AHRENHOLZ ET AL.: ATLANTIC MENHADEN POPULATION AND FISHERY 



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AGE IN YEARS 



Figure 7. — Deviations in annual VPA (virtual population analysis) estimates of numbers at age 

 present in the population and age specific fishing mortality rates for Atlantic menhaden resulting 

 by varying the initial rate of annual F by the multiples shown. The estimates are for the 1955 year 

 class (initial F = 0.7006). 



here should be considered reasonably precise (and 

 stable) relative to the initial F values. 



Since F and M are additive with respect to Z, 

 errors in these computations resulting from an 

 incorrect selection of the rate of M are additive 

 with respect to subsequent estimates of F, and 

 estimates of numbers at age present in the popu- 

 lation will differ in a proportional fashion. In 

 other words, if our selection of the estimate of M 



is too great, numbers at age are overestimated, 

 and if M is too low, the reverse is true (Fig. 10). 

 Similarly, estimates of year class size vary by a 

 nearly constant proportion (Fig. 11). The range of 

 available estimates of M is relatively narrow, 

 hence it is unlikely that conclusions reached in 

 this report would be altered even if the estimate 

 of M for these analyses were allowed to vary ran- 

 domly within these bounds between years. 



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