Dynamics of Refuge and Harvesting Impacts on Fish Ecosystem

Building artificial refuges for filter-feeding fish and regular harvesting of adult fish are common aquaculture strategies. To study how these strategies alleviate the predation conflict in the polyculture of filter-feeding fish and carnivorous fish, this paper establishes a predator–prey system with Holling-type II functional response and digestion delay based on the Leslie–Gower model. Stability analysis shows that the equilibria of both fish-extinct and predator-free situations are unstable node and saddle point, respectively. Due to the refuge effect and digestion delay, the prey-free equilibrium may exhibit five dynamic behaviors: stable, unstable, Hopf bifurcation, transcritical bifurcation, and Hopf–transcritical bifurcation. Under the condition of persistent survival, the system has a unique coexistence equilibrium that may be stable or undergo Hopf bifurcation. This paper derives strict bifurcation conditions for the generation of periodic solution and the global stability criteria at this point. Sensitivity analysis shows that harvesting behavior will inevitably lead to the decrease of carnivorous fish, and that refuging prey and harvesting predators can promote the expansion of the filter-feeding fish population. Interestingly, we find that the refuge effect does not always lead to the decrease of carnivorous fish. When the refuge rate is less than a certain threshold, the number of filter-feeding fish increases. Notably, this threshold is inversely proportional to the harvesting intensity of the predator. Numerical simulations reveal that adequate refuge protection significantly enhances prey survival and system stability, increasing the harvesting effort on the predator population effectively which controls the predator density, promotes sustainable coexistence, prolongs digestion delay and also induces destabilizing oscillations that threaten ecological balance.