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

Area of Science:

• Complex adaptive systems
• Systems biology
• Urban studies
• Organizational science

Background:

• Function diversity and specialization are fundamental properties of complex adaptive systems.
• Previous understanding lacked overarching principles, appearing domain-specific.
• Disparate systems exhibit unique patterns in function diversification and specialization.

Purpose of the Study:

• To introduce an empirical framework and mathematical model for function diversification and specialization.
• To enable cross-system comparisons from microorganisms to metropolitan areas.
• To explain the observed scaling laws in function growth across diverse systems.

Main Methods:

• Developed an empirical framework and a generalized Yule-Simon mathematical model.
• Introduced diversification and specialization parameters to the model.
• Analyzed function diversity and specialization across bacteria, federal agencies, universities, corporations, and cities.

Main Results:

• The number of functions scales sublinearly with system size (exponents 0.35–0.57), consistent with Heaps' law, except for cities which show logarithmic scaling.
• The generalized Yule-Simon model with diversification and specialization parameters explains these empirical findings.
• System goals and structure influence the creation of new functions (e.g., federal agencies prioritize coverage, cities slow new occupations).
• Function growth follows a universal pattern once introduced across all analyzed systems.

Conclusions:

• A unified framework can describe function diversification and specialization across diverse complex systems.
• The model provides insights into the universal and system-specific drivers of functional emergence and scaling.
• Understanding these principles is crucial for managing and predicting the evolution of complex systems.