Optimal harvest strategy based on a discrete age-structured model with monthly fishing effort for chub mackerel, Scomber japonicus, in South Korea

Abstract

Currently, the catch of fishery resources in South Korea has fallen more than 40%, from 1.73 million tons in 1986 to 1.01 million tons in 2018. In particular, the amount of chub mackerel, one of the most favored fish species by South Koreans, caught in 2017 was 103,870 tons, which was only 25% of the total catch, compared with 415,003 tons in 1996. The total allowable catch system and the closed season are currently in place as a countermeasure to the continued decline in fishery resources; however, their effectiveness is questionable. Our study aims to maximize fishing profits by controlling the monthly fishing effort while maintaining the amount of chub mackerel. Discrete age-structured mathematical model was established with an optimal harvest control system. Density-dependent mortality was applied at the juvenile stage to reflect fish mortality because it is highly dependent on population density in the underage phase. The conditions of the parameters guaranteeing the existence of optimal harvest strategies were demonstrated and obtained using Pontryagin's maximum principle. We compared an optimal harvest strategies and the actual harvest strategies of fishing effort from July 2010 to June 2020. In addition, we compared the profit and biomass of the optimal harvest strategies when designating one month in a year as closed season. We also conducted sensitivity analysis by varying the price of chub mackerel and cost of fishing effort. As a result, the optimal harvest strategies are to have the highest amount of fishing effort from August to September and gradually reduce the amount of effort. The optimal harvest strategies could improve the maximum economic yield and the maximum sustainable yield by 11.9% and 10.9%, respectively, over the observed strategy. To the best of our knowledge, forecasting analysis of the maximum economic yield and closed season conducted based on optimal harvest control system for Chub mackerel in South Korea. The appropriate allocation of monthly fishing effort can increase sustainable catch and profit. In addition, it is better to implement a closed season in July to maximize the profit of fishing and in June to the resource recovery.