In social insect biology, one of the most paradoxical observations is the apparent decrease in per capita brood production with increasing group size. One of the principal explanations of this observation uses the tenets of central limit theorem to hypothesize that despite the decrease in per capita mean, the reduced variance associated with increasing group size could sufficiently explain the paradox (Wenzel and Pickering, 1991). Implicit in this explanation, however, is the assumption that the pertinent sampling space approximates to a gaussian distribution. In contrast, the real life sampling space faced by most social insect groups in terms of variables such as foraging more closely resembles a non-uniform, clumped distribution. Using computer simulations and experimental observations in a closed foraging arena, we compare the foraging success of various species of the paper wasp Polistes under different patterns of resource distribution. Our results suggest that the predictions of the central limit theorem for a clumped distribution significantly differ from those of a uniform or a gaussian distribution. Such differences could explain the different modes of work organization and foraging patterns seen in various groups in terms of the resource ecology of the group.
Keywords: foraging
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