Striated Populations in Disordered Environments with Advection

TL;DR

This paper studies how fluid flow and environmental heterogeneity influence microbial populations, revealing that strong advection induces asymmetric, flow-driven striation patterns in population density, confirmed by analytical and numerical methods.

Contribution

It introduces a generalized FKPP model incorporating advection and spatial disorder, demonstrating the emergence of flow-driven striations in steady-state populations, supported by analytical and simulation results.

Findings

Flow speed linearly increases longitudinal correlation length.

Transverse correlation length remains finite and velocity-independent.

Theoretical predictions align with lattice Boltzmann simulations.

Abstract

Growth in static and controlled environments such as a Petri dish can be used to study the spatial population dynamics of microorganisms. However, natural populations such as marine microbes experience fluid advection and often grow up in heterogeneous environments. We investigate a generalized Fisher-Kolmogorov-Petrovsky-Piscounov (FKPP) equation describing single species population subject to a constant flow field and quenched random spatially inhomogeneous growth rates with a fertile overall growth condition. We analytically and numerically demonstrate that the non-equilibrium steady-state population density develops a flow-driven striation pattern. The striations are highly asymmetric with a longitudinal correlation length that diverges linearly with the flow speed and a transverse correlation length that approaches a finite velocity-independent value. Linear response theory is developed to study the statistics of the steady states. Theoretical predictions show excellent agreement with the numerical steady states of the generalized FKPP equation obtained from Lattice Boltzmann simulations. These findings suggest that, although the growth disorder can be spatially uncorrelated, correlated population structures with striations emerge naturally at sufficiently strong advection.