Server System and Queuing Models of Leaf Harvesting by Leaf-Cutting Ants

Two models consider the maximum possible output from a system of servers and take account of queuing time and "traffic intensity" resulting from dense social foraging to predict the role of service and queuing processes in attine leaf harvesting.

Abstract

Because leaf-cutting ants are eusocial organisms, the foraging behavior of individual workers is likely to have evolved in ways that enhance the success of workers as a group rather than as individual foragers. Harvesting leaf tissue is often an especially concentrated group activity in forest-dwelling Atta ants. Under such circumstances, group foraging success might be enhanced if individual workers reduce their cutting time, thereby taking smaller fragments individually but allowing a greater number of their nest mates to obtain fragments per unit time. I model a foraging situation of this kind as a service process. One model considers the maximum possible output from a system of servers, and a second model takes account of queuing time and "traffic intensity" resulting from dense social foraging. Quantitative predictions of the models are compared with fragment masses taken during natural foraging by Atta colombica ants on Barro Colorado Island, Panama. Natural fragment masses are nearly always too small to maximize individual worker foraging rates or energetic efficiency, but reasonably close to the sizes that maximize whole-colony foraging rate. The models also predict the mean and distribution of cutting times, the queuing time (which might be measured as latency from arrival at a resource site to initiation of a cut), and the ratio of actively cutting workers to queuing workers at equilibrium. The variety of quantitative predictions would allow extensive empirical testing of the model. If the role of service and queuing processes in attine leaf harvesting were confirmed by experiment, additional questions may be raised concerning the cognitive mechanisms by which ants recognize congestion and adjust fragment cutting appropriately.