LAI ET AL.: AGE DETERMINATION OF PACIFIC COD 



considered to be sufficient for all age groups. 

 Beamish et al. (1978, figs. 12 and 13) showed that 

 the difference between readers was substantial 

 even in age groups 1 and 2. In our study, we found 

 that age readings from the scale method had low 

 precision, and that scale ages were much younger 

 than those obtained by any other method. 



In this study, validation for age groups 1-6 

 showed that dorsal fin rays gave the most reliable 

 ages for Pacific cod and thus should be used in the 

 future. This method provided estimates of mean 

 length at age that agreed most closely to observed 

 growth of the 1977 year class, and the precision of 

 this method was the highest attained in this 

 study. Another major advantage of this ageing 

 method is that additional fin rays can be taken 

 from fish with a previous history of fin-ray re- 

 moval to verify the accuracy of age determina- 

 tions between time of release and recapture. 



We used the Monte Carlo method to convert 

 scale ages to dorsal fin-ray ages. The results indi- 

 cated that the previously collected scale age data 

 can be used in age-dependent methods of stock 

 assessment. Since the 1983-84 classification prob- 

 abilities used in this study were completely inde- 

 pendent of the 1979-80 scale age data, the method 

 appears to be robust with respect to interannual 

 variability in the classification probabilities for 

 Pacific cod. However, application of this method 

 to other species will require caution when the 

 classification probabilities are applied to the data 

 from different years, since interannual variabil- 

 ity could be a source of error. Still, any errors that 

 arise will probably be smaller than those pro- 

 duced from an inappropriate ageing method. 



Analytical methods, such as those of Pella and 

 Robertson (1979) and Cook (1982), could also be 

 used for converting scale age-length keys to dor- 

 sal fin-ray age-length keys. However, these meth- 

 ods are mathematically more complicated and 

 occasionally yield negative values in some of the 

 converted age-length keys (Cook 1982). The 

 method of Hoenig and Heisey (1987)^ is of partic- 

 ular interest because it avoids negative values by 

 applying an incomplete E-M (estimation and 

 maximization) algorithm to fit a log-linear model 

 to the classification matrix. Nevertheless, this 

 method may not be valid if there is a substantial 

 systematic ageing error (as in our case, dorsal 



^Hoenig, J. M., and D. M. Heisey, 1987. Using log-linear 

 models with the EM algorithm to correct estimates of stock 

 composition and convert to age. Manuscr. in prep. Rosenstiel 

 School of Marine and Atmospheric Science, University of 

 Miami, Miami, FL. 



fin-ray ages vs. scale ages) because too many 

 empty cells are in the classification matrix. Alter- 

 natively, the method of Barlow (1984) can also be 

 used for this purpose, although the result will be 

 very similar to our Monte Carlo method, as Bar- 

 low's method is a deterministic version of our 

 own. 



ACKNOWLEDGMENTS 



This study was funded by Northwest and 

 Alaska Fisheries Center, National Marine Fish- 

 eries Service, NOAA, Seattle, WA. We thank 

 Richard G. Bakkala for providing length frequen- 

 cies and the scale age-length keys. Particular 

 thanks are due to Richard J. Beamish and an 

 anonymous reviewer for their constructive com- 

 ments. 



LITERATURE CITED 



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Barlow, J. 



1984. Mortality estimation: biased results from unbiased 

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Beamish. R J 



1981. Use of sections of fin-rays to age walleye pollock, 

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Cook, R C 



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Dixon, W J (editor) 



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FlENBERG, S E 



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