in 1977 with instantaneous natural mortality (M) = 0.30 

 for all ages (ICNAF 1974). This level of F was chosen as a 

 first approximation since the fishing effort index in 1977 

 was about half the 1976 index implying a similar reduc- 

 tion in fishing mortality from earlier estimates for 1976 of 

 about 0.60-0.70. A linear regression between the 1968-75 

 fishing effort indices and the mean F values for ages 3 

 and older from the cohort analysis predicted an F of 0.374 

 for 1977 based on the fishing effort index for 1977. A sec- 

 ond cohort analysis was performed using 0.38 as the ter- 

 minal F in 1977. A second linear regression using the 

 revised F values from this cohort analysis predicted F = 

 0.389 for 1977. A third cohort analysis was performed us- 

 ing F = 0.39 for 1977 (Table 3). A third linear regression 

 predicted F = 0.391 for 1977 (Table 2, Fig. 5); therefore, 

 F = 0.39 was accepted as the best estimate. 



























Y 



.121 +. 00000059 X 











. 









r= .991 











- 











74 



X*" 75 



^1 



.626 



- 









73 

















71 



/■rz F 77=- 391 











68 





70 

















69 

















■ 









" 











250.000 5O0.CQC 750,000 



FISHING EFFORT INDEX 



Figure 5. — Relationship between fishing mortality for Atlantic 

 mackerel from cohort analysis and fishing effort derived from 

 spring survey catch per tow and total catch. 



Power curve relationships, fitted by least squares, be- 

 tween 1) autumn survey catch per tow (numbers) at 

 age and year-class size at age 1 determined from cohort 

 analysis for 1963-73 (Table 4, Fig. 6), 2) spring survey 

 catch per tow at age 1 and year-class size at age 1 for 

 1967-73 (Table 5, Fig. 7), and 3) spring survey catch per 

 tow at age 2 and year-class size at age 2 for 1966-73 

 (Table 5, Fig. 8) were used to estimate the sizes of the 

 1974-76 year classes. 



For age groups incompletely recruited to the fishery, 

 the ratio of fishing mortality at each such age to fishing 

 mortality of fully recruited ages (the latter considered 

 here to be the mean F for ages 3 and older) was used as a 

 measure of partial recruitment to the fishery. Partial re- 

 cruitment coefficients were calculated for ages 1 and 2 for 

 calendar years 1962-77. 



Age-specific F and stock size (N) values were deter- 

 mined for 1962-77 using cohort analysis. The value for N 

 at each age in 1978 was calculated using the relation- 

 ship: 



Table 4. — Catch per tow (number) of age I) Atlantic- 

 mackerel from the U.S. autumn bottom trawl surveys 

 (strata 1-2. 5-6, 9-10, 13, 16, 19-21, 23, 25-26) and year- 

 class size (millions of fish) at age 1 from cohort 

 analysis. 



Year 

 class 



Autumn survey 

 ageO 



Cohort analysis 

 age 1 



1963 



0.087 



1964 



0.022 



1965 



0.134 



1966 



0.170 



1967 



15.709 



1968 



0.215 



'1969 



38.504 



1970 



0.027 



1971 



0.517 



1972 



0.119 



1973 



0.339 



1974 



0.648 



1975 



0.012 



1976 



0.000 



'Not used. 





"Calculated. 





429.5 



542.2 



1,212.9 



3,165.3 



7,786.5 



3,114.3 



3,244.9 



1,657.5 



1,711.9 



1,212.6 



1,981.2 



2 (2,515.6) 



2 (614.3) 



-(0) 



AUTUMN SURVEY CATCH PER TOW - AGE 1 NUMBERS OF FISH ) 



Figure 6. — Power curve relationship between Atlantic mackerel 

 year-class size at age 1 from cohort analysis and autumn survey 

 catch per tow at age 0. The 1969 point was not used in calculating 

 the curve. 



Table 5. — Catch per tow (number) of age 1 and 2 Atlantic mackerel 

 from the U.S. spring bottom trawl surveys (strata 1-25, 61-76) and 

 year-class size (millions of fish) at ages 1 and 2 from cohort analysis. 







Age 1 





Age 2 



Year 



Spring 



Cohort 



Spring 



Cohort 



class 



survey 



analysis 



survey 



analysis 



1966 



— 



3,165.3 



21.661 



2,344.1 



1967 



197.993 



7,786.5 



'1.190 



5,617.3 



1968 



'0.299 



3,114.3 



12.435 



2,300.1 



1969 



6.208 



3,244.9 



13.390 



2.226.5 



1970 



2.954 



1,657.5 



5.545 



1,161.4 



1971 



12.093 



1,711.9 



6.683 



1,248.9 



1972 



1.949 



1,212.6 



0.749 



759.4 



1973 



2.067 



1,981.2 



1.101 



1,385.1 



1974 



5.330 



2 (2,103.9) 



4.928 



2 (1,488.3) 



1975 



0.447 



-(915.3) 



0.254 



: (651.8) 



1976 



0.043 



-(416.9) 



— 



— 



N i + 1 = N, 



(2) 



'Not used. 

 -Calculated. 



