FISHERY BULLETIN: VOL. 85, NO. 2 



< 

 > 



II 

 Q 



0.15 n 



0.14 



0.13 



0.12 H 



0.1 1 



0.10 



0.09 



0.08 



0.07 



0.06 



0.05 



0.04 



0.03 - 



0.02 - 



0.01 



0.00 



" PACIFIC COD. FIXED SUBSAMPLE 

  PACIFIC COD, RANDOM SUBSAMPLE 



SABLEFISH. FIXED SUBSAMPLE 



SABLEFISH. RANDOM SUBSAMPLE 



POLLOCK, FIXED SUBSAMPLE 



POLLOCK. RANDOM SUBSAMPLE 





10000 



30000 50000 



TOTAL COST C 



70000 



(MINUTES) 



90000 



Figure 1.— The relationship of D (= yVartot) and total cost for Pacific cod, sablefish, and walleye 

 pollock, using fixed or random age subsample. 



returns is reached beyond this total cost and the 

 curves become flatter for C greater than 10,000. 

 These results indicate that setting a precision at D 

 = 0.02, 0.025, and 0.03 respectively for Pacific cod, 

 walleye pollock, and sablefish using random age sub- 

 samples would represent a reasonable compromise 

 between cost and precision. Increasing total cost 

 beyond this level will show no more gains from the 

 ALK. 



DISCUSSION 



It is obvious that the random subsampling scheme 

 is superior to the fixed subsampling scheme. How- 

 ever, it is more important to realize that there is 

 a cap on total cost for ALK. This cap represents the 

 most effective budget for ALK. Vartot of estimated 

 age composition will not decrease significantly for 

 a greater budget. For the three species, total cost 

 of 10,000 minutes (about 70 working days) is the up- 

 per limit. This indicates that approximately 2,000 

 length observations and 800 random age subsamples 

 for sablefish, 2,500 and 1,200 for walleye pollock, 

 and 3,000 and 600 for Pacific cod represent the best 



compromise between cost and precision of estimates 

 (VVartot = 0.03, 0.025, and 0.02 for the three 



species respectively). 



Although it can be argued that minimizing Vartot 

 may not be sufficient for optimum sampling design 

 for all age classes, it is necessary to consider that 

 some age classes are rare in the commercial catch 

 and are therefore difficult to sample precisely. How- 

 ever, these age classes do not generally represent 

 significant contributions to biomass, and it therefore 

 seems reasonable to concentrate on the major age 

 classes. If these rare age classes are important to 

 population dynamics, the optimum allocation can be 

 addressed as a multiple minima. The objective func- 

 tion can be rewritten as 



M{N,n) = Z w, Var(p,), for i = 1, 2, . . ., A 



where w, is weighting factor. A larger w, must be 

 given to those age classes which are of interest, 

 whereas the mathematical expressions of optimum 

 allocation are the same as Equations (7) to (14), and 

 subject to the same cost function (Equation (6)), ex- 



182 



