The effects of random and seasonal environmental fluctuations on optimal harvesting and stocking
The effects of random and seasonal environmental fluctuations on optimal harvesting and stocking
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DOI：
10.1007/s00285-022-01750-2
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发表时间：
2021-09
影响因子：
1.9
通讯作者：
Alexandru Hening;K. Tran;Sergiu Ungureanu
中科院分区：
文献类型：
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作者：
Alexandru Hening;K. Tran;Sergiu Ungureanu
我们分析了受随机和季节性环境波动影响的种群的收获和放养。主要的新奇之处在于它有三层环境波动。第一层是由于环境在不同的环境状态之间随机切换。这类似于突然的环境变化或灾难。第二层是由于季节变化，其中季节之间的动态变化很大。最后，第三层是由于环境随机性的持续存在——在季节或随机状态切换之间，物种受到波动的影响，这些波动可以用白噪声来模拟。这个框架更现实，因为它既可以捕捉显著的随机和确定性环境变化，也可以捕捉非生物因素的小而频繁的波动。我们的框架还允许收获的价格或成本发生确定性和随机变化，这从经济角度来看更为现实。季节性波动和随机波动的综合影响使得无法解析地找到最优的收获-放养策略。我们通过开发严格的数值近似并证明它们收敛于最优的收获-放养策略来绕过这个障碍。我们将我们的方法应用于多个种群模型，并探索价格或成本和环境波动如何影响最佳收获-放养策略。结果表明，在许多情况下，最佳的收获和放养方式不是阈值型的。
We analyze the harvesting and stocking of a population that is affected by random and seasonal environmental fluctuations. The main novelty comes from having three layers of environmental fluctuations. The first layer is due to the environment switching at random times between different environmental states. This is similar to having sudden environmental changes or catastrophes. The second layer is due to seasonal variation, where there is a significant change in the dynamics between seasons. Finally, the third layer is due to the constant presence of environmental stochasticity—between the seasonal or random regime switches, the species is affected by fluctuations which can be modelled by white noise. This framework is more realistic because it can capture both significant random and deterministic environmental shifts as well as small and frequent fluctuations in abiotic factors. Our framework also allows for the price or cost of harvesting to change deterministically and stochastically, something that is more realistic from an economic point of view. The combined effects of seasonal and random fluctuations make it impossible to find the optimal harvesting-stocking strategy analytically. We get around this roadblock by developing rigorous numerical approximations and proving that they converge to the optimal harvesting-stocking strategy. We apply our methods to multiple population models and explore how prices, or costs, and environmental fluctuations influence the optimal harvesting-stocking strategy. We show that in many situations the optimal way of harvesting and stocking is not of threshold type.