Effects of heterogeneity on spread and persistence in rivers.

The question how aquatic populations persist in rivers when individuals are constantly lost due to downstream drift has been termed the "drift paradox." Recent modeling approaches have revealed diffusion-mediated persistence as a solution. We study logistically growing populations with and without a benthic stage and consider spatially varying growth rates. We use idealized hydrodynamic equations to link river cross-sectional area to flow speed and assume heterogeneity in the form of alternating patches, i.e., piecewise constant conditions. We derive implicit formulae for the persistence boundary and for the dispersion relation of the wave speed. We explicitly discuss the influence of flow speed, cross-sectional area and benthic stage on both persistence and upstream invasion speed.