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Fishery Bulletin 9I|4). 1993 



Table 1 



Parameters for simulating a stock of widow 

 rockfish: annual recruitment was 10" fish per 

 year; natural mortality 1 was 0.15 per year. 

 Selectivity parameters- (Curve B (Fig. 1), 

 100% selection at age 8): lower inflection age 

 was 6.0 years; lower slope was 2.5 per year; 

 upper inflection age was 12.0 years; and the 

 upper slope was 0.3 per year. 



'From Hightower and Lenarz ( 1990). 

 -The equation for the double-logistic selec- 

 tion curve and the meaning of these param- 

 eters are described in Methot ( 1990). 

 'From Barss and Echeverria (1987). 



In the first set of experiments, I exam- 

 ined combinations of three factors to de- 

 termine how they affect bias in the esti- 

 mates from the Stock Synthesis program. 

 They were 1) the age of full selection was 

 either gradually increasing or decreasing 

 from year to year, or it varied randomly; 

 2) the annual fishing mortality coefficients 

 were either increasing, decreasing, or con- 

 stant; and 3) the program was either 

 given the true values of annual recruit- 

 ment or it was required to estimate these 

 values. For simplicity, I limited my ex- 

 periments to these three factors, although 

 undoubtedly there are others that can 

 also have significant effects. Examples are 

 trends in annual recruitment, the level 

 of natural mortality, or the shape of the 

 selectivity curve. 



True values for the selectivity coeffi- 

 cients were generated from a double lo- 

 gistic function (Methot, 1990) and were 



similar to those reported for widow rockfish in Hightower and Lenarz 

 (1990). The strongly domed shape of the selectivity curve (Fig. 1), 

 which may be due to the movement of older individuals into deeper, 

 less heavily fished waters, seems to be a common feature for many 

 of the groundfish stocks in the U.S. Pacific Northwest. 



To simulate temporal changes in selectivity, I shifted the selectiv- 

 ity coefficients forward or backward by one age class (Fig. 1). When 

 selectivity increased, 100% selection occurred at age 7 for the first 

 three years (Curve A), at age 8 for the next four years (Curve B), 

 and at age 9 for the last three years (Curve C). When selectivity 

 decreased, full selection occurred at age 9 for the first three years, 

 at age 8 for the next four years, and at age 7 for the last three 

 years. To measure the effects of "random" changes in selectivity, I 

 generated data sets for 10 trials. Selectivity in the first year of each 

 trial always followed selection curve B, but the sequence of curves 

 that applied in the subsequent years came from a random shuffling 

 of the sequence AAABBBCCC (Fig. 2). Curve A applied in three 

 randomly chosen years, curve B applied in three other randomly 

 selected years, and curve C applied in the remaining three years. I 

 did not examine other forms of change in selectivity, such as varia- 

 tion in the basic shape of the curve. 



When simulating an increasing trend in fishing mortality, the 

 fishing mortality coefficients changed linearly from 0.10 to 0.28 per 

 year, at increments of 0.02 per year. When the trend was decreas- 

 ing, the fishing mortality coefficients varied from 0.28 to 0.10 per 

 year, at increments of -0.02 per year. When there was no trend in 

 fishing mortality, the fishing mortality was 0.20 per year, which is 

 approximately the rate of fishing that reduces the reproductive out- 

 put from this simulated stock to 35% of its unexploited level when 

 full selection is at age 8 years (Fig. 1, Curve B). 



All methods for analyzing catch-at-age data require additional 

 information with which to tune the analysis and thereby resolve a 

 basic indeterminacy in the model for catch 1 (Shepherd and Nicholson, 

 1986). In the most recent assessment for widow rockfish, Hightower 

 and Lenarz (1990) tuned the Stock Synthesis analysis to a single 

 fishing mortality coefficient, but in many contemporary assessments 

 of other Pacific groundfish stocks the Stock Synthesis runs have 

 been tuned to estimates of abundance-at-age or biomass from re- 

 search vessel surveys. In the sensitivity analysis, I gave the Stock 

 Synthesis program auxiliary data for tuning either in the form of 

 the true annual fishing mortality coefficients or the true propor- 

 tions-at-age. 



Sensitivity of other stock assessment programs that 

 assume constant selectivity 



To confirm that the assumption of constant selectivity, rather than 

 some unique feature of the Stock Synthesis program, was respon- 

 sible for any bias in the results, I experimented with two other 



'Catch-at-age is approximately equal to the product of stock abundance-at-age and 

 fishing mortality-at-age. If only catch data are available, one cannot distinguish 

 between a case of large abundance and low fishing mortality versus one of small 

 abundance and high fishing mortality. 



