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279 



large biases. However, the standard errors for James' 

 estimators tended to be larger, so in terms of mean 

 square error the superior estimation method depended 

 on the assumptions we made concerning variability. 



Weighted Fabens' estimators performed well when 

 error was restricted to observational error, but were 

 badly biased when variability in L_ was introduced 

 into the simulation. In contrast, James' estimators per- 

 formed well when there was no observational error 

 and error was due only to variability in L,. The 

 unweighted Fabens' estimators were biased when er- 

 ror was solely observational, and biased when vari- 

 ability was due solely to variability in L,, but biases 

 apparently canceled when both errors were present. 



It is difficult to recommend the unweighted or 

 weighted Fabens' estimators because they are both sub- 

 ject to large biases. It seems difficult to assume biases 

 will cancel, or that there will be no variability in the 

 data due to variability in L,„. 



On the other hand, the James' estimators appeared 

 unbiased but tended to have larger standard errors. 

 Our experience with analyzing the small sample-size 

 dataset available for Pacific cod indicates that James' 

 estimators may require at least moderate sample sizes, 

 the required size depending on variability in the data. 

 If sample sizes are sufficiently large, reducing bias 

 can be far more important than increasing efficiency. 

 Therefore, it seems important that James' estimators 

 be used to at least guard against possible biases. More 

 experience with James' method will probably be needed 

 before researchers can finally decide the correct scope 

 of application for this new method. 



In this paper we have used von Bertalanffy param- 

 eter estimates based on direct ages as the yardstick by 

 which to measure bias for the three different estima- 

 tors. Of course, von Bertalanffy parameter estimates 

 based on length-at-age data might themselves be bi- 

 ased. Except for the small sample-size dataset avail- 

 able for Pacific cod, James' estimators compared well 

 with estimates based on direct age data. Unweighted 

 Fabens' estimators compared well with estimates based 

 on direct ages for one dataset. Weighted Fabens' esti- 

 mators of L appeared to be biased high for all three 

 datasets. 



This pattern of bias suggests that the tag-recapture 

 data in these actual datasets contain significant 

 amounts of variability due to variability in L„. This is 

 also evidenced by the length-at-age data (see Figs. 4,7). 

 For the three stocks of fish studied in this paper, we 

 conclude that there are no inconsistencies in growth 

 described by direct ages and growth described by tag- 

 recapture data. Without James' estimators, this con- 

 clusion could not be made. We feel that James' method 

 represents a significant step forward, and that datasets 



previously analyzed using Fabens' method might ben- 

 efit by being reexamined using James' method. How- 

 ever, results may be the same as Fabens' estimates, or 

 quite different, depending upon the nature of variabil- 

 ity in the data. 



Still, problems remain when evaluating growth from 

 tag- recapture data. McFarlane & Beamish (1990) con- 

 cluded that external tags could markedly affect the 

 growth of sablefish. We have shown that different 

 fishing gear types may select for slower- or faster- 

 growing individuals. For the west coast sablefish tag- 

 recapture datasets, growth increments appeared larger 

 for fish recovered with pot gear compared with trawl 

 gear. Therefore, sampling gears always play a role in 

 describing the growth parameters we estimate. 



Acknowledgments 



We thank R.A. Mailer, an anonymous referee, and the 

 editorial staff of the journal for comments that greatly 

 facilitated our revision. We thank FR. Shaw for provid- 

 ing access to the sablefish tag-recovery database. This 

 study was motivated by original insights into tag-re- 

 capture growth parameter estimation from I.R. James. 



Citations 



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