On the stability of the stock‐harvesting system controlled by a feedback management procedure

Abstract

SummaryStability of the stock‐harvesting system regulated by a feedback control procedure of catch quota is examined. In the procedure considered, catch quota is changed proportionally to the difference between current and the target stock level (with a proportionality constant h) and to the annual stock growth rate (with a proportionality constant g). Condition for the local stability of the target equilibrium is obtained as a function of the stock‐recruitment relation, survival probability of adults, target stock level, time lag before implementation of regulation, age of sexual maturity of the stock, and proportionality constants g and h. It is shown that, (1) the procedure has the stabilizing effect; it can stabilize the target stock level that is unstable under constant harvest, (2) lower target stock level favors larger g and smaller h, when the target is set around MSYL (the stock level that gives MSY), (3) the degree of stability, measured by the time required to recover the target stock level, is an increasing function of the target stock level, (4) stability and sustainable yield are in trade‐off, (5) time delay caused by the time needed before sexual maturity does not affect the stability significantly, but the effect of the time lag before implementation of regulation is significant. Comparison between harvest‐control and effort‐control procedures is also made, and the advantage of the latter in terms of stability is shown.