Evolution flows like water. In a wide river, changes are smooth and slow, while a mountain stream churns with every stone. Population size and mutation rate set the channel: broad and calm, or narrow and rapid-filled.

Scientists built a mathematical model based on the stochastic process theory of Andrey Markov, accounting for time, population size, mutation rate, and effect size. In large groups, evolution moves at a leisurely pace — mutations accumulate over centuries and mostly fade without a trace, like ink dropped in a river. In small groups, it surges: a beneficial mutation can sweep through the entire population in just a few generations, like a stone redirecting a stream.

Such calculations allow us to predict how species will respond to environmental change. By managing the level of chaos in populations, we can slow unwanted evolution, say, in agricultural pests. Biology gains a tool for precise forecasts instead of vague generalities.