发表机构
Linnéuniversitetet（林奈大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文构建了鱼类种群的空间显式非线性生物量模型，推导了最优收获控制及伴随诊断，并通过数值模拟揭示了扩散对空间异质性的影响及收获决策的未来价值。
AI 中文摘要
我们针对被开发鱼类种群开发了一个空间显式非线性生物量模型，该模型结合了密度依赖的Beverton-Holt生产、自然死亡率、扩散驱动的空间运动以及收获。从由产卵种群生物量数据启发的简化生物量模型出发，我们推导出一个具有Neumann边界条件和空间分布收获的反应-扩散模型。我们确立了生物量动力学的正性、有界性和适定性，并确定了一个临界收获阈值，该阈值区分了空间均匀平衡的持续存在与灭绝状态。随后，我们提出了一个分布式最优收获问题，并推导了相应的状态-伴随最优性系统以及收获控制的逐点投影特征。伴随变量提供了收获目标中生物量边际未来价值的度量，并提供了一种补充生物量丰度本身的诊断工具。数值模拟考察了生物量、伴随变量和最优收获努力的耦合演化。结果表明，扩散逐渐减少了生物量中初始的空间异质性，而计算得到的伴随场和最优收获场在所考虑的参数范围内表现出有限的空间变化。这些结果说明了状态-伴随-控制耦合框架如何将空间生物量动态与未来管理价值和收获决策联系起来。
英文摘要
We develop a spatially explicit nonlinear biomass model for exploited fish populations incorporating density-dependent Beverton-Holt production, natural mortality, diffusion driven spatial movement, and harvesting. Starting from a reduced biomass model motivated by spawning stock biomass data, we derive a reaction-diffusion model with Neumann boundary conditions and spatially distributed harvesting. We establish positivity, boundedness, and well-posedness of the biomass dynamics, and identify a critical harvesting threshold separating persistence and extinction regimes of spatially homogeneous equilibria. A distributed optimal harvesting problem is then formulated, and the corresponding state-adjoint optimality system and pointwise projection characterization of the harvesting control are derived. The adjoint variable provides a measure of the marginal future value of biomass within the harvesting objective and offers a diagnostic that complements biomass abundance alone. Numerical simulations examine the coupled evolution of biomass, the adjoint variable, and optimal harvesting effort. The results show that diffusion progressively reduces the initial spatial heterogeneity in biomass, while the computed adjoint and optimal harvesting fields exhibit limited spatial variation under the parameter regime considered. These results illustrate how the coupled state-adjoint-control framework links spatial biomass dynamics with future management value and harvesting decisions.
