Modularity and reliability in the organization of organisms

An organism persists only if it satisfies internal and external constraints. Within the organism networks of processes meet the constraints. In such networks a principle of matching often obtains: the pattern of coupling among processes matches the correlation among constraints. That is, a module-a cluster of coupled processes-meets a constraint. Dissociable modules meet dissociable constraints. A hierarchy of modules meets a hierarchy of constraints. We have inquired whether such matching is predicted by an optimality criterion in a simple example. We find that in an ensemble of networks with unreliable processes, the networks that meet the constraints with highest reliability obey the principle of matching. The difference in reliability between modular and nonmodular networks that meet the same constraints is a function of the probability of success per process. Our results suggest that this difference is maximal at a probability of success that increases monotonically with the number of processes in the network.