From cells to companies: Study shows how funcation diversity scales within complex systems

What is it about?

We find Heaps' law, empirical regularity first identified in how diversity of vocabulary scales in books, also describes function diversity in cells and many human organizations (with cities being a notable exception). Through modeling the growth process and empirically estimating key parameters, we find that while systems differ in how they add new functions, once a function is introduced, its growth follows a common sublinear preferential attachment process.

Featured Image

Photo by Navy Medicine on Unsplash

Photo by Navy Medicine on Unsplash

Why is it important?

This study uncovers simple, general rules for how complex systems — from microbes and cells to companies, government agencies, and cities — grow and become more complex. As these systems get bigger, they add new kinds of functions, but at a slowing rate, and the pattern of growth follows predictable mathematical laws. We show that differences across systems (for example, cities versus federal agencies) reflect their goals and structure, yet once new functions appear, they expand in strikingly similar ways. By revealing shared principles behind diversification and specialization, the study helps us better understand — and potentially better design — complex biological, social, and economic systems.