Competition in a group of equal foragers

Using techniques from renewal process theory, we build a stochastic model for gain accumulation in a group of equal competitors foraging in a patchy environment. The model for gain of the individuals is based on the waiting times between subsequent prey encounters by the group. These waiting times depend on the number of foragers in the group. A single parameter of this dependency encompasses a variety of foraging scenarios, from co-operation to scramble. With constant patch size, correlations between gains of any pair of foragers are negative. This dependency is most intense in small groups. Increased variation in patch size makes correlations in gains between group members positive irrespective of the group size. For a solitary forager, variance in gain approaches zero with increasing time in the patch. For an individual member in a group, variance grows monotonically. Thus, depending on the patch departure rule controlling the time to be spent in the patch, solitary foragers may have a smaller variance in gain than members in a group. As solitary foragers also potentially harvest all prey in the patch, it is hard to believe that grouping behavior would evolve solely on the basis of foraging.