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Fishery Bulletin 105(4) 



Several other points are worth noting. Changing the 

 level of overdispersion in the data (scenarios 6 and 

 7) had the greatest influence on the CVs across all 

 parameters. The only exception was that constraining 

 natural mortality to be constant (scenario 8) had a 

 greater effect on the CV of the natural mortality- 

 rate estimation. Constraining natural mortality to be 

 constant (scenario 8) not only reduced the CV of the 

 M estimate substantially, but also the CV of the Fg 

 estimate. Similarly, constraining fishing mortality to 

 be linear (scenario 9) substantially reduced the CV 

 of the Fg estimate, but also the M^ estimate, and to a 

 lesser degree the M^ estimate. Interestingly, however, 

 neither of these constraints affected the CVs of the 

 Pj and A estimates. Also of interest is that allowing 

 reporting rates to vary across years (scenario 10) had 

 only a small effect on the precision of the mortality rate 

 and abundance estimates. The reporting-rate estimates 

 themselves were less precise and had a high tendency to 

 hit the upper bound of one, but usually these parameters 

 are not the ones of primary interest. Lastly, we note 

 that having five recapture years but only three release 

 years (scenario 12) resulted in much higher CVs for the 

 F3, F^, and f, estimates, and increasingly so with age 

 (with a CV of 0.75 for F^). Thus, having more recapture 

 years allows for more years of fishing mortality rates 

 to be estimated, but these estimates quickly become 

 uninformative unless the number of release years is 

 also increased. 



High correlations were present between many of 

 the parameter estimates (Table 4; results are shown 

 for scenario 1, but the patterns are very similar 

 for all scenarios). Given the nature of the model, 

 high correlations were expected, and have already 

 been documented and discussed for the BP model in 

 Polacheck et al. (2006). For example, to yield the same 

 number of tag returns in a particular year, a higher 



estimate of fishing mortality for that year could be 

 compensated by a higher estimate of natural mortality 

 for the previous year, so that estimates of F- and M, j 

 tend to be positively correlated. Alternatively, it could 

 be compensated by a higher estimate of the reporting 

 rate; hence estimates of F, and A tend to be negatively 

 correlated. When two parameters have highly correlated 

 estimates, a large CV for one of these parameters will 

 tend to mean a large CV for the other parameter. 

 This may explain some of the results observed above. 

 For example, in scenarios 1-7, 9, and 10, estimates 

 of F5 and M4 were highly correlated; therefore the 

 high uncertainty in Fg is likely due to the very high 

 uncertainty in M^. An analogous statement can be made 

 about F3 and M.^ in scenario 11. The high correlation 

 between estimates of Fg and M^ also explains why, 

 in scenarios 8 and 9, constraints that improved the 

 precision of one of these parameters also improved the 

 precision of the other. 



The Hessian-based standard error estimates in 

 relation to the standard errors derived from the 

 simulations are presented in Table 5. In all of the 

 scenarios with (/i=3, the Hessian-based standard errors 

 were underestimated by a factor close to V3 = 1.73, and 

 had a mean across all parameters and scenarios of 

 1.67 (ranging from 1.45 to 1.91). In the scenario with 

 (p=l (i.e., multinomial data), the Hessian-based and 

 simulation-based standard errors were very similar, as 

 expected. In the scenario with qi=9, the Hessian-based 

 estimates were underestimated by a factor reasonably 

 close to V'9 = 3.0 — the largest exception being a factor of 

 2.49 for Pj. Nevertheless, these results indicate that if 

 q^ can be estimated after fitting the model (e.g., from 

 the residuals), then multiplying the Hessian-based 

 standard error estimates by V(p can provide improved, 

 and perhaps adequate, estimates of the true standard 

 errors. Further investigation of additional scenarios 



