Abstract.— Modern methods for 

 fish stock assessment are often based 

 on age-structured models that sepa- 

 rate each coefficient of fishing mor- 

 tality at age into a time-specific fac- 

 tor (the rate of fishing mortality on 

 the fully exploited age-classes) and 

 an age-specific factor (a selectivity 

 coefficient that measures the rela- 

 tive vulnerability of the particular 

 age-class). The assumption that the 

 selectivity coefficients are constant 

 through time greatly simplifies the 

 assessment process because it allows 

 for a reduction in the number of un- 

 known parameters. However, if the 

 assumption is incorrect, it can lead 

 to incorrect estimates of stock status. 

 The most recent stock assessment 

 for Pacific widow rockfish (Sebastes 

 entomelas) was based on the un- 

 tested assumption that the selectiv- 

 ity coefficients have not changed over 

 the years. This assessment was de- 

 rived from an analysis of catch-at- 

 age data by using an assessment 

 method known as the Stock Synthe- 

 sis program. The work described 

 here examined the sensitivity of the 

 assessment results to the assump- 

 tion of constant selectivity. Simula- 

 tion experiments with the Stock Syn- 

 thesis program showed that the 

 stock size estimates for widow rock- 

 fish can be highly sensitive to mod- 

 est changes in selectivity. Experi- 

 ments with two other assessment 

 techniques, which also assume con- 

 stant selectivity (the CAGE AN pro- 

 gram of Deriso, Quinn, and Neal and 

 the multiplicative catch-at-age model 

 of Shepherd and Nicholson), showed 

 that these methods are similarly 

 sensitive to changes in selectivity. 



The assumption of constant 

 selectivity and the stock assessment 

 for widow rockfish, Sebastes entomelas 



David B. Sampson 



Coastal Oregon Marine Experiment Station 



Hatfield Marine Science Center, Oregon State University 



Newport, OR 97365 



Manuscript accepted 21 May 1993. 

 Fishery Bulletin 91:676-689 1993) 



In general, individual fish in a stock 

 are not equally likely to be caught and 

 different age-classes of fish do not ex- 

 perience identical rates of fishing mor- 

 tality. In the fisheries literature this 

 phenomenon is usually described as 

 "selectivity" or "availability" or "par- 

 tial recruitment" (Megrey, 1989). In 

 some instances selectivity results 

 from the physical properties of the 

 fishing gear. For example, younger 

 and smaller fish may pass unharmed 

 through the meshes of a trawl, 

 whereas older and larger individuals 

 may sense and avoid an approaching 

 net. Alternatively, selectivity can re- 

 sult when different age-classes of fish 

 occupy geographic regions that are not 

 fished with the same intensity. If 

 younger fish are offshore and older 

 ones are inshore, for example, then 

 the age distribution of fish in the catch 

 will depend not just on the stock's age 

 distribution but also on the fishing 

 locations. Selectivity coefficients, 

 which measure the relative influence 

 of fishing on the age structure of the 

 stock, are fundamental parameters in 

 the analysis of catch-at-age data. 



Many stock assessment procedures 

 attempt to reconcile observations of 

 catch-at-age with an underlying age- 

 structured population model and 

 thereby reconstruct the demographic 

 history of the stock (Megrey, 1989). 

 If different age-classes experience 

 the same relative susceptibility to 

 fishing each year, then one can model 

 each annual age-specific rate of 

 fishing mortality as the simple prod- 



uct (S a -F y ) of an age effect (the selec- 

 tivity coefficient, S a ) and a year ef- 

 fect (the fishing mortality coefficient, 

 F y ). Because there are an infinite 

 number of (S a , F y ) pairs that corre- 

 spond to a given age-specific rate of 

 fishing mortality, the selectivity co- 

 efficient for at least one age class 

 must be assumed constant. If the 

 largest S„ is set equal to one, then 

 the F Y values correspond to the rate 

 of fishing mortality on the fully ex- 

 ploited age classes. 



Formulating the fishing mortality 

 coefficient as the product of a year- 

 effect and an age-effect greatly sim- 

 plifies an analysis of catch-at-age 

 data because it reduces the number 

 of essential parameters. For example, 

 if the catch-at-age matrix contains 

 data for A ages and Y years, and if 

 the selectivity coefficients are con- 

 stant for all years, then there are only 

 iA+Y) unknown parameters. How- 

 ever, if the selectivity coefficients 

 change every year, then there are 

 (A-F) unknown parameters. 



Constant selectivity, and the con- 

 sequent separability of fishing mor- 

 tality into age and year effects, is a 

 fundamental assumption for numer- 

 ous stock assessment procedures, in- 

 cluding separable Virtual Population 

 Analysis (Pope and Shepherd, 1982), 

 the CAGEAN program (Deriso et al., 

 1985, 1989), the multiplicative model 

 of Shepherd and Nicholson (1986, 

 1991), and the Stock Synthesis pro- 

 gram (Methot 1989, 1990). Fish 

 stocks that have recently been as- 



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