  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 resource-limited 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. We
discuss the results of this paper in the context of simulations with digital
life. 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.
