URoL:EN: Towards a unified theory of regulatory functions and networks across biological and social systems

Proposed work. Our starting premise is that regulatory organizational networks are a universal feature of human organizations, biological organisms and human-engineered mechanical systems. Unlike human social organizations where the precise structure of these networks are rarely accessible, many organizational principles are well-understood in biological and mechanical systems. Consequently, we propose to use them to provide insight for understanding human organizational principles by building an overarching framework that can be generalized to both human and non-human systems. Our proposed work consists of two major parts: (1) empirical analyses of organizational network costs using a scaling framework, and (2) quantitative theory construction motivated by the empirical analysis, that predicts the cost of organizational networks based on size, functional complexity, and centralized or decentralized organizational type. We will use scaling analysis of empirical data as a point of departure for revealing underlying principles and constructing a theoretical framework. This strategy has been successfully and widely used across biology [3,4], ecology [5], firms and cities [6], based on analyzing how aggregated organizational properties of a system vary with its size. Our preliminary analysis (Fig. 1) strongly supports our premise, showing that various measures for the cost of organizational networks across diverse systems scale in a remarkably similar way, obeying simple power laws with the same functional form, N^β, where N is the number of constituents. Of equal importance, the exponents β enable different systems to be quantitatively compared, and thus classified: (1) decentralized organizations (cities and bacteria genes) exhibit superlinear scaling (β>1), indicating that the cost of regulatory networks grows faster than the system size itself; (2) centralized organizations (federal agencies and universities) exhibit sublinear scaling (β <1), indicating a systematic economy of scale. In future work, we propose to incorporate additional data on companies from the US and elsewhere, such as the RAIS database offered by the Brazil Ministry of Economy, which has unusually detailed employee-level information for all registered companies in Brazil. Based on our empirical analyses across these diverse systems, we will construct mathematical models that predict the cost of organizational networks (such as the number of managers and administrators) in an organization. We anticipate that our hierarchical network-based models will be characterised by three dominant parameters: size, functional complexity of components in the network, and degrees of centralization. Our results will not only reveal how these factors affect the cost of organizational networks, but also demarcate regimes of sublinear and superlinear scaling. Although the organizational network structures are difficult to observe in a large range of companies, we can compare our models' predictions on the network's aggregated properties (such as the number of supervisors and depth of hierarchical trees) with that reported in datasets. Finally, we will develop a set of metrics to measure organizational infrastructure's effectiveness-- how an entity's organizational costs compared to others, while adjusted for its size, complexity, and organizational type.