NELSON and AHRENHOLZ: CHARACTERISTICS OF GULF MENHADEN 



Table 3.— Population size (in millions) of gulf 

 menhaden on 4 April estimated by cohort 

 analysis, 1964-77. 



and western areas reaching the more intensively 

 fished waters, or simply a sampling variance. The 

 F estimates from cohort analysis for age-3 and age-4 

 fish are somewhat suspect, especially for age 4, since 

 the cohort analysis technique used (iterating to a 

 preset F 2 ) actually makes the F 3 and F 4 estimates 

 of a forward computational nature, rather than 

 backward as for age 1. The divergent nature of the 

 estimates is clearly evident in the values for age 4, 

 although the mean value is realistic for subsequent 

 yield computations, and numbers of fish at this age 

 are of very low magnitude as well. 



Because a year class is well represented in the 

 fishery for only 3 yr, a short time span is available 

 for the convergence of estimates of numbers and 

 fishing mortality. This short time span was ap- 



25 r 



Figure 3— Population number of gulf menha- 

 den as of 4 April 1964-77, Estimated from 

 cohort analysis on 1960-76 year classes. 



CO 



c 

 o 



LU 

 N 

 CO 



O 



I- 

 < 

 -J 



a. 

 O 



0. 



  ' I I 1 1 1 



1964 65 66 67 68 69 70 71 72 73 74 75 76 77 



YEAR 



Table 4.— Annual instantaneous fishing mortality rate (F) 

 for gulf menhaden for ages 1-3, by year, 1964-77, and fishing 

 mortality rate applied at age 4 (age 3 for year classes 

 without age-4 landings) to initiate the cohort analysis. 



parently adequate, however, as cohort runs on the 

 year classes with 4-yr-olds in the landings, using 

 starting estimates of F for age 4 obtained from catch 

 curves, converged to very similar estimates to those 

 obtained by the analysis used here. Ulltang (1977) 

 emphasized that when F is high, convergence is 

 rapid. 



The short-term impact of the fishery on the stock 

 can be assessed by comparing the estimated number- 

 at-age in the population for any given year with the 

 number-at-age landed by the fishery, or simply by 

 using the estimated rate of fishing and calculating 

 the exploitation rate (u) by 



u n = (F n (1 - e-^W )Wn + M). 



(4) 



initial F set equal to 10.0. 



From 1964 to 1977 the fishery took an average of 

 31% of the 1-yr-olds in the population and about 61% 

 of the older fish each year. At these exploitation rates 



315 



