Optimal harvesting strategy for hairtail, Trichiurus Lepturus, in Korea Sea using discrete-time age-structured model

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.