On the stability of the stock-harvesting system controlled by a feedback management procedure |
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Authors: | Yasushi Harada Kazumi Sakuramoto and Syoiti Tanaka |
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Institution: | (1) Department of Fisheries Resource Management, Tokyo University of Fisheries, Minato, 108 Tokyo, Japan |
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Abstract: | Summary Stability 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
constanth) and to the annual stock growth rate (with a proportionality constantg). 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 constantsg andh. 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 largerg and smallerh, 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. |
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Keywords: | renewable resource management local stability resilience mathematical model population dynamics |
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