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This paper is devoted to a nonlocal reaction-diffusion-advection model that describes the spatial dynamics of freshwater organisms in a river with a directional motion. Our goal is to investigate how the advection rate affects the dynamic behaviors of species. We first establish the well-posedness of global solutions, where the regularized problem containing a viscosity term and the re-established maximum principle play an important role. And we then show the existence/nonexistence, uniqueness, and stability of nontrivial stationary solutions by analyzing the principal eigenvalue of integro-differential operator (especially studying the monotonicity of the principal eigenvalue with respect to the advection rate), which enables us to understand the longtime behaviors of solutions and obtain the sharp criteria for persistence or extinction. Furthermore, we study the limiting behaviors of solutions with respect to the advection rate and find that the sufficiently large directional motion will cause species extinction in all situations. Lastly, the numerical simulations verify our theoretical proofs., Comment: 39 pages;8 figures

This paper is devoted to a nonlocal dispersal logistic model with seasonal succession in one-dimensional bounded habitat, where the seasonal succession accounts for the effect of two different seasons. Firstly, we provide the persistence-extinction criterion for the species, which is different from that for local diffusion model. Then we show the asymptotic profile of the time-periodic positive solution as the species persists in long run., Comment: 22pages