Diffusive noise controls early stages of genetic demixing

TL;DR

This paper develops an exact fluctuating hydrodynamic model for the stepping-stone population genetics model, revealing that diffusive noise critically influences early genetic demixing and diversity loss.

Contribution

It introduces a novel exact hydrodynamic description incorporating diffusive noise, emphasizing its importance in spatial population genetics models.

Findings

Diffusive noise significantly impacts early genetic demixing.

Scaling of density fluctuations is dominated by diffusive noise at early times.

Existing models need additional terms to account for diffusive noise effects.

Abstract

Theoretical descriptions of the stepping-stone model, a cornerstone of spatial population genetics, have long overlooked diffusive noise arising from migration dynamics. We derive an exact 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 density fluctuations in a spatial domain displays an early-time behaviour dominated by diffusive noise. Our exact 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.