The Allee Effect in Compressible Flows

We investigate the interplay between microbial population dynamics exhibiting an Allee effect and advection in a compressible, turbulent flow field. The convergence and divergence inherent to compressible turbulence continuously generate regions of high and low microbial density in space and lower the average population density. The Allee effect, which describes reduced growth rates at low population densities, introduces a critical threshold below which extinction occurs. Consequently, population survival depends sensitively on the statistical properties of the turbulent flow.

Numerically, we demonstrate the existence of a critical strength of the Allee effect beyond which a population advected by the turbulent flow always goes extinct. We further examine how this critical Allee strength depends on both the time scale of the flow and the degree of its compressibility. Finally, we show that this critical threshold can be derived analytically in the asymptotic limits where the flow occurs on much faster or much slower time scales than the reproduction of microbials.