When does division of labor lead to increased system output?

This paper develops a set of simplified dynamical models with which to explore the conditions under which division of labor leads to optimized system output, as measured by the rate of production of a given product. We consider two models: in the first model, we consider the flow of some resource into a compartment, and the conversion of this resource into some product. In the second model, we consider the growth of autoreplicating systems. In this case, we divide the replication and metabolic tasks among different agents. The general features that emerge from our models is that division of labor is favored when the resource to agent ratio is at intermediate values, and when the time cost associated with transporting intermediate products is small compared to characteristic process times. The results of our model are consistent with the behavior of the cellular slime mold Dictyostelium discodeum, which switches from a single-celled to a multi-celled state when resources become limited. We also argue that division of labor in the context of our replication model suggests an evolutionary basis for the emergence of the stem-cell-based tissue architecture in complex organisms. Finally, the results of this paper may be useful for understanding how, in an economic context, firm productivity is maximized at intermediate firm sizes.