ECOLOGICAL AND EVOLUTIONARY DYNAMICS IN PERIODIC AND ADVECTIVE HABITATS

We study the dynamics of reaction-diffusion-advection models for single and two competing species in one-dimensional periodic habitats, where the individuals are subject to both diffusion and advection. We investigate the monotone dependence of the principal eigenvalue on diffusion and drift rates. As applications, we first consider the persistence and spatial spreading of a single species and establish the critical threshold for the persistence as well as the monotone dependence of the minimal wave speed on the drift rate. We also consider two competing species model and study the local and global stability of semi-trivial steady states. Furthermore, the existence of evolutionarily singular strategies is established, which helps gain deeper insight into the evolution of dispersal in advective environments.