Nippon Suisan Gakkaishi
This paper proposes a stock mangement system to approach the catch level to MSY through the effort-catch control using the data of abundance indices. Dynamics of stock size is assumed to be relativelyindependent of environmental fluctuation and the basic model used for the dynamics is the surplus production one. The levels of the effort and catch quota are modified every three years using the indices for the difference between the stock levels at present and MSY. The approximated value of the first order derivative of the function of the surplus production is calculated from the data of abundance indices and is used for the indices. The conditions for the stable MYS point are obtained from the mathematical analysis of the local stability. The simulations using the Pella-Tomlinson model for the surplus production showed that the trajectory converged to MSY point or diverged, depending upon the local stability and initial conditions. The simulations with the stochastic data of the abundance indices indicated that the stock size and catch fluctuated widely, however, that the fluctuation was modified by the minor change of the system. The problems in the application and the modification of the system are discussed.