FISHERY BULLETIN: VOL. 75, NO. 1 



TABLE 12. — Weighting coefficients calculated by stock from untransformed and retrans- 

 formed survey data, 1963-74, southern New England, Georges Bank, and Gulf of Maine 

 area (strata 1-30 and 36-40). 



1 Estimated mean catch per tow values computed from transformed data according to the relation, E(y st ) = 

 ex P(ysf + S 2 /2), where y st and S 2 represent the mean and estimated population variance, respectively, on the 

 transformed scale. 



2 Weightmg coefficients calculated by individual stock for cod, haddock, silver hake, red hake, yellowtail, and 

 herring, stock areas are given in Figure 1 Stock areas for the remaining species are equivalent to all strata in SA 

 5 and 6 covered during 1967-74 



/=1 [ C A + l] 



3 Weightmg coefficients calculated as ^ where C, = stratified mean catch per tow (tons) in year/ 



and S, + 1 = stock size at the beginning of the following year All values « 10 8 . 



Coefficient of variation calculated over all years 



5 Weighting coefficients computed separately for 1967-68 and 1969-74 data due to apparent changes in 

 catchability 



k 

 1 



Cv/Wj 



.7 = 1 L - 



for all i 



(6) 



where C y refers to stratified mean catch per tow for 

 the 7th stock in the itb. year and Wj refers to the 

 weighting coefficient for thejth stock (Tables 13, 

 14), summation being over k stocks. For the 

 purposes of this paper, we consider each computed 

 estimate as representing stock size at the begin- 

 ning of the year following collection of the survey 

 data (i + 1), as catchability coefficients were 

 calculated by relating catch per tow values in 

 autumn of year i to stock size at the beginning of 

 year i + 1 (above). Note that with the exception of 

 1970 figures for "all data" (Tables 13, 14), values 

 computed from retransformed data agree 

 reasonably well with those computed from un- 

 transformed values; consequently the general 



appropriateness of assuming a lognormal dis- 

 tribution for these data is confirmed. 



The average stock size estimate for 1964-66 

 obtained for all species of 5.0 x 10 6 tons (Table 14) 

 is almost identical to that obtained by Edwards 

 (1968) for the same area and period (5.1 x 10 6 



TABLE 13.— Stock size estimates (tons x 10 3 ) for ICNAF Sub- 

 area 5 and Statistical Area 6, 1967-74, Middle Atlantic, southern 

 New England, Georges Bank, and Gulf of Maine, inclusive 

 (strata 61-76, 1-30, and 36-40). 



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