The Pattern and Effectiveness of Forager Allocation Among Flower Patches by Honey Bee Colonies

To gather its food efficiently, a colony of honey bees must allocate its foragers among flower patches in accordance with their profitabilities. Previous empirical studies have revealed the mechanisms of the allocation process, but tell us neither the allocation pattern that results nor its effectiveness. To investigate these topics, we develop a system of differential equations that models the allocation process in a hypothetical colony of bees whose behavior closely approximates the observed behavior of real bees. We find that our hypothetical colony tends toward a specific allocation of foragers among flower patches, one in which each forager experiences the same rate of "value" accumulation regardless of which patch she is visiting (the equal value rate allocation). Moreover, we show that no allocation brings value to the hypothetical colonyʹs hive more than twice as quickly as the equal value rate allocation. To test the accuracy of our model and its predictions about the allocation patterns of honey bee colonies, we use the model to generate predictions about the patterns of dancing and other variables for different flower patches that should be observed in real colonies. The results of one empirical test confirm the modelʹs prediction that at equilibrium the foragers from different patches will experience equal rates of value accumulation.