JOINT CHINOOK TECHNICAL COMMITTEE
Joint Chinook Technical Committee. Evaluation of Three Methods for Predicting the Abundance Index for Chinook Salmon Available to the Southeast Alaska Troll Fishery. TCCHINOOK (97)-3. September, 1997.
In June 1996, the U.S. commissioners of the Pacific Salmon Commission (PSC) agreed on the elements of an abundance-based management regime for the all-gear chinook salmon fisheries in Southeast Alaska (SEAK). The U.S. letter of agreement (LOA) requested the PSC Chinook Technical Committee (CTC) to develop "a technically feasible procedure for estimating the aggregate abundance of chinook available to the SEAK fishery using inseason fishery performance data, for the purpose of adjusting preseason forecasts of harvest levels beginning in 1997" (Allen et al. 1996).
The bilateral CTC evaluated three methods for predicting the estimated abundance index of chinook available to the SEAK troll fishery. The assessments were based on data collected for the period 1979 through 1996 as well as abundance forecasts for 1997, which were either provided by agencies or represented by the PSC chinook model estimates. The years used in each assessment varied, depending on the appropriateness of the data, but each method was compared with estimated chinook abundance indices from the PSC chinook model calibration 9702 ( CTC Report TCCHINOOK (97)-2). The three methods compared follow:
PSC Chinook Model Forecast. The preseason forecast of the estimated chinook abundance index for the SEAK troll fishery is based on the PSC chinook model.
Inseason Prediction. A prediction of the estimated abundance indices for year i is based on fishery performance data from the troll fishery in year i and PSC chinook model estimated abundance indices. Various measures of fishery performance were assessed before selecting the statistic used in this report (Power Troll Statistic (PTS) = power troll catch per permit making a landing during the first 5 days of the summer troll season).
Bayesian Prediction. The application of Bayesian statistics to predict the estimated chinook abundance index is introduced. This method integrates information from both of the above methods and can be used inseason. This method does not introduce any new data into the estimation, but it combines the above methods based on the reliability of their historical relationships. Further, this method incorporates explicit estimates of the uncertainty in each of the above methods used to estimate the CTC abundance index.
The ability of each method to predict the estimated abundance index from the PSC chinook model was examined through retrospective analyses. The models were assessed by leaving one year of data out from a relationship, recalculating the relationship, and then predicting the value for the year omitted. This process, called hindcasting (PSC model) or jackknifing (inseason and Bayesian models), allows comparison of several predictions per model by comparing each prediction with the value actually observed, but omitted. The criteria for comparison between models were the mean percent error (MPE, the expected average error over time, a measure of bias), the mean absolute percent error (MAPE, the average annual error, a measure of uncertainty), and the maximum positive and negative errors (also measures of uncertainty and range of values).
The PTS and Bayesian predictions exhibited smaller MAPE, and lesser ranges of maximum errors than the model forecast abundance index. The Bayesian model exhibited the smallest MPE and the smallest maximum positive deviation. Consequently, the Bayesian method is the preferred method for predicting the estimated abundance index for the SEAK troll fishery.
Comparison of errors and range of errors by method determined from hindcasting for the 1987-1996 period (see text Table 12).
|
|
CTC Model Forecast |
Inseason Prediction |
Bayesian Prediction |
|
MPE |
+3% |
+3% |
+1% |
|
MAPE |
10% |
8% |
8% |
|
MAX + |
+25% |
+22% |
+15% |
|
MAX - |
-15% |
-8% |
-13% |
The Bayesian method generates a distribution of abundance index values, given the PTS value observed in the current fishery and the CTC forecast abundance index. The CTC recommends that the mode of this Bayesian posterior distribution be used as the "most probable" value of the estimated abundance of chinook salmon in the SEAK troll fishery. The CTC also notes that the uncertainty about the predicted abundance index is also estimated. The CTC recommends that the PSC consider how the new information on uncertainty could also be usefully employed in management.
The CTC also notes that the current analysis of probability distributions relies upon limited data sets: 10 years for the hindcasted PSC model forecasts and 17 years for the PTS. However, future improvements in the PSC model forecasts are likely, and improved measures of inseason fishery performance may be identified. There are also concerns about the time trends in the error about the preseason forecast of the abundance index. The CTC recommends reevaluation of procedures to estimate abundance of chinook available to the SEAK fishery using inseason information prior to the 1999 fishing season.
This report is limited to the technical development of an inseason procedure that incorporates the PTS and provides an estimated abundance index for chinook available to the all-gear SEAK fishery. The CTC did not evaluate the extent to which variations in stock distributions influence the abundance index for the SEAK chinook fishery. Concerns of some CTC members with issues that may arise when integrating inseason adjustments to abundance for the SEAK fishery with regimes for other fisheries to achieve management objectives for harvest sharing and stock rebuilding are not addressed, because these considerations are beyond the scope of this technical assignment.
The Canadian CTC members wish to clarify that their review of the techniques in this report does not imply endorsement of any aspect of the U.S. LOA or the application of this technique to one fishery in isolation of others.