Stability properties of discrete stock-production models

The paper focuses on the stability analysis of a certain class of catch- and effort-controlled discrete stock - production models for optimal management of exploited populations, which were used as official methods for Cape hake assessments in the International Commission for the Southeast Atlantic Fishery (ICSEAF) during 1988-1990, and are still used for forecasting TACs of this species and other commercially fished stocks. In spite of the formal approach used, the problem is of the utmost practical importance as instability of a model raises the inaccuracy of the resultant estimates, providing also failures at the stage of the model fitting and total allowable catch (TAC) forecasting. So, clarification of the stability conditions of stock - production models enables their more deliberate and effective use in management of marine living resources. The effort-controlled models exhibit higher stability as compared with the catch-controlled ones: the fishing effort acts as a recovering force which suppresses the perturbations initiated in the model by the inevitable errors in estimating the initial population level. Therefore, the optimal management strategies and the TAC forecasts derived from the effort-controlled models are less risky than those obtained with the use of the catch-controlled ones.