Abstract Hairtail, Trichiurus Lepturus, is the major fishery resource in Korea and so has been occupying a large portion of total catches for a longtime. However, since the 1980s, the catch has fallen sharply. A climatic change and over-fishing of immature hairtails have decreased the resource in Korea Sea, which caused reduction in the catch. So, we should analyze this phenomenon and need to manage them. Thus, in this study, we first propose a discrete time age-structured model of hairtails from their biological features. Especially, since hairtail is the representative fish with characteristics of cannibalism in the marine ecosystem, we set the recruitment as Ricker type. Furthermore, for the environmental effect on its spawning, the sea surface temperature in the spawning ground is included in the model. Next, we find an optimal harvesting strategy for preserving the immature hairtails while simultaneously maximizing the corresponding profit of the fishing. The discrete-time optimal control problem is conducted as the extension of Pontryagin’s Maximum Principle to discrete system. Moreover, to suggest the optimal harvesting strategy in the future, the forecast of sea surface temperature should be accompanied. This is carried out by wavelet-ARIMA forecasting method. By using numerical simulations, we obtain that in the perspective of conservation, the limited fishing is the best for management of hairtails. On the other hand, in terms of balance between the conservation and economic profits, the optimal harvesting strategy is better than the limited fishing.

中文翻译：

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使用离散时间结构模型的韩国海带鱼 Trichiurus Lepturus 的最佳捕捞策略

摘要 Trichiurus Lepturus 带鱼是韩国的主要渔业资源，长期以来一直占据总渔获量的很大一部分。然而，自 1980 年代以来，渔获量急剧下降。气候变化和未成熟带鱼的过度捕捞减少了韩国海的资源，导致渔获量减少。所以，我们应该对这种现象进行分析，并需要对其进行管理。因此，在这项研究中，我们首先根据头发的生物学特征提出了一个离散时间年龄结构的带鱼模型。特别是带鱼是海洋生态系统中具有同类相食特征的代表性鱼类，我们将招募设置为Ricker型。此外，考虑到环境对其产卵的影响，模型中还包括产卵地的海面温度。下一个，我们找到了一种最佳捕捞策略，可以保留未成熟的带鱼，同时最大化相应的捕捞利润。离散时间最优控制问题是作为庞特里亚金最大原理对离散系统的推广而进行的。此外，为了提出未来的最佳捕捞策略，还应伴随海面温度的预测。这是通过小波-ARIMA 预测方法进行的。通过数值模拟，我们得出，从保护的角度来看，有限捕捞是带鱼管理的最佳选择。另一方面，在保护和经济效益的平衡方面，最优捕捞策略优于有限捕捞。