The Correlated Collapse

Classical demographic theory predicts that population volatility should decline as the square root of population size. More people means more independent demographic events — births, deaths, migrations — and the law of large numbers smooths them into a stable average. A village of 100 might fluctuate wildly; a nation of millions should be rock-solid.

Using census data from 228 indigenous societies in Brazil, the researchers (arXiv:2510.07660) show this prediction fails. Volatility does decline with size, but far more slowly than the square-root law predicts. Large populations fluctuate as though they were much smaller than they actually are.

The mechanism is correlation. The law of large numbers requires independence — each person’s demographic fate must be unrelated to everyone else’s. But people in societies are not independent. They cooperate, share subsistence practices, use overlapping land, and face common shocks: the same drought, the same epidemic, the same failed harvest. These correlations synchronize demographic events across the population, drastically reducing the effective number of independent demographic units.

A society of 10,000 people who share food sources, disease exposure, and livelihood strategies might have an effective demographic size of only a few hundred. The law of large numbers operates on the effective size, not the census count. The buffering that size should provide — the statistical averaging that makes large populations stable — is consumed by the very cooperation that makes large populations possible.

The structural insight: the thing that makes a population a society (correlated behavior, shared institutions, collective risk exposure) is precisely the thing that prevents it from being demographically stable. Size and stability are coupled through cooperation, and the coupling is destructive. Scaling up a population does not scale up its resilience, because the mechanism of scaling — social coordination — is also the mechanism of synchronization.

“Demographic synchrony increases the vulnerability of human societies to collapse,” arXiv:2510.07660 (2025).