Multiparameter analysis of the persistence-extinction thresholds in benthic-drift patch models

In this paper, we investigate the global dynamics of the benthic-drift patch model, in which individuals in the benthic zone remain stationary while those in the drift zone undergo diffusion and advection with the water flow. We establish threshold dynamics via the principal eigenvalue of the linearized system at the zero equilibrium and hierarchically analyze the effects of the population transfer rates between the drift and benthic zones, the diffusion rate, and the advection rate on the principal eigenvalue as well as on the dynamical behavior. Our analysis reveals that diffusion and advection may either promote or hinder species persistence, depending on the habitat suitability of individual patches, particularly at the downstream end.