© 1987 by ICES/CIEM International Council for the Exploration of the Sea/Conseil International pour l'Exploration de la Mer
A calculation of optimal fishing mortalities
MAFF, Directorate of Fisheries Research, Fisheries Laboratory Lowestoft Suffolk NR330HT, England
Static minimization techniques are used to find the trajectory of fishing mortality rate with time from a deterministic, age-structured, bioeconomic model of a fishery so as to maximize a time-discounted profit. Restrictions are put on the year-to-year rate of change of the control variable which is the fishing mortality rate and on the minimum permissible spawning stock size at the end of the time period. Results are considered over periods of 20 to 100 years. Characteristically the solutions take the form of an initial movement of the stock towards a particular stock size, an intermediate state of either a stable or oscillatory form, and a final movement near the end of the time period. The average fishing mortality rate, and hence stock size, is determined in a way explained largely by simple models of optimal harvesting and is sensitive to the value of the discount rate. In the particular model described here the discount rate also determines whether the intermediate state is oscillatory or stable.