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Fishery Bulletin 105(4) 



the BP model has similarities with an age-structured 

 Jolly-Seber (JS) model (Jolly, 1965; Seber, 1965; Pollock, 

 1981). Both the BP and JS models have a likelihood 

 component for the recapture data, from which survival 

 rates can be estimated. For the BP model, this compo- 

 nent equates to a Brownie model, and for the JS model, 

 it equates to a Cormack- Jolly-Seber (CJS) model (Cor- 

 mack, 1964). Additionally, they both have a likelihood 

 component involving the total number of animals sam- 

 pled, from which abundance can be estimated (i.e., the 

 Petersen component). However, for the JS model there 

 is an unresolved problem with the Petersen component 

 regarding how the information from unmarked animals 

 should be integrated into the likelihood, and a variety 

 of approaches have been developed to address this prob- 

 lem (see section 4.3 of Schwarz and Seber, 1999, and 

 references therein). The Petersen component of the BP 

 model (i.e., the catch component) is more general and 

 integration into the likelihood is more straightforward. 



A recognized problem with applying tagging exper- 

 iments in fishery situations is that of nonreporting. 

 When recapture information comes from commercial 

 fisheries, it is unlikely that all recaptured tags will be 

 reported, or that the rate of reporting will be known. 

 Although Brownie models can provide estimates of to- 

 tal mortality rates when reporting rates are unknown 

 (Brownie et al., 1985), the separation of natural mor- 

 tality from fishing mortality generally requires that 

 reporting rates are either known or estimable (Pollock 

 et al., 1991; Hoenig et al., 1998a). Petersen models 

 also require reporting rates to determine abundance 

 estimates. 



A number of methods exist for estimating reporting 

 rates (see Pollock et al., 2001). For some methods, such 

 as planted (also called "seeded") tag experiments, the 

 data are independent of the tag-recapture and related 

 catch data from the primary tagging study. In develop- 

 ing the BP model, we assumed that independent re- 

 porting rate data were available; therefore a likelihood 

 could be constructed for these data and simply multi- 

 plied to the likelihoods for the tag-recapture and catch 

 data. Another common method for estimating report- 

 ing rates is to have observers monitor a portion of the 

 catches. Under the assumption that 100% of tags will 

 be returned (i.e., reported) from the observed catches, 

 the reporting rate for the unobserved catches can be 

 estimated by using the relative return rate of tags from 

 the unobserved versus observed catches (Hearn et al., 

 1999). In the case of longline fisheries, where fish are 

 not brought into port for processing, the use of observers 

 to estimate reporting rates is probably the most viable 

 approach. Unlike data from a planted tag experiment, 

 observer data cannot be considered independent of the 

 tagging or related catch data and therefore incorporat- 

 ing the estimation of reporting rates into the BP model 

 is more complicated. 



Pollock et al. (2002) showed how a standard Brownie 

 model can be modified to include the estimation of re- 

 porting rates when one component of a multicomponent 

 fishery has 100% reporting rates (e.g., one component 



has observers). This modification required that supple- 

 mentary catch data be brought into the model to assist 

 in the estimation of reporting rates. Pollock et al. (2002) 

 acknowledged that uncertainty in the catch data was 

 not accounted for in their model, and also that it would 

 be resourceful to take advantage of the extra informa- 

 tion provided by the catch data to estimate population 

 size. As a topic of future research, they advocated the 

 development of an integrated analysis that estimates 

 all parameters (fishing mortality, natural mortality, 

 population size, and reporting rates) within a single 

 likelihood. 



In this article, the BP model is extended to include 

 the estimation of reporting rates by using observer data. 

 We will refer to this extended model as the BPO model, 

 short for the Brownie-Petersen model with observers. 

 The BPO model fulfills the goal of Pollock et al. (2002) 

 for an integrated likelihood that can provide joint es- 

 timates of mortality rates, abundance, and reporting 

 rates, and it also directly incorporates uncertainty in 

 the catch data. Results from applying the model to simu- 

 lated data are presented which demonstrate the accura- 

 cy and precision that can be achieved in the parameter 

 estimates under various scenarios (e.g., different param- 

 eter values, different numbers of release and recapture 

 years, different parameter constraints). Tag-recapture 

 data and catch data from most field studies will exhibit 

 more variability than the model predicts (i.e., will be 

 overdispersed). Thus, extra variability was included in 

 the simulated data sets to investigate the consequences 

 of applying the model to overdispersed data. Finally, a 

 practical illustration is given of how the model can be 

 used to evaluate the trade-off between releasing more 

 tags and increasing the level of observer coverage in 

 terms of the accuracy and precision of the parameter 

 estimates. Polacheck and Hearn (2003) investigated 

 this issue using a much simpler model (e.g., only one 

 release event; only fishing mortality rates estimated) 

 and making many simplifying assumptions (e.g., natural 

 mortality known; no uncertainty in the catch data; no 

 overdispersion in the data). The BPO model provides 

 a much more comprehensive framework for evaluating 

 such trade-offs and can thereby make an important 

 contribution to the successful and cost-effective manage- 

 ment of tagging programs for commercial fisheries. 



Materials and methods 



Model description 



Consider a multiyear tagging study in which a single 

 cohort offish is tagged in A consecutive years starting at 

 age 1 (i.e., at age 1 in year 1, age 2 in year 2, up to age A 

 in year A). Fish from this cohort are subsequently caught 

 in a fishery over years, or ages, 1 to / (/>A), and a per- 

 centage of the tags that are recaptured each year are 

 reported. Observers monitor a portion of the catches, and 

 100% of recaptured tags are reported from the observed 

 component of the fishery. Furthermore, all fish caught 



