Efficiency in competitive group foraging

Many animals such as albatrosses are known to exhibit foraging patterns where the distances they travel in a given direction are drawn from a heavy-tailed Levy distribution. Previous studies have shown under sparse resources, solitary foragers perform an optimally efficient search with Levy exponent equal to 2. However, in nature, there also exist situations where multiple foragers interact with each other either cooperatively or competitively. We develop a stochastic agent-based simulation that models competitive foraging. In our system, each forager has a territory with a certain size around itself which is not accessible by the others. Our results for various system sizes show that by increasing the size of the territory, and the number of agents, the efficiency of the search decreases, and the optimal Levy exponent shifts toward values larger than 2, indicating that more localized searches are more efficient in the presence of competition. In addition, we compare our analytical solution to the one for solitary foragers. Finally, we show that the variance among the efficiencies of the agents increases with increasing Levy exponent. Thus, by performing more localized searches, foragers might increase mean efficiency, but with the risk of increasing fluctuations in efficiency.