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

Abstract

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. © 1982, The Japanese Society of Fisheries Science. All rights reserved.