Central-place foraging in honey bees: the effect of travel time and nectar flow on crop filling

Crop-filling by honeybees foraging at sources of variable nectar flow at a fixed distance from the hive has been shown to maximize energetic efficiency, defined as ratio of energy gained to energy spent. Predictions based on maximisation of rate of energy gain, defined as net energy gained per unit time foraging, are significantly different from observed behaviour (Schmid-Hempel et al. 1985). In this paper we consider the effect of varying travel times in addition to flow rate. The predictions of an extended version of our theoretical model are confronted with experimental results obtained by Núñez (1982). Núñez found that bees filled their crops more fully for higher flows and longer travel times. We show that when the cost of carrying a load is considered, this trend can be predicted by maximising either energetic efficiency or net rate of gain. Figure 1 shows, however, that maximisation of net rate of gain can only produce an acceptable quantitative fit if unreasonably high costs are assumed to result from carrying the load. Energetic efficiency instead generates a good quantitative fit for acceptable assumptions about this cost (Fig. 2).