506 



Fishery Bulletin 105(4) 



500 1500 



O 5 = 0.05 



A 5 = 0.1 



+ 5 = 0.2 



X 6 = 0.5 



500 



1500 



2500 



Number of taq releases 



Figure 5 



Effect of changing the number of tag releases at various proportions of 

 observer coverage (6) on the coefficient of variation (CV) of the parameter 

 estimates. Results are shown for scenario 8 (see Table 1) and are based 

 on 1000 simulation runs per combination of tag releases and observer 

 coverage. M = natural mortality rate (assumed to be constant for scenario 

 8); F,= fishing mortality rate for age i fish; Pj= population size of tagged 

 cohort at age 1; A = tag reporting rate for the unobserved component of 

 the fishery (assumed to be constant for scenario 8). 



maximizing the separate components would not be the 

 overall maximum likelihood estimates because there 

 is information in the catch data about the mortality 

 rates. Furthermore, we assert that even in the model 

 by Pollock et al. (2002), the estimates obtained from the 

 two-step likelihood procedure are only the maximum 

 likelihood estimates of the overall likelihood when the 

 reporting rates are allowed to vary by year and age, 

 and not, as the study would indicate, when there are 

 any constraints on these parameters. 



The BPO model allows for simultaneous estimation of 

 age-specific fishing mortality rates, natural mortality 

 rates, and reporting rates, as well as cohort size 

 at first tagging, for a cohort tagged in consecutive 

 years. All parameters appear to be estimated with 

 reasonable accuracy, but the level of precision that can 

 be achieved varies greatly, depending on the specifics 

 of the population, the fishery, and the experimental 

 design, and also on the parameter. Nevertheless, 

 some general observations can be made based on our 

 simulations. Cohort size appears to be estimated well in 

 all situations (with a CV between 0.10 and 0.20 in the 

 majority of scenarios considered). With the exception of 

 the oldest age of fish at recapture, the fishing mortality 

 rates also tend to be estimated with good precision 

 (CVs of less than 0.20 achievable in many situations). 



In general, natural mortality is estimated poorly in 

 comparison to the other parameters, with CVs above 

 0.60 in many cases. If, however, natural mortality can 

 be assumed constant over enough release years (or 

 otherwise constrained), then it too can be estimated 

 with reasonable precision (e.g., CV on the order of 0.20 

 for our scenario 8 with 1000 releases per year). 



Reducing the number of parameters that need to 

 be estimated through imposing parameter constraints 

 can greatly improve the accuracy and precision of the 

 estimates. However, this is only true if the constraints 

 imposed approximate reality; for example, modeling 

 natural mortality as a constant will not lead to better 

 parameter estimates if in fact natural mortality changes 

 significantly with age. In practice, standard model 

 selection techniques, such as Akaike's information 

 criterion (AIC; Akaike, 1974) and its many variations 

 (e.g., AICj, for small sample sizes, QAIC for overdispersed 

 data; see Burnham and Anderson, 1998, and references 

 therein), can be used to determine which parameter 

 constraints are most supported by the data. 



For ease of presentation, the model was developed for, 

 and applied to, one cohort of tagged fish. In practice, it 

 is likely that several cohorts (i.e., age classes) would 

 be tagged in each year of tagging. If all parameters 

 being estimated are both year- and age-dependent, then 



