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Fishery Bulletin 103(2) 



Life-history parameters 



The correlation (p) between L A and K was assumed to 

 be zero in the base model and negative in sensitivity 

 analyses. The effect of correlation depended on variation 

 in the growth parameters. When the CV was zero for 

 either parameter, correlation had no effect on selection 

 differentials (Tables 2 and 3). When the CV was posi- 

 tive for both, a negative correlation decreased selection 

 differentials in relation to those from the base model 

 (Tables 2 and 3). For decreased values of the correlation 

 coefficient (i.e., stronger negative correlation), the per- 

 cent selection differentials on K decreased, whereas the 

 percent selection differentials on L x either decreased or 

 remained constant. The percent selection differentials on 

 the size near age t ranged from 3.7% to -0.1% for values 

 of p from to -1. The percent selection differentials on 

 L x remained relatively constant, ranging from 2.1% to 

 2.5%, with the highest at p=0 (Fig. 5). 



Knife-edge maturity (/3 m = oc ) resulted in larger selec- 

 tion differentials than did other maturity curves (Tables 

 2 and 3 1. As the slope of the maturity curve became more 

 gradual, the selection differentials decreased. For /3 m 

 values greater than 1, the selection differentials on size 

 were similar to those of the knife-edge case (Fig. 5). 



The effect of M on selection differentials was relative- 

 ly small (Tables 2 and 3). Changes in M from 0.1 to 0.8 

 led to small changes in selection differentials (Fig. 5). 

 The largest selection differentials tended to occur near 

 intermediate values of M (Tables 2 and 3, Fig. 5). This 

 nonlinear response in the selection differentials is not 

 surprising because changes in M affected the values of 

 K, A m , and maximum age nonlinearly (Table 1). 



Changes in the M/K ratio did not reveal a clear trend 

 (Tables 2 and 3, Fig. 5). As with M, the M/K ratio af- 

 fects other parameters; therefore changes in M/K could 

 be expected to produce a nonlinear response in the 

 selection differentials. The percent selection differen- 

 tial on L x was lowest at an intermediate value of Ml 

 K-2 (Table 3). The percent selection differentials on K 

 showed no consistent trend (Table 2). For M/K values 

 from 0.5 to 2.5, the selection differentials on size across 

 ages ranged from 2.3% to 4.0% (Fig. 5). 



Decreases in the spawning season duration (Z) s ) 

 caused a near linear increase in the selection differen- 

 tials (Tables 2 and 3, Fig. 5). A compressed spawning 

 duration of one month resulted in a range of 5.0% to 

 7.4% selection differential on size across ages (Fig. 5). 

 Of all the life-history parameters examined in this 

 analysis, spawning duration had the greatest effect. 



Fishery parameters 



A limit (L u ) on sizes susceptible to the fishery decreased 

 the selection differentials (Tables 2 and 3, Fig. 5). The 

 percent selection differential at all ages was zero for 

 L u = 800 and -0.1% for L u = 700 (Fig. 5). In these analy- 

 ses, F was held constant. Consequently, smaller values 

 of L u correspond to fewer fish removed. An alternative 

 approach would have been to maintain constant catch 



2 4 6 



Fishing motality (per year) 



Figure 4 



Selection differentials on growth parameters 

 (A) K and (B) L ml computed as functions of 

 fishing mortality. Parameter values are the 

 same as those in the base model. 



by increasing F, which would have led to selection dif- 

 ferentials larger than those in Tables 2 and 3. 



Knife-edge selectivity (ji s = x) caused larger selec- 

 tion differentials than did selectivity curves with more 

 gradual slopes (Tables 2 and 3). For )3 S greater than 

 0.1, the selection differential rapidly converged to that 

 of the knife-edge case (Fig. 5). As with L u , F was held 

 constant across /3 S sensitivity analyses. 



A change in the ages of fishery selectivity had little 

 effect on selection differentials (Tables 2 and 3, Fig. 

 5). When selectivity was set to a larger age or size, the 

 selection differential decreased slightly. In this case, 

 selectivity was occurring after maturity, allowing more 

 fish to reproduce before reaching sizes selected by the 

 fishery. However if harvest had been held constant in- 

 stead of F, the selection differentials would have been 

 larger. When selectivity was set to a smaller age or size, 

 the selection differential decreased slightly or remained 

 constant. This result is due to a reduction in the time 

 exposed to differential fishing mortality. Differential 

 fishing mortality occurs only on the sizes where se- 

 lectivity is less than one; otherwise fishing mortality 

 is constant for all individuals. Under von Bertalanffy 

 growth, younger fish grow more quickly. A decrease 

 in the age or size of selectivity shifts the fishing pres- 

 sure to ages with quicker growth, reducing the time 



