NOTE Lai: Age-length key to estimate age composition of fish population 



385 



+ (b+v-m. 



(20) 



min. C = CjAT + c 2 n" 



The solutions given in Eq. 16-20 are similar to that of 

 Lai (1987), provided that the matrix W is an identity 

 matrix. 



Example 



The lemon sole (= English sole Pleuronectes uetulus) 

 example of Jinn et al. (1987) is used to illustrate the 

 length-based optimal sampling design. The ALK and 

 per-unit costs are summarized in Table 1. The total 

 cost is C=$229.15, and the per-unit cost for collecting 

 a length offish is c,=$0.15. For simplicity without loss 

 of generality, consider the special case: w jk =0 for j*k. 

 Three different sets of w n are used to reflect different 

 aspects of interest: 



Case 1 



11,1,1,1,1,11 



A , 



P,s; 



equal interest in estimating all 



Case 2 (10,30,30,10,1,1): increase precision of four 

 major age-classes with larger Var(p,); 



Case 3 11,1,1,1,10,601: interest in older but rare age- 

 classes. 



The results obtained from length-based design are 

 compared with those from fixed- and proportional-age 

 subsampling schemes. The average per-unit cost for 

 ageing a fish (c,) is calculated as the weighted mean of 

 c,„ which is c 2 =$1.96. The optimal set of IN', n,'| and 

 min. X subject to the given total cost of $229.15 are 

 computed using Eq. 9 and 10 for length-based age 

 subsampling, Eq. 15 and 16 for fixed-age subsampling, 

 and Eq. 18 and 19 for proportional-age subsampling. 



Precision improves substantially when length-based 

 age subsampling rather than fixed-age subsampling is 



used in all three cases (Table 2). In the first two cases, 

 however, precision improves marginally by using 

 length-based age rather than proportional-age 

 subsamplings. When rare and older fish (ages 8 and 9, 

 Case 3) are of interest, precision is substantially im- 

 proved by using length-based age instead of propor- 

 tional-age subsampling. This is due to the fact that 

 proportional-age subsampling is not designed to in- 

 crease age subsamples from length-strata consisting 

 of older age-classes. 



The optimal set of (N\ n,*) and min. C subject to a 

 desired precision level of -Z*=0.01 are computed from 

 Eq. 9 and 11 for length-based age subsampling, Eq. 15 

 and 17 for fixed-age subsampling, and Eq. 18 and 20 

 for proportional-age subsampling. Tables 2 and 3 show 

 similar trends. The cost efficiency of length-based age 

 subsampling is superior to fixed-age subsampling in 

 all cases. However, cost efficiency is only marginally 



