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Fishery Bulletin 97(3), 1999 



M outside the model at the "best," most reasonable 

 value, then estimate absolute abundance with the 

 population model. 



The likelihood surface was mapped to examine the 

 parameter relationship between q and M (Table 2, 

 panel 1). I found it useful to fix one parameter, then 

 estimate the other parameter, thus ensuring that the 

 peak of the likelihood ridge as a function ofq and M 

 was found. An alternate, seemingly useful approach 

 IS a grid over fixed values of g and M. I do not recom- 

 mend this approach. It is difficult and time consum- 

 ing to design a grid fine enough and large enough to 

 map the peak of the likelihood ridge. In earlier mod- 

 eling, not described in this paper, this approach led 

 me to declare incorrectly a global minimum over q 

 and M because the grid was too coarse and the like- 

 lihood ridge poorly mapped. 



Thompson ( 1994 ) demonstrated analytically that 

 M and the degree of curvature of dome-shape are 

 confounded because fish may "disappear" with age, 

 owing to natural death or decreased vulnerability. 

 Survey catchability and selectivity also were con- 

 founded (Table 2, panel 3). Fish recruited later (panel 

 4) or were less vulnerable when older (panel 5), de- 

 pending on the value of survey catchability. Older 

 fish were less vulnerable when fixed q was less than 

 estimated q (panel 5). 



The lower vulnerability of older fish for lower 

 catchability values is a clue as to why abundance esti- 

 mation is less reliable when selectivity is dome-shaped. 

 Absolute biomass is inferred in the model ft-om how 

 the catches affect the survey index, as described in the 

 introduction, and this effect implies some specific esti- 

 mate for absolute abundance. Older fish were less vul- 

 nerable to compensate for lower survey catchability, 

 which helps to maintain the absolute biomass estimate 

 implied by the catch and survey index. Estimated bio- 

 mass is similar with either higher catchability or lower 

 vulnerability of older fish, i.e. greater degree of curva- 

 ture of dome-shape. This parameter interaction prob- 

 ably is why abundance estimation is more difficult when 

 selectivity is dome-shaped. 



In some cases, selectivity can be estimated inde- 

 pendently to eliminate the problem of confounding 

 parameters with selectivity. If a species is surveyed 

 by two overlapping surveys and gear selectivity is 

 known for one survey, then the unknown gear selec- 

 tivity can be estimated by comparing the survey 

 length compositions (Kimura, 1978). This approach 

 helps to estimate gear selectivity, but not to estimate 

 availability with age, where availability at age is the 

 fraction of the population within the survey area by 

 age. Modeling availability at age will depend on sur- 

 vey coverage in relation to ontogenetic changes in 

 spatial distribution. 



The age-structured model presented here is a tool 

 for interpreting the data collected from the sablefish 

 fishery and longline survey. Simulations and an ex- 

 amination of parameter relationships help one to 

 understand how the tool performs, its reliability, and 

 its strengths and weaknesses. The population model 

 appears reliable for interpreting the sablefish data 

 and has been adopted for estimating abundance and 

 setting quotas for sablefish management. The con- 

 clusions regarding data and model requirements for 

 estimating abundance and parameter interactions 

 with abundance estimates should be generally ap- 

 plicable to other species. The sablefish age-structured 

 model is like other north Pacific age-structured mod- 

 els except for the assumption of a discrete fishery. In 

 one respect, these simulations were a more difficult 

 test of an age-structured model to estimate abun- 

 dance because one scenario examined length data 

 alone, an imprecise measure of age structure. 



Acknowledgments 



The analysis benefitted from an on-going dialogue 

 with Jeff Fujioka. I thank Dan Kimura, Jerry Pella, 

 and Jon Heifetz for reviewing earlier versions and 

 two anonymous reviewers for improving the presen- 

 tation of this paper. 



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