Global optimization from suboptimal parts: foraging sensu lato by leaf-cutting ants

Central-place foraging theory has been unable to explain the load selection behavior of leaf-cutting ants (Atta spp., Attini: Formicidae). We suggest that this is due to incomplete consideration of the sequence of behaviors involved in resource acquisition by these ants. Unlike most central-place foragers, leaf-cutting ants do not return to their nests with food. Instead, the leaf fragments they gather must be processed within the nest to convert them to substrate for fungal gardens. We have shown previously that leaf fragment size affects the rate of distribution and processing of leaf tissue inside laboratory nests of Atta colombica. Including these tasks in the calculation of foraging rate may help explain load selection and other features of central-place foraging by Atta colonies. Here we develop a mathematical model of the complete sequence of external and internal tasks that lead to addition of substrate to fungal gardens. Using realistic parameter values, the leaf fragment sizes predicted to maximize a colony's rate of foraging in this broad sense correspond well with the mean fragment sizes actually collected by Atta colonies in the field. The optimal fragment size for global performance in the model is below the size that would maximize the delivery rate by above-ground foragers. The globally optimal size also fails to maximize the rate of either fragment distribution or fragment processing within the nest. Our results show how maximum collective performance of an ensemble of linked tasks may require behavior that would appear suboptimal in a piecemeal analysis of tasks.