Enhanced (hydrodynamic) transport induced by population growth in reaction–diffusion systems with application to population genetics

We consider a system made up of different physical, chemical, or biological species undergoing replication, transformation, and disappearance processes, as well as slow diffusive motion. We show that for systems with net growth the balance between kinetics and the diffusion process may lead to fast, enhanced hydrodynamic transport. Solitary waves in the system, if they exist, stabilize the enhanced transport, leading to constant transport speeds. We apply our theory to the problem of determining the original mutation position from the current geographic distribution of a given mutation. We show that our theory is in good agreement with a simulation study of the mutation problem presented in the literature. It is possible to evaluate migratory trajectories from measured data related to the current distribution of mutations in human populations.