Eveson et aL: Incorporating fishery observer data into an integrated catch-at-age and multiyear tagging model 499 



stant reporting rate and allows reporting rates to differ 

 across years. This scenario has the maximum number 

 of parameters that can be estimated by the model (i.e., 

 the model is saturated). 



In terms of experimental design (factor 3), the effect 

 of varying the number of tag releases and the propor- 

 tion of observer coverage is investigated in detail in the 

 next section; therefore only variations to the numbers 

 of release and recapture years are considered here. In 

 particular, scenario 11 reduces the number of release 

 and recapture years from five to three, whereas sce- 

 nario 12 still has five recapture years but only three 

 release years. For both scenarios, natural mortality was 

 constrained to be equal at ages 2 and above, because 

 only two natural mortality parameters can be estimated 

 with three release years. For scenario 12, this meant 

 constraining natural mortality to be equal at ages 2 to 

 5. In such a case, alternative constraints may be pref- 

 erable, such as assuming natural mortality is a linear 

 function of age. This was the approach taken in our 

 application of the BP model to SBT data in Polacheck 

 et al. (2006). 



For each scenario in Table 1, 1000 sets of data were 

 generated, as described above for scenario 1, and fitted 

 by using the BPO model. For each parameter estimated, 

 the percent median bias and the CV of the 1000 esti- 

 mates were calculated, where percent median bias is 

 defined as (median-true)/truexlOO% and CV is defined 

 as SD/true (where SD denotes standard deviation). The 

 median was used instead of the mean in calculating the 

 bias because many of the parameter estimates had a 

 skewed distribution, making the median a better mea- 

 sure of centrality (see "Results" section). The SDs of the 

 parameter estimates obtained from the 1000 simulation 

 runs (which approximate the true standard errors of 

 the estimates) were compared with the standard error 

 estimates obtained from the inverse Hessian matrix 

 (these are obtained for every run; therefore we averaged 

 the standard errors over the 1000 runs). The purpose 

 was to see how much the Hessian-based standard errors 

 were underestimated by applying a model that does not 

 account for overdispersion in the data. 



Trade-off between number of releases and observer 

 coverage Of the factors that affect model performance, 

 only the experimental design can be directly controlled 

 by the researcher in a real application. Although model 

 parameterization is superficially in the researcher's 

 control, it is the true parameter values that will deter- 

 mine whether any parameter constraints are advanta- 

 geous (i.e., imposing constraints on parameters that 

 do not represent the true situation will lead to poorer 

 model performance, not improved performance). Thus, in 

 designing a tagging experiment and deciding how best 

 to distribute resources, it would be very useful for the 

 researcher to know the level of performance that can 

 be achieved under different designs, as well as which 

 design elements have the most influence on the results. 

 Here, we illustrate how the BPO model can be used to 

 provide such information. In particular, simulations are 



used to evaluate how well the parameters are estimated 

 with different numbers of tag releases and different 

 proportions of observer coverage, and to evaluate the 

 trade-off between releasing more tags versus increas- 

 ing observer coverage (i.e., to evaluate which leads to 

 larger improvements in accuracy and precision of the 

 parameter estimates). 



Initially, simulations were carried out under scenario 

 1. For simplicity, the number of releases was kept the 

 same for all release ages (i.e., N^=N for all a) and the 

 proportion of observer coverage was the same over all 

 recapture years (i.e., d^ = d for all ;). N was varied from 

 250 to 2500, and d from 0.05 to 0.50. For each combina- 

 tion oi^ N and d, 1000 tag-recapture and corresponding 

 catch data sets were generated, as described in the pre- 

 vious section, and fitted by using the BPO model. The 

 results were used to evaluate how the percent median 

 bias and CV of the parameter estimates changed as 

 the number of releases and level of observer coverage 

 changed. 



For a true field study, the researcher would need to 

 carry out such simulations using parameter values and 

 model constraints that roughly represent the population 

 and fishery dynamics for their situation. Our purpose 

 was not to provide guidance on appropriate numbers of 

 releases and observer coverage for any specific situation, 

 but to illustrate how the model could be used to this 

 end. Nevertheless, it is of interest to know whether the 

 general findings using scenario 1 are likely to remain 

 similar under other scenarios. The absolute levels of 

 accuracy and precision that can be achieved will clearly 

 depend on the scenario, but it is less clear whether the 

 relative changes in these measures from increasing 

 tag releases or increasing observer coverage will be 

 highly scenario dependent. To investigate, we repeated 

 the trade-off simulations using a subset of the other 

 scenarios (4, 6, 8, 10, 11, and 12). 



Results 



Model performance 



The biases in the medians of the parameter estimates 

 were small for almost all parameters and scenarios 

 (Table 2). A few of the natural mortality estimates had 

 negative biases of greater than 59c, but this result more 

 likely reflects the large variability and non-normality of 

 these estimates (see next paragraph) than true biases. 

 Histograms of the parameter estimates revealed 

 features that are important for evaluating biases. In 

 particular, the natural mortality estimates often hit the 

 lower bound of zero, and the proportion that did so was 

 highest when the variability was largest (e.g., scenario 

 7, which has a high amount of overdispersion; Fig. 1). 

 This feature makes it difficult to assess bias for these 

 parameters and explains why the median biases seen 

 in some of the natural mortality-rate estimates, such as 

 scenario 7, are not likely to be meaningful. In scenarios 

 5, 7, and 10, the reporting-rate estimates often hit their 



