed since last resource encounter, whereas GUD foragers switched modes based on a generalized measure of local resource density. Lévy walks were used to model movement in each search mode. A single-parameter, µ, can be tuned to produce Lévy walks that range from straight-line motion to Brownian motion. We identified the optimal parameters (µextensive, µintensive, switching threshold) for GUT and GUD foragers using a genetic algorithm and compared the performance of GUT and GUD foragers on landscapes with different levels of resource aggregation.
Results/Conclusions
Our results show that GUT foragers search about 7% less efficiently than GUD foragers. This difference is consistent across all levels of resource aggregation and suggests that a forager can use time since last resource encounter as a proxy for local resource density. For both GUT and GUD foragers, efficiency and variability in efficiency increased with resource aggregation. GUD foragers had slightly less variability in efficiency than GUT foragers across all levels of resource aggregation. Efficiency was most sensitive to the intensive search mode parameter (µintensive), particularly for landscapes with clumped resources. Efficiency was least sensitive to the switching threshold parameter. In contradiction to generally accepted theory, straight-line trajectories, characterized by µ=1, were not clearly and consistently identified as optimal extensive search behavior. We identified potential mechanisms that could account for the difference between analytic predictions and in silico behavior. In conclusion, we found that foragers that switch modes based on a rule-of-thumb (GUT) can nearly match the efficiency of foragers that switch modes based on information about resource density (GUD).
