How much regulation do we need from genomes to society?
Regulatory functions are essential in both socioeconomic and biological systems, from corporate managers to regulatory genes. Regulatory functions come with substantial costs and benefits, and the balance of the two is often taken for granted. A fundamental question for all complex systems becomes how much regulatory function do they need for their size and function? Here, we present empirical evidence that regulatory functions scale systematically across diverse systems: biological organisms (bacterial and eukaryotic genomes), human organizations (companies, federal agencies, universities), and decentralized entities (Wikipedia, cities). We combine an analysis of large data sets from each of these domains with a simple conceptual model. The model predicts that the scaling of regulatory costs shifts with system structure. Well-mixed small systems exhibit superlinear scaling between size and regulatory function, while modular large ones show sublinear or linear scaling, both in agreement with data. Finally, we find that socioeconomic systems that contain more diverse occupational functions tend to have more regulatory costs than expected from the scaling relationships, confirming the hypothesis that the type and complexity of interactions also play a role in regulatory costs. Our cross-system comparison offers a mechanistic framework for understanding regulatory function and can potentially guide efforts to analyze the costs and benefits of regulatory function in diverse systems.