Economic Data Collection for Amendment 91/Chinook Bycatch Incentive Monitoring

ESSR Program staff collaborated extensively with Council staff and members of industry to refine data collection instruments to monitor the effectiveness of management measures and incentive mechanisms adopted under Amendment 91 to promote reduction of Chinook salmon bycatch in the American Fisheries Act (AFA) pollock fisheries. Associated draft regulatory language and Paperwork Reduction Act documentation were developed in collaboration with NMFS Alaska Regional office staff in preparation for Council review in October.

Survey instruments have been developed for collecting data according to Council directives to support the monitoring of market activity and prices for transfers of the Chinook prohibited species catch (PSC) allocation within the Incentive Plan Agreement structure approved under Amendment 91, as well as surveys of pollock vessel captains regarding Chinook salmon avoidance and fuel consumption and costs for participating vessels. Draft survey instruments were reviewed in an industry workshop held at the AFSC in June, and feedback provided therein provided a significant basis for clarifying monitoring objectives and improving the survey instruments, which are currently under revision for presentation to the Council in October. If approved by the Council, data collection is expected to be implemented in 2012.

By Brian Garber-Yonts, Ron Felthoven, and Alan Haynie

Implementation of Annual Crab and Amendment 80 Economic Data Reports

Annual economic data reporting requirements for the BSAI crab and Amendment 80 groundfish fisheries include June submission deadlines for the previous calendar year fisheries. Economic data report programs were administered for the second and sixth year of data reporting in the Amendment 80 and BSAI crab fisheries, respectively.

By Brian Garber-Yonts

Advances in Bioeconomic Models of North Pacific Crab Stocks

Bioeconomic models usually assume population dynamics that do not represent explicitly the biological fundamentals of individual growth because including these processes makes the mathematics of a model too difficult to analyze. However, the AFSC's ocean acidification research plan calls for an analysis of the economic effects of ocean acidification on North Pacific crab fisheries, and biological fundamentals should not be ignored. Therefore, we are developing a more realistic bioeconomic model that can be applied to North Pacific crab stocks, one in which growth and survival processes are explicit and depend on an animal's size.

While biological models with these properties are readily available, the challenge is in coupling the biological and economic models such that the resulting bioeconomic model is actually useful for analysis. The objective here is to solve for a set of dynamic decision rules that solve an inter-temporal optimization problem under uncertainty (e.g., maximizing expected present value of fishery profits), subject to the constraints of a size-structured biological growth model. In this case, the mathematics are too daunting unless a careful path is followed that preserves the linearity of the optimal decision rules. An advantage of this approach is that it provides regression equations that can be used with maximum likelihood estimation and testing.

We consider first the treatment of fishing effort as a scalar variable in a bioeconomic model in which size-structured stock dynamics are explicit. In this case, scalar effort is multiplied by a selectivity vector to produce a multivariate catch variable that applies to size classes in the model. The optimal decision rules are found by solving the roots of a characteristic polynomial for the bioeconomic model.

We conducted an analysis that ascertained the following: 1) Solving the dynamic optimization in the most basic form of the bioeconomic model (i.e., linear constraint, quadratic objective, scalar control and scalar stock) reduces to finding the roots of a cubic polynomial; and 2) If the catch is drawn from multiple size classes, then the degree of the characteristic polynomial grows. For example, if the catch is drawn from two size classes then the characteristic polynomial is quintic. After that, adding a size class to the selectivity vector for the catch increases the degree of the polynomial by 1, for example, with three size classes in the catch the degree is 6, and with four size classes in the catch the degree is 7.

Consequently, we are not necessarily constrained in how many size classes that we include in the dynamic optimization, but we will be constrained in the number of size classes in the model that appear in the catch for the directed fishery. To keep the bioeconomic model tractable, we are currently working on a male-only model for eastern Bering Sea snow crab with five size-classes to capture the basic dynamics.

By Mike Dalton, Brian Garber-Yonts, and André Punt