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Fishery Bulletin 91(4), 1993 



Figure 2 



Simulations with random variation in selectivity. The effects of random varia- 

 tion in selectivity were simulated by shuffling the sequence of selectivity curves 

 (AAABBBCCC, Fig. 1) that applied in each of the nine years after the first. 

 The ten sequences shown here were used. 



ity constant, and recruitment estimated), and the esti- 

 mated age distribution in the final year was grossly 

 incorrect (Fig. 3A). The estimated numbers of five-year- 

 old to seven-year-old fish were much too high and the 

 numbers of fish 15 years and older were all slightly 

 too high. When selectivity shifted towards older ages, 

 the biomass estimate for the final year was as much 

 as 597c too low (Table 3A; selectivity increasing, tuned 

 to fishing mortality, fishing mortality increasing, and 

 recruitment estimated) and the program underesti- 

 mated the numbers of very young and very old fish 

 (Fig. 3B). 



In these experiments, bias in a particular estimate 

 was not a simple linear function of the factors exam- 

 ined, but instead involved complicated interactions be- 

 tween factors. Nevertheless, some general effects 

 seemed to apply. When the Stock Synthesis program 

 was tuned to fishing mortality and used to estimate 



recruitment, shifts in selectivity towards 

 older ages (selectivity increasing) always 

 induced negative bias in the estimates of 

 average biomass, and shifts in selectiv- 

 ity towards younger ages (selectivity de- 

 creasing) always induced positive bias 

 (Table 3, A and B). When the recruit- 

 ment values were known or tuning to 

 the proportion-at-age data was used, 

 however, trends in selectivity had no con- 

 sistent effect on the direction of bias. 

 Estimation of recruitment values, often, 

 but not always, increased the magnitude 

 of the bias in the estimates of bio- 

 mass (Table 3, A and B) and abundance 

 (Table 3C). Tuning to proportion-at- 

 age data, instead of to annual fishing 

 mortality coefficients, often decreased 

 the amount of bias in the estimates of 

 biomass, abundance, and recruitment. 

 Bias in these estimates usually was 

 smallest when the trend in fishing 

 mortality was increasing and largest 

 when the trend in fishing mortality was 

 decreasing. 



When the Stock Synthesis program es- 

 timated recruitment, improvements in 

 the fit were observed relative to those 

 obtained when recruitment values were 

 known (Table 3D). To the assessment sci- 

 entist interpreting these results, the im- 

 proved fit would suggest that the pro- 

 gram had provided better estimates, 

 when, in fact, the estimates were more 

 biased and less reliable. When selectiv- 

 ity shifted toward older fish, there was a systematic 

 change from year to year in the catch-at-age data, 

 which the program attempted to match by imposing a 

 decreasing trend in recruitment (Fig. 4). When selec- 

 tivity shifted towards younger fish, the program im- 

 posed an increasing trend in recruitment. Similar dis- 

 tortions occurred when the program was tuned to the 

 true proportion-at-age data. This last result suggests 

 that using age-frequency data from research vessel sur- 

 veys will not eliminate the bias induced by changes in 

 selectivity, even though survey data may not be sub- 

 ject to the changes in selectivity that the fishery might 

 experience. 



When selectivity varied randomly (Table 4), the mag- 

 nitude of the bias in the estimate of the final year's 

 average biomass was usually less than what occurred 

 when selectivity had a trend (Table 3A), but the gen- 

 eral patterns seen in the earlier experiments remained. 



