A generalization of the harvesting functions and the stock updating functions in age-structured bioeconomic models is outlined. Using this generalization everything from completely uniformly distributed fish to extreme schooling is taken care of. The classical Beverton-Holt model comes out as a special case of the generalized model. Both the theoretical outline as well as practical numerical examples are provided, and the generalization can be applied both for simulation as well as optimization purposes given appropriate software.
Here we apply advanced non-linear programming to maximize the net present value in a bioeconomic setting where the new updating and harvesting functions are used as constraints. This is possible thanks to new software, such as KNITRO, for solving highly nonlinear problems. Applications of this generalized model produce interesting new results. One such practical result is that pulse fishing seems to become less and less economically profitable as we move from uniformly distributed fish to schooling species. The main reason why pulse fishing cease to be optimal in schooling fisheries, is that the economies of scale present in search fisheries gradually disappear when we move from search fisheries to schooling fisheries. This may have important implications for how fish stocks ought to be managed in the future, especially with respect to total allowable catches based on bioeconomic criteria.
Steinshamn, Stein Ivar. 2010. Generalization of Age-Structured Models in Theory and Practice. 12 pages. In: Proceedings of the Fifteenth Biennial Conference of the International Institute of Fisheries Economics & Trade, July 13-16, 2010, Montpellier, France: Economics of Fish Resources and Aquatic Ecosystems: Balancing Uses, Balancing Costs. Compiled by Ann L. Shriver. International Institute of Fisheries Economics & Trade, Corvallis, Oregon, USA, 2010.
Funding Statement (additional comments about funding)
US National Oceanic and Atmospheric Administration (NOAA) Fisheries Division, Agence Française de Développement, Ministère de l’Enseignement Supérieur et de la Recherche, Ministère de L’Alimentation de L’Agriculture et de la Pêche, Ministère de l’Énergie, du Développement Durable et de la Mer, La Région Languedoc Rouslilon, Département Hérault, Montpellier Agglomèration, The Department of Fisheries and Oceans, Canada, and AquaFish Collaborative Research Support Program (CRSP).