Optimal distributions of central-place foragers: honey bee foraging in a mass flowering crop

The ideal-free distribution and central-place foraging are important ecological models that can explain the distribution of foraging organisms in their environment. However, this model ignores distance-based foraging costs from a central place (hive, nest), whereas central-place foraging ignores competition. Different foraging currencies and cooperation between foragers also create different optimal distributions of foragers, but are limited to a simple two-patch model. We present a hybrid model of the ideal-free distribution that uses realistic competitive effects although accounting for distance-based foraging, and test it using honey bees (Apis mellifera L.) foraging in canola fields (Brassica napus L.). Our simulations show that foragers maximizing efficiency (energy profits ÷losses) prioritize distance to their aggregation more than those maximizing net-rate (energy profits ÷time), and that social foragers move to more distant patches to maximize group benefits, meaning that social foragers do not approach an ideal-free distribution. Simulated efficiency-maximizers had a hump-shaped relationship of trip times with distance, spending shorter amounts of time in both nearby and far-away patches. Canola fields were far more attractive to simulated foragers than semi-natural areas, suggesting limited foraging on semi-natural lands during the bloom period of canola. Finally, we found that the observed distribution of honey bees in canola fields most closely resembled the optimal distribution of solitary efficiency-maximizers. Our model has both theoretical and practical uses, as it allows us to model central-place forager distributions in complex landscapes as well as providing information on appropriate hive stocking rates for agricultural pollination.