The Effect of Movement Behavior on Population Density in Patchy Landscapes

Many biological populations reside in increasingly fragmented landscapes, where habitat quality may change abruptly in space. Individuals adjust their movement behavior to local habitat quality and show preferences for some habitat types over others. Several recent publications explore how such individual movement behavior affects population-level dynamics in a framework of reaction-diffusion systems that are coupled through discontinuous boundary conditions. While most of those works are based on linear analysis, we study positive steady states of the nonlinear equations. We prove existence, uniqueness and global stability, and we classify their qualitative shape depending on movement behavior. We apply our results to study the question why and under which conditions the total population abundance at steady state may exceed the total carrying capacity of the landscape.