The Management of a Stock-Fishery System by Manipulating the Catch Quota Based on the Difference between Present and Target Stock Levels

The dynamical properties of a fishery management system are studied. The system is such that the catch quota YT is decided on the basis of replacement yield (RY)T adjusted by (PT-PU)/τ where τ is a constant and PT and PU are the present and target stock levels respectively. Both (RY)T and PU are subject to estimation error. If τ〉1, the expectation of PT converges to PU in an asymptotic manner and the variance of PT increases with time to a constant. If the estimation error is a biased one the converging point is shifted from PU depending on the size and direction of the bias. A small value of τ allows quick approach to the target but is accompanied by a large yearly fluctuation in YT and a high stock level for complete closure of fishing. The stock may be depleted by chance below the minimum level which the stock can maintain if τ is set at a large value, but the possibility of destruction of stock can be neglected if PU is set at or larger than MSY level. In the initial stage of exploitation of a new stock, either a different procedure or a different τ value for calculating YT should be used.