diversity in complex systems

Diversity is everywhere—more proteins as single cells evolve, more cell types in multicellular life, more species in an ecology, more occupations in a city. It’s usually chalked up as a byproduct of evolution itself, but exactly how systems generate and expand their diversity of functional elements is still an open question, and one we think is tightly linked to how those systems get regulated.

We’ve built a generative model that maps the growth of functional elements in proteomes, federal agencies, and city occupations onto a single stochastic process, explaining statistical patterns—like self-similar rank-frequency distributions—shared across all three. We’ve since extended it to microbial ecosystems, which turn out to occupy a genuinely different region of the model’s parameter space than anything else we’ve studied so far.

Next, we’re deriving analytic solutions to sharpen the model’s predictions, extending it to new kinds of data, and connecting it to explicit evolutionary models—using genetic algorithms to encode selective pressures—so we can eventually explain why a given system’s diversity is beneficial, not just describe it statistically.

A few open questions we’re chasing:

  • Does one generative process explain diversification across proteomes, cities, federal agencies, and ecologies?
  • Why do microbial ecosystems sit in a different part of that model’s parameter space than everything else?
  • What selective pressures make a given functional diversity beneficial?

Research from the $R^3$ Lab on diversity in biology and other complex systems: