FISHERY BULLETIN: VOL. 84, NO. 2 



Weight-length regression coefficients were calcu- 

 lated for each of three 2-mo intervals for the major 

 portion of the fishing season for each year class, 

 1960-77. No systematic variation in the parameter 

 estimates was apparent within years by 2-mo inter- 

 vals, so the data were pooled between seasons and 

 years. An overall weight-length relationship was ob- 

 tained from a GM-functional regression (Ricker 

 1973) on the pooled data. The results are 



log, w = 3.2669 log, I - 12.1851 (2) 



where w = weight in g, and 



I = fork length in mm. 



The correlation coefficient (r) was 0.976 and the sam- 

 ple size was 168,397. 



COHORT ANALYSIS 



Estimates of mortality rates and population sizes 

 were obtained by using the Cohort Analysis tech- 

 nique developed by Murphy (1965) and later modified 

 by Tomlinson (1970). Calculations were made with 

 the computer program MURPHY (Tomlinson 1970). 

 This technique does not involve estimates of CPUE. 

 The backward estimation procedure was used. Since 

 the catch equations and general method of applica- 

 tion are given in Tomlinson's paper, discussion here 

 will be limited to the source and nature of input data 

 and parameters. 



The calendar year was divided into four periods 

 (quarters) of approximately equal length: 



Quarter 1 = 1 January to 3 April, 

 Quarter 2 = 4 April to 3 July, 

 Quarter 3 = 4 July to 3 October, 

 Quarter 4 = 4 October to 31 December. 



Numbers of fish at each age landed quarterly were 

 sums of weekly estimates obtained by sampling 

 methods outlined by Nicholson (1978). Annual sum- 

 maries of these data were given earlier (Table 1). 



An estimate of the annual rate of instantaneous 

 natural mortality (M) was obtained from an analysis 

 of mark-recapture data (Ahrenholz 1981). M, equal 

 to 1.1 (0.275 per quarter), was assumed to be con- 

 stant for all ages and seasons. 



Because backward sequential computations, using 

 a range of trial estimates of input F (instantaneous 

 fishing mortality) for the oldest age, tend to con- 

 verge on the correct value of F for the youngest and 

 forward calculations tend to diverge (unless true 

 starting values are used), it is desirable to begin with 



the oldest age for which reliable landing data are 

 available (Ricker 1975). Because of aging difficulties 

 (Nicholson and Schaaf 1978), we assumed that catch 

 estimates of older fish, mainly age 4, were not 

 reliable, hence for most year classes estimates of the 

 annual rate of instantaneous fishing mortality (F) 

 for age-2 fish were derived from catches of age 2 and 

 age 3 from 



F n = (log, C n - log, C n+1 ) - M 



(3) 



where C = annual catch in numbers at age (n) from 

 a given cohort. 



Initial starting values of F for the oldest age group 

 landed in a year class were adjusted by trial and er- 

 ror until the sum of the quarterly Fs for age-2 fish 

 were virtually equal to the estimate of annual F 2 

 derived from Equation (3). This technique was ap- 

 plicable for all year classes except 1960 and 1961, 

 where no 2-yr-old fish were available in the landing 

 data, the 1976 year class where no 3-yr-old fish were 

 available in the landing data, and the 1972 year class, 

 where the 2-yr-old fish apparently were not fully 

 recruited. For the 1960 and 1961 year classes, trial 

 and error adjustments were made to the starting F 

 value until the annual F z estimate for the 1961 year 

 class and the annual F 4 estimate of the 1960 year 

 class were virtually equal to the unweighted mean 

 F 3 estimate derived from the sequential computa- 

 tions of the 1963-71 and 1973-75 year classes. 

 Similarly, the mean F 2 estimate was used for the 

 1976 year class and the mean F 3 estimate for the 

 1972 year class. 



Estimates of number- at-age by quarter by year 

 class obtained from cohort analysis permitted the 

 reconstruction of population structure for the ex- 

 ploited gulf menhaden stock from 1964 to 1977 

 (Table 3). Numbers of newly recruited age-1 fish 

 varied as much as threefold between years. Because 

 age-1 fish were numerically the most abundant age 

 group each year, the population size fluctuated in 

 close concert with their numbers (Fig. 3). 



Resultant age-specific annual Fs by fishing season 

 demonstrate that 1-yr-olds are incompletely re- 

 cruited to the fishery and that age 2's are fully re- 

 cruited (Table 4). These results are in accord with 

 those of Ahrenholz (1981), who concluded that fish 

 from more distant eastern and western, areas of the 

 Gulf of Mexico (Gulf) shifted toward the more heavily 

 fished central Gulf areas as they aged. The slightly 

 higher values for both the weighted and unweighted 

 mean F's for 3- and 4-yr-olds could be due to either 

 small numbers of fish from the most distant eastern 



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