Heifetz et al,: Age validation and analysis of ageing error for Anoplopoma fimbria 



261 



2 units above the AIC value for case 1. For the reader 

 and known-age data set, a model with a and X con- 

 strained to (case 6) provided the best fit with the 

 fewest parameters. The AIC value for a model with 

 only A constrained to (case 4) was only 0.5 units 

 above the minimum. The closeness of the AIC val- 

 ues for these two cases indicates that case 6 provides 

 only a slightly better model fit than case 4. The differ- 

 ence between case 4 and case 6 is best understood by 

 comparing estimated standard deviation and bias at 

 age (Fig. 3). Case 4 results in a nonlinear relationship 

 between standard deviation and age, and the standard 

 deviation approaches an asymptote near age 9; whereas 

 for case 6, the standard deviation increases linearly 

 with age. Bias is linear for both cases, and case 6 has 

 higher absolute bias than case 4 for most ages. 



Estimates of ageing errors based on comparison of 

 known ages to reader ages were considerably higher 

 than estimates obtained from between-reader vari- 

 ability (Fig. 4). For example, for age 2-9 fish, accord- 

 ing to primary reader and tester ages, the estimates 

 of the probability of assigning the true age was 0.95- 

 0.46. In contrast, according to the estimates from 

 reader and known ages, the probability was only 

 0.71-0.19. This discrepancy was expected because 

 agreement between readers was considerably greater 

 than between reader and known ages. Thus, use of 

 between-reader agreement to assess ageing error 

 may lead to a false sense of the true error. 



In conclusion, use of ageing errors based on known- 

 age samples may help improve stock assessment of 

 sablefish. Future analysis of ageing errors for sable- 

 fish may require consideration of the time of year 

 otoliths are taken because, as Anderl and Heifetz- have 

 shown, ageing error may depend on the season when 

 an age sample is taken. Precaution should be taken in 

 extending our results to fish older than age 9. Results 

 should be compared between stock assessments that 

 use parameter estimates for the ageing-error matrix 

 based on case 4 and case 6. If a sample is obtained that 

 includes older known-age fish, the ageing-error matrix 

 can be estimated for older fish. We expect such a sample 

 to be available in the future as the fish tagged as juve- 

 niles by Rutecki and Varosi ( 1997a) continue to be re- 

 covered. For many species other than sablefish, knowm- 

 age specimens are not available. For such species, vari- 

 ability between readers may be the only data available 

 to assess ageing error Such data are valuable for evalu- 

 ating the precision and consistency of ageing criteria 

 applied by different readers. Estimates derived solely 

 from between-reader variability should be viewed as 

 minimum estimates of ageing error. 



Acknowledgments 



Critical reviews by Dave Clausen, Jerome Pella, Mike 

 Sigler, Jeff Fujioka, and two anonymous referees 



