Task partitioning in insect societies. I. Effect of colony size on queueing delay and colony ergonomic efficiency

The collection and handling of colony resources such as food, water, and nest construction material is often divided into subtasks in which the material is passed from one worker to another. This is known as task partitioning. When material is transferred directly from one individual to another, queueing delays frequently occur because individuals must sometimes wait for a transfer partner. A stochastic simulation model was written to study the effect of colony size on these delays. Queueing delay decreases roughly exponentially with colony size because stochastic fluctuations in the arrival of individuals are lower in larger colonies. These results support empirical studies of Polybia occidentalis and other theoretical studies of honeybees. The effect of the relative number of individuals in the two subtask groups was also studied. There is a unique optimal ratio of the number of workers associated with each of the subtasks that simultaneously minimizes mean queueing delay and maximizes colony nectar-processing rate. Deviations from this optimal ratio, for example, as a result of forager mortality or changes in nectar productivity that affect foraging trip duration, increase mean queueing delays greatly, especially in smaller colonies.