The group-size paradox:: effects of learning and patch departure rules

In many species, foraging in groups can enhance individual fitness. However, groups are often predicted to be larger than the size that maximizes individual fitness. This is because individual foragers are expected to continue joining a group until the fitness in the group falls to the level experienced by solitary foragers. If such a process were pervasive, social foraging, paradoxically, would provide little evolutionary advantages. We propose a solution to the group-size paradox by allowing foragers to learn about habitat quality and leave food patches when their current intake rate falls below that expected for the whole habitat. By using a simulation model, we show that under a wide range of population sizes, foragers using such rules abandon under- and overcrowded patches, ensuring that group size remains close to the optimal value. The results hold in habitats with varying patch quality, but we note that the lack of food renewal in patches can disrupt the process of group formation. We conclude that groups of optimal sizes can occur frequently if fitness functions are peaked and resources patchily distributed, without the need to invoke relatedness between joiners and established group members, group defense against joiners, or other mechanisms that were proposed earlier to prevent groups from becoming too large.