Theoretical descriptions of the stepping-stone model, a cornerstone of spatial population genetics, have long overlooked diffusive noise arising from migration dynamics. We derive a fluctuating hydrodynamic description of this model from microscopic rules, which we then use to demonstrate that diffusive noise significantly alters early-time genetic demixing, which we characterize through heterozygosity, a key measure of diversity. Combining macroscopic fluctuation theory and microscopic simulations, we demonstrate that the scaling of allele-number fluctuations in a spatial domain displays an early-time behavior dominated by diffusive noise. Our results underscore the need for additional terms in existing continuum theories and highlight the necessity of including diffusive noise in models of spatially structured populations.

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• Biological fluid dynamics
• Evolutionary & population dynamics
• Fluctuations & noise
• Nonequilibrium lattice models
• Population dynamics
• Path-integral methods
• Statistical hydrodynamics