Sampson Constant selectivity and stock assessment for Sebastes entomelas 



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Figure 8 



Stock synthesis's estimates of biomass and recruitment for a 

 heavily fished stock with selectivity decreasing. The Stock 

 Synthesis program was applied to simulated widow rockfish 

 data in which the fishing mortality rate was constant at 0.60 

 per year, the natural mortality rate was 0.30 per year, and 

 selectivity shifted to younger ages. Again, the estimates were 

 more biased than the ones from the corresponding earlier 

 experiment. 



ability in catch-at-age. Stock Synthesis assumes mul- 

 tinomial error, but CAGEAN assumes lognormal er- 

 ror. Using simulation techniques, Kimura (1990) di- 

 rectly compared estimates derived by using these 

 alternative assumptions and found little difference be- 

 tween the estimates obtained. 



Another difference between Stock Synthesis and 

 CAGEAN is in their method for modeling selectivity. 

 The Stock Synthesis program uses a double-logistic 

 curve to model selectivity as a smooth function of age, 

 but the CAGEAN-PC program estimates the selectiv- 

 ity coefficients independently for each age. Because 

 the true selectivity coefficients were based on double- 

 logistic curves, this difference between the two pro- 

 grams should be only a minor factor. Kimura (1990) 

 found that the assumption of a functional form for 

 selectivity had little effect on his analyses of simu- 

 lated catch-at-age data, provided the true selectivity 



coefficients conformed to the general shape of the se- 

 lectivity function. 



The dilemma for the assessment scientist is to de- 

 velop a framework for analyzing fisheries data that is 

 simple to use and yet is adequate to describe the com- 

 plex dynamics of a living and constantly changing fish 

 stock. The assessment scientist has the difficult task 

 of interpreting diverse and possibly conflicting infor- 

 mation. He needs tools with which to weigh these data 

 objectively and to draw from them reliable conclusions 

 about the status of a stock. Stock Synthesis, CAGEAN, 

 and the multiplicative catch-at-age analysis were de- 

 signed to be such tools. 



In principle, one can use the Stock Synthesis and 

 CAGEAN programs to test for shifts in selectivity. Both 

 programs support a limited form of variable selectivity 

 in which abrupt changes can occur at pre-specified 

 times with constant selectivity during the intervening 

 periods. With either program it is a relatively simple, 

 but tedious, matter to re-analyze the data by using 

 different times for the selectivity changes. For example, 

 I applied the CAGEAN program to the simulated widow 

 rockfish data set given in Table 2A, with the data 

 partitioned into two periods of constant selectivity, and 

 I allowed the timing of the selectivity change to occur 

 between all possible adjacent years. The resulting pat- 

 tern in the residual sums of squares 4 (Fig. 9, upper 

 panel) clearly indicates the true change in selectivity 

 that occurred between the third and fourth years. I 

 repeated the process with the data series partitioned 

 into three periods of constant selectivity, one for the 

 first three years, and the other periods for the remain- 

 ing years. The CAGEAN program was able to fit the 

 data exactly when selectivity changed between the sev- 

 enth and eighth years (Fig. 9, lower panel). 



Although the current versions of the Stock Synthe- 

 sis and CAGEAN programs can be applied in the above 

 fashion to explore systematically for changes in selec- 

 tion, such a brute force approach to model building is 

 extremely repetitious and time-consuming. I hope that 

 the next generation of stock assessment programs will 

 automate this process in a manner similar to existing 

 stepwise regression programs, and thereby allow the 

 user to test rigorously for variations in selectivity. 



The model used for stock assessment should not force 

 the data to fit a particular structure unless there is 

 evidence that the structure is real or that it does not 

 appreciably distort the results of the assessment. The 



'CAGEAN defines the residual sum of squares as 



II log,k-l-log,(c) I 2 

 where c and c are the observed and predicted catch-at-age. 



