684 



Fishery Bulletin 91(4). 1993 



Table 3 (Continued) 



Increasing selectivity 



Decreasing selectivity 



Mean (%) 



SD(%) 



Improvement 

 infit(%) 



Meaner) 



Tuned to fishing mortality 



F increasing -30.0 45.3 



F decreasing -38.0 42.1 



F constant -32.8 45.2 

 Tuned to proportion-at-age 



F increasing -13.5 40.0 



F decreasing -21.9 39.2 



^constant -13.3 41.1 



45.7 

 56.7 

 51.9 



25.6 



37.7 

 30.9 



24.3 

 29.8 

 30.7 



0.5 

 -4.6 

 -2.5 



'Bias is measured here as the relative error of the estimated value, (estimate - true I / true. 



2 The Stock Synthesis program estimates average biomass for each year of the input data series. The values here are the averages and 



standard deviations of the ten annual estimates. 

 'The Stock Synthesis program can estimate recruitment for each year of the input data series. The values here are the averages and 



standard deviations of the ten annual estimates. 

 'The "improvement in fit" is measured here by the relative increase in the value of the log-likelihood when the Stock Synthesis program 



estimates the annual recruitment rather than being given the true values. This is defined as 



{V-L )l L 



where L is the value of the log-likelihood when the program was given the true annual recruitment values, and L' is the value of the log- 

 likelihood when the program estimated the annual recruitment values. The log-likelihood is given by 



£» J,  X„ p».„ log,(p v „ I; 



where J is the number of fish in the (y )th catch-at-age sample, p ya is the observed proportion of fish in the (_v)th sample that are from 

 the (a)th age class, andp lo is the predicted proportion offish in the (ylth sample from the (nlth age class (Methot, 19901. 



Sensitivity of other stock assessment 

 programs that assume constant selectivity 



The results of the experiments with CAGEAN and the 

 multiplicative catch-at-age model indicate that these 

 assessment methods, like the Stock Synthesis program, 

 are also sensitive to violations of the constant selectiv- 

 ity assumption. When selectivity increased, both the 

 Stock Synthesis and CAGEAN programs incorrectly 

 produced a large decrease in the biomass of the simu- 

 lated population during the last few years, and large 

 declines in recruitment (Fig. 5). The multiplicative 

 catch-at-age model does not provide estimates of bio- 

 mass, but its estimates of relative recruitment were 

 almost identical to those from the CAGEAN program. 

 When selectivity decreased, the Stock Synthesis pro- 

 gram and the CAGEAN program both overestimated 

 the biomass in the last few years, but the estimates 

 from the CAGEAN program were grossly incorrect ( Fig. 

 6). Both the CAGEAN program and the multiplicative 

 catch-at-age model estimated very large increases in 

 recruitment. 



Sensitivity of the Stock Synthesis program 

 when applied to data from a heavily 

 exploited stock 



When the Stock Synthesis program was applied to data 

 for a simulated population suffering heavy exploita- 

 tion, the program produced estimates of biomass and 

 recruitment that were even more biased than in the 



