Present ICES practice uses the geometric mean of the past 10 years of recruitment as a prediction (ICES 2001) . We recalculated these predictions for each year in the assessment time series starting with the 1983 year class (i.e., the time series begins in 1973 and we used the years 1973–1982 to predict log recruitment for 1983). This process was repeated for all years in the time series up to the 1999 yearclass by advancing the 10-year averaging window forward one year at a time.
We next used our temperature time series to derive a separate time series of predictions. For these predictions, we first derived new relationships between temperature and log recruitment for the years that were available up to, but excluding, the year for which prediction was being made. That is, we derived a temperature – log recruitment model for years 1973–1982 and used this model to estimate log recruitment for 1983. This process was repeated the next year by including the following year’s (1983) temperature and recruitment data and developing a new model to predict log recruitment in the coming year (1984). This procedure was repeated for all years in the time series and ensured that recruitment for the prediction year class was excluded from the data set used to derive the model. In this way, the predictions were produced using the recruitment and environmental information from all years available to a typical assessment working group.
The three time series of recruitment (observed + two series of predictions) could then be used for comparisons. For each year from 1983 to 1999, we calculated the differences between the observed log recruitment and predicted log recruitment, as derived using (a) the 10-year mean and (b) a temperature – log recruitment model. The difference between the observed and predicted log recruitment is the prediction error and should be as small as possible. The mean square error is a measure of the uncertainty of the predictions. We calculated prediction error and uncertainty for both sets of predictions. This comparison showed that the temperature-based predictions were less biased (smaller error) and were more certain than those derived using the 10-year mean (Fig. A1). We repeated the entire analysis with both the ice cover (ICE) and North Atlantic Oscillation (NAOJF) data and found similar results. In all cases, the environmental variables outperformed the existing technology (Fig. A1).
|
|
| FIG. A1. Comparison of recruitment prediction error (mean deviation of observed from predicted recruitment) and mean square error (error bars) of recruitment predicted using different methods (ICES: recruitment estimated as geometric mean of previous 10 years; Temp., NAOJF, and ICE: recruitment estimated using environmental regression models (Table B1). Predictions were generated for each year class 1983–1999. |
ICES [International Council for Exploration of the Sea]. 2001. Report of the Baltic Fisheries Assessment Working Group. ICES CM 2001/ACFM:18.