catch projections for 1978. The fishing mortality esti- 

 mate for 1977 would be 0.435 instead of 0.39 and the pro- 

 jected spawning stock biomass in 1978 would be about 

 390,000 t instead of 402,500 t. A catch of about 25,000 t, 

 instead of 23,500 1, could be taken in 1978 and still main- 

 tain the spawning stock in 1979 at the 1978 level. 



DISCUSSION 



The accuracy of the projected catch options for 1978 

 and the resultant spawning stock biomass levels in 1979 

 (Table 15) is dependent upon the accuracy of the data 

 and parameters used in the analysis. The variability and 

 bias associated with these data and parameters are evi- 

 dent. 



The U.S. recreational catches (Table 6) are estimated 

 and lack any measure of accuracy or reliability, and the 

 validity of the international commercial statistics is un- 

 certain. The numbers at age in the catch (Table 8) were 

 generated from length and age samples contributed by 

 various countries, and although ICNAF established 

 recommended sampling procedures, the validity of the 

 samples is unknown. Anderson et al. (see footnote 11) 

 found significant differences in age interpretation and 

 age-length keys between countries during 1970-76, 

 particularly in 1976. As indicated earlier, country age- 

 length keys for 1976 were combined in an attempt to 

 modulate these differences. The procedure recom- 

 mended by ICNAF specifies stratified age samples, 

 whereas Kimura (1977) showed that random age samples 

 are more accurate. 



The U.S. bottom trawl survey data provided the basis 

 for estimating the size of the recruiting year classes 

 (Tables 4 and 5, Figs. 6-8) and also for predicting fishing 

 mortality in 1977 (Table 2, Fig. 5). Although confidence 

 limits were not given for any of these estimates, survey 

 catch-per-tow data in general are subject to high vari- 

 ability (Grosslein 1971), and particularly so for Atlantic 

 mackerel (Anderson 1976; Sissenwine 1978) since it is a 

 pelagic schooling species. Therefore, even though the 

 relationships using survey catch-per-tow data to predict 

 year-class sizes and fishing mortality are statistically sig- 

 nificant, the predicted values are necessarily somewhat 

 imprecise. 



The values for instantaneous natural mortality (M = 

 0.30) and partial recruitment coefficients, although hav- 

 ing a basis for being chosen, introduce additional uncer- 

 tainty to the final results. 



In view of all the variability and uncertainty in the 

 data, the results of this assessment must be treated with 

 appropriate caution. Given the catch and stock size 

 projections, fishery managers may set allowable catch 

 levels for 1978 appropriate to management objectives 

 which they have adopted. Since highly precise projec- 

 tions are currently not available, the decision process 

 should include consideration of the acceptable level of 

 risk of failing to achieve management objectives. If an 

 objective is to rebuild the stock by a certain percentage 

 from 1978 to 1979, it may be wise to set the catch in 1978 

 at a level corresponding to a greater percentage increase 



in stock size as a safety factor to guard against the prob- 

 ability that the predicted stock size and recruitment 

 levels are, in fact, overestimated. According to the Fish- 

 ery Conservation and Management Act of 1976 enacted 

 by Congress, the level of catch must consider relevant 

 economic, social, or ecological factors. Since economic 

 and social factors are beyond the scope of this paper, only 

 ecological or biological considerations will be discussed. 

 The historical relationship between Atlantic mackerel 

 spawning stock and recruitment is shown in Figure 9. 

 The spawning biomass estimated for 1978 is slightly 

 below the 1962-67 level when, prior to the recent decade 

 of intensive international fishing, catches averaged only 

 about 25,000 t and stock size was relatively stable. The 

 spawning biomass of about 500,000 t present in 1962-67 

 produced year classes ranging from the weakest (1962-63) 

 to the strongest (1967). The large spawning stocks pres- 

 ent during the late 1960's-early 1970's produced both 

 above- and below-average year classes. It appears that 

 for Atlantic mackerel, as for most species, spawning 

 stock size alone exerts little influence on the size of a year 

 class unless perhaps the spawning stock is reduced to ex- 

 tremely low levels. Lett and Kohler 15 found in popula- 

 tion simulations of Atlantic herring, Clupea harengus, in 

 the Gulf of St. Lawrence that recruitment was indepen- 

 dent of spawning stock size over a fairly wide range, and 

 that a stock-recruitment relationship emerged only when 

 the stock was collapsing due to overfishing. Environ- 

 mental factors are obviously a major influence on Atlan- 

 tic mackerel year-class size, but the present state of 

 knowledge concerning this influence is inadequate for 

 assessment use. Consequently, it is virtually impossible 

 to define an optimum or minimum spawning stock size 

 at or above which level adequate recruitment can be 

 predicted or below which weak recruitment is likely. 

 However, since spawning stock size has continued a 

 steady decline and recent year classes (1975-76) appear 

 to be as weak as any observed previously, there is reason 

 for concluding that the spawning stock should not be al- 

 lowed to fall much below the projected 1978 level. 



LITERATURE CITED 



ANDERSON, E. D. 



1976. Measures of abundance of Atlantic mackerel off the north- 

 eastern coast of the United States. Int. Comm. Northwest Atl. 

 Fish. Res. Bull. 12:5-21. 



ANDERSON, E. D., and F. P. ALMEIDA. 



1977. Distribution of Atlantic mackerel in ICNAF Subarea 5 and 

 Statistical Area 6 based on research vessel spring bottom trawl 

 surveys, 1968-76. Int. Comm. Northwest Atl. Fish. Sel. Pap. 

 2:33-44. 



CLARK. J. R. 



[1962.) The 1960 salt-water angling survey. U.S. Fish Wildl. 

 Serv., Circ. 153. 36 p. 

 COCHRAN, W. G. 



1953. Sampling techniques. John Wiley & Sons, Inc., N.Y.. 330 p. 



15 Lett, P.F., and A. C. Kohler. 1976. Recruitment: a problem of 

 multispecies interaction and environmental perturbation with special 

 reference to Gulf of St. Lawrence herring {Clupea harengus L.). Int. 

 Comm. Northwest Atl. Fish. Res. Doc. 76A1/4, Ser. No. 3763 (mimeogr.), 

 40 p. 



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