In this paper, a seasonally switching single-species $ \theta $-logistic harvesting model with alternating closed and open seasons is developed, and the effects of nonlinear density dependence on fish population persistence and sustainable harvesting are investigated. Theoretical analysis identifies a critical closed-season duration threshold that depends strictly on harvesting intensity. When fishing pressure is excessive, the population persists in a stable positive periodic state if the closed season exceeds this threshold; otherwise, it inevitably tends toward extinction. Notably, while the closed-season threshold is independent of the density-dependence parameter, the population biomass levels and harvesting outcomes are profoundly influenced by this parameter. We analyze the maximum annual sustainable yield (MASY) within the persistence region and demonstrate that it is attained only in the absence of a closed season under idealized continuous harvesting. Numerical simulations confirm that a larger density-dependence parameter enhances population recovery, raises the stable periodic population level, and increases the MASY. Furthermore, a resilience-constrained yield-efficiency index (RCYEI) is proposed by integrating annual sustainable yield, catch per unit effort (CPUE), and ecological safety constraints to circumvent the drawbacks of yield-only optimization. The results indicate that placing greater emphasis on yield raises the optimal harvesting intensity, whereas stricter ecological safety requirements limit the allowable harvesting pressure. A larger density-dependence parameter also expands the ecologically feasible region, enabling the population to withstand higher fishing pressure under identical safety requirements. These findings provide rigorous theoretical insights and practical guidance for designing sustainable seasonal harvesting strategies under ecological safety constraints.
Citation: Qiuran Wang, Wei You, E. K. Makarov, Shengqiang Liu. Optimal harvesting policy for a single-species $ \theta $-logistic model with seasonal succession[J]. Mathematical Biosciences and Engineering, 2026, 23(10): 3037-3060. doi: 10.3934/mbe.2026105
In this paper, a seasonally switching single-species $ \theta $-logistic harvesting model with alternating closed and open seasons is developed, and the effects of nonlinear density dependence on fish population persistence and sustainable harvesting are investigated. Theoretical analysis identifies a critical closed-season duration threshold that depends strictly on harvesting intensity. When fishing pressure is excessive, the population persists in a stable positive periodic state if the closed season exceeds this threshold; otherwise, it inevitably tends toward extinction. Notably, while the closed-season threshold is independent of the density-dependence parameter, the population biomass levels and harvesting outcomes are profoundly influenced by this parameter. We analyze the maximum annual sustainable yield (MASY) within the persistence region and demonstrate that it is attained only in the absence of a closed season under idealized continuous harvesting. Numerical simulations confirm that a larger density-dependence parameter enhances population recovery, raises the stable periodic population level, and increases the MASY. Furthermore, a resilience-constrained yield-efficiency index (RCYEI) is proposed by integrating annual sustainable yield, catch per unit effort (CPUE), and ecological safety constraints to circumvent the drawbacks of yield-only optimization. The results indicate that placing greater emphasis on yield raises the optimal harvesting intensity, whereas stricter ecological safety requirements limit the allowable harvesting pressure. A larger density-dependence parameter also expands the ecologically feasible region, enabling the population to withstand higher fishing pressure under identical safety requirements. These findings provide rigorous theoretical insights and practical guidance for designing sustainable seasonal harvesting strategies under ecological safety constraints.
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Qiuran Wang, Wei You, E. K. Makarov, Shengqiang Liu. Optimal harvesting policy for a single-species $ \theta $-logistic model with seasonal succession[J]. Mathematical Biosciences and Engineering, 2026, 23(10): 3037-3060. doi: 10.3934/mbe.2026105
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