Coupled Ecological-Economic Feedbacks in a Polluted Fishery: Threshold Dynamics, Hysteresis, and Sustainable Harvesting

Abstract

Freshwater fisheries are increasingly threatened by environmental pollution and growing market demand, requiring management strategies that balance ecological sustainability with economic returns. We develop a bioeconomic fishery model for a polluted lake that integrates fish population dynamics, environmental pollution, adaptive harvesting effort, endogenous fish price, pollution-control investment, and policy-regulated harvesting-cost control within a unified ecological-economic framework. The model exhibits multiple stable states, including sustainable harvesting, harvesting-free, and fish-extinction regimes. A critical pollution-input threshold is identified beyond which the fish-extinction equilibrium becomes locally stable, indicating an increased risk of population collapse. Increasing pollution induces bistability, whereas sufficiently high market demand destabilizes the coexistence equilibrium through a Hopf bifurcation, producing persistent oscillations. The interaction between pollution and market demand further generates hysteresis, implying that restoring degraded fisheries requires substantially stronger interventions than preventing collapse. Treating the policy-regulated harvesting cost as the control variable, we derive an optimal harvesting policy consisting of a bang-bang phase followed by a singular control that maximizes the long-term harvesting revenue. Overall, our results demonstrate that coupled ecological-economic feedbacks can generate tipping points, oscillatory dynamics, and path-dependent transitions, highlighting the importance of integrated pollution control, harvesting regulation, and economic incentives for sustainable fishery management.