Sampson Constant selectivity and stock assessment for Sebastes entomelas 



677 



sessed by using one or more of these procedures in- 

 clude Pacific halibut (Hippoglossus stenolepis) in the 

 northeast Pacific (IPHC, 1991), walleye pollock 

 (Theragra chalcogramma) in the Gulf of Alaska 

 (Megrey, 1991), Dover sole (Microstomus pacificus) 

 along the U.S. west coast (Turnock and Methot, 1991), 

 and scad {Trachurus trachurus) from Atlantic waters 

 off Spain and Portugal (Borges, 1990). 



Despite the widespread application of assessment 

 methods that are based on the notion that selectivity 

 is time-invariant, I know of no published studies that 

 examine the sensitivity of these assessment procedures 

 to violations of the constant selectivity assumption. It 

 appears that often these assessment methods are ap- 

 plied without first verifying that selectivity was con- 

 stant for the stock being assessed. Gudmundsson ( 1986) 

 recommended extensive analysis to avoid mis-specify- 

 ing the catch-at-age model (for example, incorrectly 

 assuming that selectivity was constant), and he devel- 

 oped a least-squares technique for testing the separa- 

 bility assumption. However, his methodology does not 

 seem to be used widely. 



Several published papers document variations in se- 

 lectivity through time. Houghton and Flatman (1981) 

 examined selectivity coefficients for cod (Gadus 

 morhua) in the west-central North Sea and found sig- 

 nificant changes in the "exploitation pattern," which 

 they attributed to shifts in the fishing pressure ex- 

 erted by different segments of the fleet. Gudmundsson 

 (1986) speculated that changes in fish size-at-age 

 coupled with variations in the composition of the fishing 

 gear caused changes in selectivity for the Icelandic 

 stock of cod (Gadus morhua). Gordoa and Hightower 

 (1991) analyzed data from the fishery for Cape hake 

 (Merluccius capensis) off southwestern Africa and as- 

 cribed significant shifts in selectivity to the fishermen's 

 targeting on strong year classes. 



The work described here has a different focus. In 

 this paper I do not examine how selectivity in a fishery 

 has varied. Instead, I investigate whether the stock 

 assessment program used to evaluate a particular 

 stock's status is robust to changes in selectivity. For 

 this exercise I analyzed the stock assessment for widow 

 rockfish (Sebastes entomelas), an economically impor- 

 tant component of the complex of Sebastes species 

 found along the Pacific coast of North America. 

 Gunderson ( 1984) described the history and character- 

 istics of the U.S. fishery for widow rockfish off the 

 coasts of Washington, Oregon, and California. 



In this paper, I demonstrate that the stock size esti- 

 mates for widow rockfish, which are based on the un- 

 tested assumption that selectivity has been constant 

 from year to year, can be seriously biased if the as- 

 sumption is violated. Furthermore, I test two other 



assessment methods that also use the constant selec- 

 tivity assumption and show that they produce simi- 

 larly biased results. Finally, I establish that compa- 

 rable problems with bias can arise in the assessment 

 results for other fish stocks, whose biological charac- 

 teristics differ significantly from widow rockfish. 



Methods 



One technique for testing the reliability of an estima- 

 tion procedure is to produce artificial data sets with 

 known characteristics and then to estimate the pa- 

 rameter values from which the data were derived. I 

 used this approach to determine whether certain stock 

 assessment methods were sensitive to violations of the 

 constant selectivity assumption. First, I simulated 

 catch-at-age data for a fish stock in which the selectiv- 

 ity coefficients were changing slowly from year to year. 

 Next, I used the assessment programs to analyze the 

 catch-at-age data and to estimate stock biomass and 

 abundance-at-age. Finally, I measured the bias of the 

 estimates by calculating the relative errors of the esti- 

 mates. The relative error of an estimate is the differ- 

 ence between the estimate and its true value; all di- 

 vided by the true value. 



Sensitivity of the Stock Synthesis program 

 when applied to data for widow rockfish 



To investigate the sensitivity of the stock assessment 

 results for widow rockfish to the assumption of con- 

 stant selectivity, I developed a spreadsheet model to 

 generate artificial catch-at-age data, which I then ana- 

 lyzed using the Stock Synthesis program. The Stock 

 Synthesis program has been used by the Pacific Fish- 

 eries Management Council (PFMC) since 1990 to ap- 

 praise the status of many of the Pacific groundfish 

 stocks (PFMC, 1990). Methot (1989, 1990) documented 

 the principles and equations underlying the Stock Syn- 

 thesis program. 



The spreadsheet model simulates the characteris- 

 tics of an age-structured population and employs the 

 same equations as the Stock Synthesis program for 

 describing the temporal progressions in abundance- 

 at-age, biomass, catch-at-age, and total catch. The 

 model uses parameters for mortality and growth that 

 are similar to those observed in the U.S. stock of widow 

 rockfish (Table 1). I generated values for abundance- 

 at-age and catch-at-age for 10 years and 20 age classes, 

 ages 4 through 22, as well as age 23 and older (Table 

 2). In 1989, almost 95% of the U.S. coast-wide land- 

 ings of widow rockfish were fish between the ages of 

 5-10 years; about 3% of the landings were fish older 

 than 15 years (Hightower and Lenarz, 1990). 



