Scaling laws for function diversity and specialization across socioeconomic and biological complex systems.

ABSTRACT: Function diversity, the range of tasks individuals perform, and specialization, the distribution of function abundances, are fundamental to complex adaptive systems. In the absence of overarching principles, these properties have appeared domain-specific. Here, we introduce an empirical framework and a mathematical model for the diversification and specialization of functions across disparate systems, including bacteria, federal agencies, universities, corporations, and cities. We find that the number of functions grows sublinearly with system size, with exponents from 0.35 to 0.57, consistent with Heaps' law. In contrast, cities exhibit logarithmic scaling. To explain these empirical findings, we generalize the Yule-Simon model by introducing two key parameters: a diversification paramete

SUBMITTER: Yang VC 

PROVIDER: S-EPMC12912993 | biostudies-literature | 2026 Feb

REPOSITORIES: biostudies-literature