Refuge-mediated predator-prey dynamics and biomass pyramids

Refuge can greatly influence predator-prey dynamics by movements between the interior and the exterior of a refuge. The presence of refuge for prey decreases predation risk and can have important impacts on the sustainability of a predator-prey system. The principal purpose of this paper is to formulate and analyze a refuge mediated predator-prey model when the refuge is available to protect a portion of prey from predation. We study the effect of the refuge size on the biomass ratio and extend our refuge model to incorporate fishing and predator migration separately. Our study suggests that decreasing the refuge size, increasing the predator fishing, and increasing the predator emigration stabilizes the system. Here, we investigate the dependence of Hopf bifurcation on refuge size in the presence of fishing or predator migration. Moreover, we discuss their effects on the biomass pyramid and establish a condition for the emergence of an inverted biomass pyramid. We perform numerical test and sensitivity analysis to check the robustness of our results and the relative importance of all parameters. We find that high fishing pressure may destroy the inverted biomass pyramid and thus decrease the resilience of reef ecosystems. In addition, increasing the emigration rate or decreasing the immigration rate decreases the predator-prey biomass ratio. An inverted biomass pyramid can occur in the presence of a stable limit cycle.