Eveson et al.: Incorporating fishery observer data into an integrated catch-at-age and multiyear tagging model 



505 



O 5 = 0.05 

 A 5 = 0.1 

 + 6 = 0.2 

 X 5 = 0.5 



Number of tag releases 



Figure 4 



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 1 (see Table 1) and are based 

 on 1000 simulation runs per combination of tag releases and observer 

 coverage. M^ = natural mortality rate for age i fish; F^ = fishing mortality 

 rate for age i fish; Pi= 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 1). 



Discussion 



The current article extends the integrated BP model 

 for tag-recapture and catch data developed in Polacheck 

 et al. (2006) to incorporate the estimation of reporting 

 rates through observer data, which we refer to as the 

 BPO model. This is an important and practical exten- 

 sion because nonreporting of tags is a serious problem in 

 many commercial fisheries that needs to be accounted for 

 in the model to obtain meaningful results, and observer 

 data often provide the most viable means of doing so. 



In the way the BPO model was formulated, increasing 

 the level of observer coverage improves the parameter 

 estimates not only by improving the reporting rate 

 estimates, but also by improving the precision of the 

 catch-at-age data. If all fish caught in the observer 

 component were not sampled, then the improvements 

 would not be expected to be as great. As an extreme 

 case, the precision of the catch-at-age data could be 

 assumed to be independent of the level of observer cov- 



erage, in which case increasing the level of observer 

 coverage would only improve the parameter estimates 

 through the reporting-rate estimates. However, it is 

 difficult to envisage a situation where observers would 

 not take age or length samples from at least a portion 

 of the catches. 



In the study by Pollock et al. (2002), where a 

 standard Brownie model was modified to include the 

 estimation of reporting rates when one component of 

 a multicomponent fishery has observers (i.e., 100% 

 reporting rates), the authors show how the overall 

 likelihood for their model can be partitioned into two 

 conditionally independent components. They argue that 

 the reporting rates can be estimated by maximizing the 

 second likelihood component, and then plugged into the 

 first component to estimate the mortality rates, and that 

 doing so provides the maximum likelihood estimates of 

 the reporting rates and mortality rates for the joint 

 likelihood. Although a similar partitioning could be 

 done for the BPO model, the estimates obtained from 



