Yoshioka Hidekazu
Faculty of Life and Environmental Science, Shimane University, Nishikawatsu-cho, Matsue, 1060, Japan.
Theory Biosci. 2019 Nov;138(2):277-303. doi: 10.1007/s12064-019-00292-4. Epub 2019 Apr 11.
A stochastic differential game model for animal migration between two habitats under uncertain environment, a new population dynamics model, is formulated. Its novelty is the use of an impulse control formalism to naturally describe migrations with different timings and magnitudes that the conventional models could not handle. Uncertainty of the environment that the population faces with is formulated in the context of the multiplier robust control. The optimal migration strategy to give the maximized minimal profit is found through a Hamilton-Jacobi-Bellman quasi-variational inequality (HJBQVI). A key message from HJBQVI is that its free boundary determines the optimal migration strategy. Solving the HJBQVI is carried out with a specialized stable and convergent finite difference scheme. This paper theoretically suggests that the sub-additivity of the performance index, the index to be optimized through the migration, critically affects the resulting strategy. The computational results with the established scheme are consistent with the theoretical predictions and support importance of the sub-additivity property. Social interaction to reduce the net mortality rate is also quantified, suggesting a linkage between the present and existing population dynamics models.
提出了一种用于描述不确定环境下动物在两个栖息地之间迁徙的随机微分博弈模型,这是一种新的种群动力学模型。其新颖之处在于使用脉冲控制形式来自然地描述传统模型无法处理的不同时间和规模的迁徙。种群所面临的环境不确定性是在乘子鲁棒控制的背景下进行表述的。通过哈密顿 - 雅可比 - 贝尔曼拟变分不等式(HJBQVI)找到使最小利润最大化的最优迁徙策略。HJBQVI的一个关键信息是其自由边界决定了最优迁徙策略。使用专门的稳定且收敛的有限差分格式来求解HJBQVI。本文从理论上表明,性能指标(即通过迁徙进行优化的指标)的次可加性对最终策略有至关重要的影响。所建立格式的计算结果与理论预测一致,并支持次可加性性质的重要性。还对降低净死亡率的社会互动进行了量化,表明了当前模型与现有种群动力学模型之间的联系。