Research Reveals Principle Linking Cells, Firms, Cities

Study finds that as systems grow, the pace of adding new functions slows down

Mar. 27, 2026 at 12:28am

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New research from MIT and the Santa Fe Institute has found that across a wide variety of complex systems - from bacterial cells to corporations to cities - the more a system grows, the fewer new functions it tends to add. The study presents a mathematical model that explains this common pattern, known as Heaps' Law, which was previously observed in linguistics.

Why it matters

This research provides insights into how organizations and other complex systems can effectively grow and add new capabilities. It suggests that simply increasing the size of a system, such as by hiring more employees, does not proportionally increase the number of new functions or job roles. To truly expand into new areas, companies and other entities need to build the right foundational infrastructure and capabilities first.

The details

The study, published in the Proceedings of the National Academies of Sciences, was co-led by Vicky Chuqiao Yang, an assistant professor at MIT Sloan, and James Holehouse, a mathematical biologist at the Santa Fe Institute. The researchers analyzed data from bacterial cells, US federal agencies, companies, universities, and metropolitan areas, and found that almost all of these systems followed the same pattern of function diversity growth described by Heaps' Law. As systems get bigger, the pace of adding new functions slows down, with organizations tending to hire more people into established roles rather than creating new ones.

  • The research was published on March 25, 2026.

The players

Vicky Chuqiao Yang

An assistant professor at the MIT Sloan School of Management and a former Santa Fe Institute Omidyar Fellow, who co-led the research.

James Holehouse

A mathematical biologist at the Santa Fe Institute, who co-led the research.

Santa Fe Institute

A nonprofit research institute that focuses on the study of complex systems.

MIT Sloan School of Management

The business school at the Massachusetts Institute of Technology.

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What they’re saying

“The perspective of this paper is through a complexity science lens, understanding the interaction between components and how this affects the overall system. Despite a lot of heterogeneity in the different types of systems we studied, our analysis finds that many systems exhibit common patterns of behavior.”

— Vicky Chuqiao Yang, Assistant Professor, MIT Sloan School of Management

“If an organization wants to add a new function category of AI, our research suggests that you can't just hire a person or people for that role and be done. To truly expand into a new function, it seems that you need certain infrastructure and existing functions to expand. If you want to become more complex, there's a foundation you first have to set up.”

— Vicky Chuqiao Yang, Assistant Professor, MIT Sloan School of Management

“One key takeaway is a striking empirical regularity in the relationship between organizational size and functional complexity. In other words, if an organization aims to be able to do a certain range of tasks, it needs to reach a certain size first.”

— James Holehouse, Mathematical Biologist, Santa Fe Institute

What’s next

The researchers plan to further explore the implications of their findings for how organizations and other complex systems can effectively grow and add new capabilities.

The takeaway

This study provides a new mathematical model for understanding the common patterns of how complexity grows across diverse systems, from cells to companies to cities. It suggests that simply increasing the size of a system does not proportionally increase its functional diversity, and that organizations need to build the right foundational capabilities before they can truly expand into new areas.