CLARK and BROWN: CHANGES IN BIOMASS OF FINFISHES AND SQUIDS 



while for 5Z cod we computed an average figure for 

 the 1970-75 period using mortality rates from the 

 above paper and obtained values for the remain- 

 ing years by adjusting this average by commercial 

 abundance indices reported by Brown and 

 Heyerdahl. 25 We followed an analogous procedure 

 in the case of "other finfish" by computing a value 

 for 1967 (chosen to be in the middle of the period) 

 assuming an F value of 0.4 and M = 0.2; we then 

 calculated commercial abundance indices from 

 historical catch data and total effort estimates for 

 SA 5 and 6 (Brown et al. in press) and obtained 

 stock size estimates for the remaining years by 

 adjusting the 1967 value by means of these 

 abundance indices according to Equation (4), as 

 above. For redfish, other flounders, and pollock, we 

 computed average values from Equation (3) using 

 available sustainable yield estimates and as- 

 sumed values of F, as follows (M = 0.2 in all cases): 



Turning to survey abundance indices, an in- 

 herent problem in any analysis of trawl data lies 

 in the fact that the computed means and variances 

 are seldom, if ever, independent. The present data 

 are no exception; Grosslein (1971) has found that 

 in the present survey individual stratum var- 

 iances are approximately proportional to the 

 squares of the stratum means, indicating that a 

 logarithmic transformation is appropriate (Steel 

 and Torrie 1960). Under these conditions, use of a 

 logarithmic scale transformation tends to nor- 

 malize the data and render means and variances 

 independent, thereby permitting use of paramet- 

 ric statistical methods (obviously, anomalous 

 fluctuations in observed trends are also reduced 



25 Brown, B. E., and E. G. Heyerdahl. 1972. An assessment of 

 the Georges Bank cod stock (Div. 5Z). Int. Comm. Northwest Atl. 

 Fish. Annu. Meet. 1972, Res. Doc. No. 117, Serial No. 2831 

 (mimeo.), 24 p. 



26 Mayo, R. K. 1975. A preliminary assessment of the redfish 

 fishery in ICNAF Subarea 5. Int. Comm. Northwest Atl. Fish. 

 Annu. Meet. 1975, Res. Doc. No. 59, Serial No. 3541 (mimeo.), 

 31 p. 



"Pollock in ICNAF Divisions 4VWX, Subarea 5, and Statis- 

 tical Area 6 are currently considered as a unit stock. Accord- 

 ingly, this figure represents the SA 5 and 6 proportion of the 

 estimated sustainable yield for this stock as determined from 

 historical catch data. 



considerably). Accordingly, we computed strati- 

 fied mean catch per tow values for all stocks using 

 In (kilograms + 1) values for each tow; strata sets 

 used are given by species and stock in Table 10. We 

 then computed estimates of stratified mean catch 

 per tow in original units by retransforming as 

 suggested by Bliss (1967:128) according to the 

 relation: 



E(y st ) = exp (y st + S 2 /2) 



(5) 



where E(y st ) represents the estimated (re- 

 transformed) stratified mean catch per tow andy s , 

 and S 2 represent the stratified mean and the 

 estimated population variance, respectively, in 

 logarithmic units, computed as in Equations (1) 

 and (2) above. We also calculated untransformed 

 (y st ) values for the stocks and strata sets in Table 

 10 for comparative purposes. 



After obtaining stock size estimates and 

 abundance indices as described above, we com- 

 puted catchability coefficients for all years by 

 dividing both untransformed and retransformed 

 stratified mean catch per tow for year i by the 

 appropriate stock size value at the beginning of 

 year i + 1 (or by the computed average stock size). 

 Deviations from the arithmetic mean were then 

 plotted by year; where trends were apparent, 



TABLE 10. — Strata sets used in computing stratified mean catch 

 per tow values by stock. 



'Strata for the Middle Atlantic area 

 2 Since 1963 (strata 1-40). 

 Alphanumeric designations refer to 

 shown in Figure 1 . 



(61-76) added in 1967. 



divisions and subdivisions of SA 5 and 6 



15 



