FISHERY BULLETIN: VOL. 75, NO. 1 



linear regressions were fitted to the data to 

 evaluate the degree of relationship. A significant 

 (P<0.01) negative trend was obtained for haddock 

 for both untransformed and retransformed data 

 (Figure 11). This could have resulted from over- 

 estimates of stock size in later years or actual 

 differences in catchability associated with 

 changing availability as stock size decreased. A 

 plot of numbers captured per tow by year during 

 the period of study suggested that actual dif- 

 ferences in catchability may have occurred (Fig- 

 ure 11); accordingly, we divided the period of study 

 into two units (1963-68 and 1969-74) for the 

 purpose of calculating weighting coefficients for 

 the species. The dividing line was taken as the 

 point in which the percentage of tows containing 

 five haddock or less reached 90%. 



In the case of species for which more than one 

 stock had been defined, some question existed as to 



whether coefficients should be computed for the 

 entire species or on a stock basis. As no consistent 

 trends had been found for these species over time, 

 one-way analysis of variance was used to test for 

 differences between stocks, using years as repli- 

 cate observations. These tests revealed significant 

 differences (P<0.05) between individual stocks for 

 all species except yellowtail (i.e., cod, silver and 

 red hake, and herring). We therefore retained 

 individual stocks as discrete units in computing 

 biomass declines (i.e., no attempt was made to 

 combine stocks on a species basis). 



After obtaining the desired sets of catchability 

 coefficients for all stocks, we obtained weighting 

 coefficients by calculating arithmetic means of 

 untransformed and retransformed sets (Tables 11, 

 12), using the entire set except in the case of 

 haddock as explained above. We then computed 

 biomass estimates by year, viz. 



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

 formed survey data, 1967-74, Middle Atlantic, southern New England, Georges Bank, and 

 Gulf of Maine area (strata 61-76, 1-30, and 36-40). 



'Estimated stratified mean catch per tow values computed from transformed data according to the relation, 

 E(yst) = oxp(y s t +S 2 /2), where y st and S 2 represent the mean and estimated population variance, respectively, 

 on the transformed scale. 



2 Weighting 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. 



/TiM+i] 



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



and S / + 1 = stock size at the beginning of the following year. All values x 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. 



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