Meandering Rivers: How Important is Lateral Variability for Species Persistence?

Models for population dynamics in rivers and streams have highlighted the importance of spatial and temporal variations for population persistence. We present a novel model that considers the longitudinal variation as introduced by the sinuosity of a meandering river where a main channel is laterally extended to point bars in bends. These regions offer different habitat conditions for aquatic populations and therefore may enhance population persistence. Our model is a nonstandard reaction-advection-diffusion model where the domain of definition consists of the real line (representing the main channel) with periodically added intervals (representing the point bars). We give an existence and uniqueness proof for solutions of the equations. We then study population persistence as the (in-) stability of the trivial solution and population spread as the minimal wave speed of traveling periodic waves. We conduct a sensitivity analysis to highlight the importance of each parameter on the model outcome. We find that sinuosity can enhance species persistence.