Maunder and Walters: Integrating environmental time series Into stock assessment models 



93 



Table 3 



Results from applying the three methods (traditional, environmental, and environmental with process error) to the snapper appli- 

 cation. Constant = recruitment is constant each year and equal to the average recruitment. EMwPE = environmental model with 

 process error, n/a = not applicable. 



Average 

 recruitment 



Constant 

 Traditional 

 Environmental 

 EMwPE 



13,315 (11,381-15,381) 



11,406 (8,500-14,603) 



13,530 (11,527-15,569) 



12,029 (9,147-15,328) 



Using the likelihood ratio test at the 0.05 level and com- 

 pensating for the difference in the number of parameters 

 being estimated in each model, we consider the environ- 

 mental model to be the model of choice. If the likelihood 

 ratio test were used, the environmental model with pro- 

 cess error would be chosen over the traditional model, 

 indicating a statistically significant correlation between 

 SST and recruitment. Due to the weaknesses of the envi- 

 ronmental model discussed above, we concentrated on the 

 results of the traditional model and the environmental 

 model with process error. 



The time series of estimated recruitments from the 

 traditional model showed very little annual variation in 

 recruitment for the first half of the time series and for the 

 last few years of the time series (Fig. lA). This indicates 

 that there is very little information in the data (catch-at- 

 age) about annual recruitment for these time periods and 

 that the prior on the recruitment residuals constrains the 

 estimated recruitment to be close to the average recruit- 

 ment. This result is consistent with the catch-at-age data, 

 which, ignoring the inconsistent data from the 1970s, 

 started in 1990. The greatest age in the catch-at-age data 

 that had individual information was age 19; therefore the 

 1971 cohort is the first for which there is information. 

 However, at the current exploitation rates, very few snap- 

 per live to be more than 10 years of age, so that there is 

 very little information about cohort size for any of the co- 

 horts produced during the 1970s. 



The environmental model with process error indicated 

 high variation in recruitment for the whole time period 

 (Fig. IB). This is due to the formulation of the recruitment 

 submodel, for which the annual anomalies are anomalies 

 from the temperature-recruitment relationship; if there is 

 no information in the data about recruitment for a par- 

 ticular year, the recruitment will follow the temperature- 

 recruitment relationship. 



The correlation of the estimated recruitment from the 

 traditional model with SST had a low r-square (0.26), but 

 it was statistically significant at the 0.05 level when a 

 two-tailed test was used. In addition, the slope of the rela- 

 tionship between recruitment and SST was much less for 

 the traditional model than for to the environmental model 

 with process error (Table 3). The estimates of recruit- 

 ment from the traditional model included a large number 

 of estimates that were close to the mean because there 



1950 1960 1970 1980 1990 2000 



B 



5 



,0 



,5 



,0 



,5 



,0 

 1950 1960 



1970 1980 

 Year 



1990 2000 



Figure 1 



Annual estimates of relative recruitment strength 

 at age 1 for the Hauraki Gulf-Bay of Plenty snap- 

 per stock from the traditional (A) and environ- 

 mental model with process error (Bl models 



was no information in the data about these recruitments. 

 Therefore, it was inappropriate to use these recruitments 

 to correlate with SST and, if used, they would result in a 

 poor fit. However, a significant correlation, as obtained in 

 this application, suggests that the correlation is probably 

 stronger than apparent from the analysis, which should 

 give confidence that a relationship exists and provide an 

 incentive to apply the integrated models. 



The environmental model with process error did not 

 show a statistically significant improvement over the 

 environmental model because, ignoring the 1970s data, 

 the catch-at-age data were available only for the last part 

 of the time period. The recruitment anomalies were esti- 

 mated for the whole time period, as well as for the initial 

 conditions. Many of these recruitment anomalies had very 



