The Evolutionary Origins of Hierarchy

Hierarchy is an important organizational property in many biological and man-made systems, ranging from neural [1, 2], ecological [3], metabolic [4], and genetic regulatory networks [5], to the organization of companies [6], cities [7], societies [8], and the Internet [9, 10]. There are many types of hierarchy [11–13], but the one most relevant for biological networks [14, 15], especially neural networks [1, 2, 16], refers to a recursive organization of modules [10, 13]. Modules are defined as highly connected clusters of entities that are only sparsely connected to entities in other clusters [17, 19, 20]. Such hierarchy has long been recognized as a ubiquitous and beneficial design principle of both natural and man-made systems [14]. For example, in complex biological systems, the hierarchical composition of modules is thought to confer greater robustness and adaptability [1, 2, 16, 21], whereas in engineered designs, a hierarchical organization of simple structures accelerates the design, production, and redesign of artifacts [19, 22, 23].