Figure 2. — Northwest Atlantic off the U.S. coast showing bottom trawl survey sampling strata and ICNAF Subarea 5 and Statistical Area 6. 



were described by Grosslein. 12 Spring indices were 

 calculated from catches in strata 1-25 and 61-76, and 

 autumn indices from catches in strata 1-2, 5-6, 9-10, 13, 

 16, 19-21, 23, and 25-26 (Fig. 2). All autumn catches and 

 the 1968-72 spring catches were made with a No. 36 

 Yankee trawl, and the 1973-77 spring catches were made 

 with a larger No. 41 trawl. The 1968-72 spring catches 

 were adjusted upwards to equivalent No. 41 trawl 

 catches using a 3.25:1 ratio between the No. 41 and No. 

 36 trawls (Anderson 1976) to establish a standardized 

 time-series of catches. A In (x + 1) transformation of the 

 station catches (kilograms) was made before calculation 

 of the mean catch-per-tow indices. The In indices were 

 then retransformed to the original scale for compati- 

 bility with other data used in the assessment. Retrans- 

 formation was accomplished by the method described by 

 Finney (1941) using the equation: 



exp(i + — ) - 1 



(1) 



where y = retransformed catch per tow, x = In catch per 

 tow, and S 2 = population variance (In scale). 



Stratified mean catch per tow (numbers) by age for the 

 1973-77 spring surveys was determined by applying age- 

 length keys to the length frequency of the stratified mean 

 catch per tow (Anderson et al. see footnote 2). Since age 

 samples were not taken prior to the 1973 spring survey, 

 only the mean catch per tow for ages 0, 1, and 2 was 

 determined prior to 1973. From the 1968-72 spring sur- 

 veys, age 1 fish were defined as those measuring 22 cm 

 and less (fork length) and age 2 fish were defined as those 

 measuring 23-29 cm. Age fish from the autumn surveys 

 were defined as those measuring 23 cm or less. 



Standardized U.S. commerical catch per day (metric 

 tons) was calculated for 1964-76 as described by 

 Anderson (1976). 



Instantaneous fishing mortality {F) in 1977 was esti- 

 mated using a technique developed by Anderson et al. 

 (see footnote 2) which assumes a linear relationship be- 

 tween fishing effort and fishing mortality. The lack of an 

 adequate measure of fishing effort or catch per effort was 

 circumvented by calculating, as an index of fishing ef- 

 fort, the quotient of total catch divided by the spring sur- 

 vey catch per tow (Table 2). Because of the aberrant 1969 

 spring value (Anderson 1976; Anderson and Almeida 

 1977) and the year-to-year fluctuations in the remaining 

 values, the 1968-77 time-series (Fig. 3) was smoothed by 



Table 2.— Estimation of fishing mortality (F) in 1977 for the ICNAF 

 Subareas 3, 4, and 5 and Statistical Area 6 Atlantic mackerel fishery. 











Fishing 







Spring 



survey catch/tow 



Catch 3 



effort 



MeanF 5 



Year 



Actual 1 



Calculated 2 



(t) 



index 4 



age 3 + 



1968 



3.998 



4.518 



109,940 



24,334 



0.155 



1969 



0.065 



3.199 



165,113 



51,614 



0.144 



1970 



2.039 



2.265 



262,681 



115,974 



0.185 



1971 



1.969 



1.604 



403,675 



251,668 



0.268 



1972 



1.332 



1.135 



431,606 



380,270 



0.316 



1973 



0.748 



0.804 



429,250 



533,893 



0.451 



1974 



0.769 



0.569 



347,220 



610,228 



0.515 



1975 



0.255 



0.403 



293,740 



728,883 



0.532 



1976 



0.317 



0.285 



243,033 



852,747 



67 (0.626) 



1977 



0.199 



0.202 



92,000 



455,446 



'HO, 391) 



12 Grosslein. M. D. 1974. Bottom trawl survey methods of the North- 

 east Fisheries Center, Woods Hole, Mass., USA. Int. Comm. North- 

 west Atl. Fish. Res. Doc. 74/96, Ser. No. 3332 (mimeogr.), 27 p. 



■Stratified mean catch (kilograms) per tow (retransformed from In to 

 linear scale). 



2 Values predicted from exponential curve calculated using actual 

 values for 1968-77 (except 1969). See Figure 4. 



3 Includes commercial and recreational catch. 



4 Catch divided by calculated spring survey catch/tow. 



5 Obtained from cohort analysis assuming F = 0.39 in 1977. 



Calculated from regression of fishing effort index on mean F for 

 1968-75: Y = 0.121 + 0.000OO059X, r = 0.991. 



T Actual value calculated from cohort analysis was 0.745, assuming 

 F = 0.39 in 1977. 



