Kope and Botsford: Recruitment of Oncorhynchus tshawytscha in central California 



267 



false detection rates (a) (Botsford and Wainwright un- 

 publ.), imply that this correction for intraseries correla- 

 tion or a similar one should be used in correlation 

 analysis. 



Deconvolution also reduced the number of significant 

 correlations. For example, at the 0.10 level, using the 

 standard test, there were only 6 significant correlations 

 with deconvolved variables, whereas there were 21 

 significant correlations for corresponding variables 

 that were not deconvolved. The fact that this ratio is 

 lower when the more conservative correlated series 

 test is used (5 with deconvolution and 13 without) is 

 to be expected because the test itself accounts for some 

 of the intraseries correlation. Although the number of 

 significant correlations is less with deconvolution, we 

 cannot recommend its use in all situations. Deconvolu- 

 tion can have two positive effects on correlation 

 analysis: (1) It can provide a better estimate of recruit- 

 ment, and (2) it can reduce intraseries correlation, 

 hence the variance of the estimate of correlation coef- 

 ficient (Kope and Botsford 1988). However it can also 

 have a negative effect. If the deconvolution is marginal- 

 ly stable, the abundance data is noisy, or the coeffi- 

 cients of the deconvolution are inaccurate, deconvolu- 

 tion can lead to a poorer estimate of recruitment. In 

 the results presented here, deconvolution introduced 

 some additional significant correlations and reduced 

 the magnitude of existing correlations (although they 

 remained significant at the same level). This suggests 

 that the deconvolved series may be a poorer proxy 

 for recruitment than the raw abundance series, and 

 that this detracts from the removal of intraseries 

 correlation. 



The practical implication for chinook salmon man- 

 agers of the correlations obtained here is primarily a 

 recommendation of where to focus further research 

 rather than a means of immediately achieving a drama- 

 tic improvement in management. Because these stocks 

 are managed by annually attempting to control effort 

 based on an attempt to predict abundance, an under- 

 standing of the factors affecting abundance is neces- 

 sary. The relationship between salmon populations and 

 oceanographic conditions during the third year has an 

 R'~ of 0.23, and hence would not produce predictions 

 that could substantially improve catch. It also does not 

 hold for oceanographic conditions in the previous 

 3-month period, hence there is little potential for long- 

 term prediction. However, the results do indicate two 

 potentially useful relationships between environment 

 and abundance. Our understanding of these relation- 

 ships could possibly be improved to the point that they 

 could be useful in management. The ability to estimate 

 numbers at each age in catch and escapement would 

 improve our ability to determine potential oceano- 

 graphic effects as well as provide a possible predictor 



of catch (i.e., 2-year olds). The current practice of differ- 

 entiating jacks from older fish on the basis of size leads 

 to considerable uncertainty that could be removed by 

 determining age through hard parts or separation of 

 modes in the size distributions each year. Also, the ex- 

 istence of a demonstrated freshwater effect implies we 

 should attempt to remove that effect from the data 

 before searching for an oceanographic effect. However, 

 this is complicated by the fact that an unknown frac- 

 tion of the annual catch is produced by hatchery fish 

 that were trucked below the delta for release, and 

 hence not exposed to that effect. Better knowledge of 

 where and when fish are released could provide the 

 basis for removal of the effects of variable release 

 numbers and release strategies from the data before 

 searching for oceanographic effects. 



In general, results from correlation analyses in fish- 

 eries will always contain an element of doubt and, by 

 themselves, are probably not strong enough evidence 

 of causal relationships that management should be 

 based on them. Poor performance of past relationships 

 argue for less dependence on them (Sissenwine 1984, 

 Drinkwater and Myers 1987, Walters and Collie 1988), 

 however, as we have shown here, there are ways of 

 improving the reliability of correlation analyses. For 

 example, smoothing with moving averages should be 

 done only when the level of measurement noise war- 

 rants it, and it should always be accompanied by some 

 means of accounting for the intraseries correlation 

 introduced. Although we agree that the resulting 

 statistical relationships do not, by themselves, provide 

 a solid basis for management, we are not as pessimistic 

 as some others (e.g., Walters and Collie 1988) regard- 

 ing the utility of correlation analysis. It supplies infor- 

 mation on patterns that allows formulation of hypoth- 

 eses that can then be tested through direct means. It 

 increases the probability of detection of relationships 

 that might otherwise be missed. Fisheries analysts can- 

 not afford to dismiss the opportunities it provides, but 

 should use it only as exploratory analysis (cf. Bakun 

 1990, Botsford et al. 1989). 



Acknowledgments 



We thank L.B. Boydstun. and Chuck Knutson of the 

 California Department of Fish and Game, D. Cayan of 

 Scripps Institution of Oceanography, and A. Bakun of 

 the National Marine Fisheries Service for their assis- 

 tance in obtaining data. This work was supported in 

 part by the NOAA, National Sea Grant College Pro- 

 gram, Department of Commerce, under grant number 

 NA80AA-D-00120, Project number R/MA-16, through 

 the California Sea Grant College Program. 



