q-bio.PE2026-07-131 minarXiv:2607.11520expressHow Chance Drives EvolutionEvolution 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.Anton Bovier·Anna KrautWright–Fisher modelEmmy Noetherevolutionstochastic processesmutationstochastic gene expressionStochastic modeling👍👎☆SimplePopularAdvanced