Competition of three species in an advective environment

Individuals in advective environments, for example rivers, coastlines, or the gut, are subject to movement with directional bias. We study how this movement bias shapes community composition by considering how the strength of movement bias affects the outcome of competition among three species. Our model is a system of three reaction–advection–diffusion equations with Danckwerts boundary conditions. Our key tool in this study is to use the dominant eigenvalue of the diffusion–advection operator in order to reduce the spatially explicit model to a spatially implicit ordinary differential equation model. After an in-depth analysis of the implicit model, we use numerical simulations of the explicit model to test the predictions obtained from the analysis. In general, we find a good qualitative agreement between the explicit and the implicit model. We find that varying the strength of advection can fundamentally alter the outcome of competition between the three species, and we characterize the possible transitions. In particular, water extraction and flow control can destabilize existing species communities or facilitate invasions of non-native species.