The Allee Effect in Compressible Flows

Microbes in marine environments are often confined to thin near-surface layers while being advected by turbulent flows. Because such constrained advection generates an effectively compressible flow, reproduction and transport interact in a nontrivial way. Here, we focus on populations whose growth is governed by an Allee effect and show that sinks and sources, generated by the compressible flow, have dramatic consequences for the survival of such species. We derive analytical expressions for the carrying capacity as a function of the Allee strength in the limit of small and large Damk\"ohler number, which measures the product of the large eddy turnover time and the organism growth rate. Numerical simulations reveal how these two limits connect. In the limit of small Damk\"ohler number, we find a maximal Allee strength, set by the statistics of the compressible flow, that leads to species extinction in fully developed turbulence.