Optimal foraging strategies for mutually avoiding competitors.

Many animals are known to exhibit foraging patterns where the distances they travel in a given direction are drawn from a heavy-tailed Lévy distribution. Previous studies have shown that, under sparse and random resource conditions, solitary non-destructive (with regenerating resources) foragers perform a maximally efficient search with Lévy exponent μ equal to 2, while for destructive foragers, efficiency decreases with μ monotonically and there is no optimal μ. However, in nature, there also exist situations where multiple foragers, displaying avoidance behavior, interact with each other competitively. To understand the effects of such competition, we develop a stochastic agent-based simulation that models competitive foraging among mutually avoiding individuals by incorporating an avoidance zone, or territory, of a certain size around each forager which is not accessible for foraging by other competitors. For non-destructive foraging, our results show that with increasing size of the territory and number of agents the optimal Lévy exponent is still approximately 2 while the overall efficiency of the search decreases. At low values of the Lévy exponent, however, increasing territory size actually increases efficiency. For destructive foraging, we show that certain kinds of avoidance can lead to qualitatively different behavior from solitary foraging, such as the existence of an optimal search with 1<μ<2. Finally, we show that the variance among the efficiencies of the agents increases with increasing Lévy exponent for both solitary and competing foragers, suggesting that reducing variance might be a selective pressure for foragers adopting lower values of μ. Taken together, our results suggest that, for multiple foragers, mutual avoidance and efficiency variance among individuals can lead to optimal Lévy searches with exponents different from those for solitary foragers.