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Foraging is crucial for animals to survive. Many species forage in groups, asindividuals communicate to share information about the location of availableresources. For example, eusocial foragers, such as honey bees and many ants,recruit members from their central hive or nest to a known foraging site.However, the optimal level of communication and recruitment depends on theoverall group size, the distribution of available resources, and the extent ofinterference between multiple individuals attempting to forage from a site. Inthis paper, we develop a discrete-time Markov chain model of eusocial foragers,who communicate information with a certain probability. We compare thestochastic model and its corresponding infinite-population limit. We find thatforaging efficiency tapers off when recruitment probability is too high -- aphenomenon that does not occur in the infinite-population model, even though itoccurs for any finite population size. The marginal inefficiency at highrecruitment probability increases as the population increases, similar to aboundary layer. In particular, we prove there is a significant gap between theforaging efficiency of finite and infinite population models in the extremecase of complete communication. We also analyze this phenomenon byapproximating the stationary distribution of foragers over sites in terms ofmean escape times from multiple quasi-steady states. We conclude that for anyfinite group of foragers, an individual who has found a resource should onlysometimes recruit others to the same resource. We discuss the relationshipbetween our analysis and multi-agent multi-arm bandit problems.

Finite population effects on optimal communication for social foragers