Invasion analysis on a predator-prey system with a variable habitat for predators in open advective environments

Community composition in aquatic environments is influenced by habitat conditions, such as location and size. We propose a system of reaction-diffusion-advection equations for a predator-prey model with variable predator habitat in open advective environments. We investigate the effects of the location and length of the predator's habitat on its invasion. Firstly, we show that the closer the predator's habitat is to the downstream, the easier the predator can invade when its habitat length is fixed. Secondly, we find that increment of the predator's habitat length facilitates its invasion when the upstream boundary of its habitat is fixed. However, increment of the predator's habitat length disadvantages its invasion when the downstream boundary of its habitat is fixed. Thirdly, we obtain the uniqueness of positive steady state when two species reside in different domains. Finally, we numerically analyze how the advection rates affect the populations persistence and spatial distributions of the populations. These findings may have important biological implications and applications on the invasion of predators in open advective environments.