AHRENHOLZ ET AL.: ATLANTIC MENHADEN POPULATION AND FISHERY 



Table 7. — Estimated number of recruits by year class at age 0.5 

 and 1.0, estimated number of spawners thiat produced the year 

 class, and estimated egg production from the spawning stock, for 

 Atlantic menhaden. 



1 Preliminary estimates. 



those for 1965-78 are from the quarterly analyses. 

 Estimates of recruitment were computed for both 

 age 1.0 and age 0.5 (Table 7). Estimates at age 1.0 

 are provided for comparative purposes, as this age 

 has been frequently used for studies on Atlantic 

 menhaden (ASMFC fn. 4). Age 0.5 is used here to 

 appropriately credit a year class with the num- 

 bers of juvenile fish removed from the population 

 by the fishery during the fall and early winter. 

 Although perhaps underestimates because the 

 value of M (0.45) may be too low for fish younger 

 than 1-yr old, these estimates are relatively con- 

 sistent. 



The degree of dependency of the number of re- 

 cruits on the size of the parental stock has been 

 examined by Schaaf and Huntsman (1972), Nel- 

 son et al. (19771, Schaaf (1979), and Reish et al. 

 (1985). All earlier workers employed the Ricker 

 ( 1954) model, but Reish et al. (1985) also used the 

 Beverton and Holt model as well as the unnor- 

 malized gamma function. The published results 

 indicate weak relationships, with substantial 

 variability about both fitted models. Nelson et al. 

 (1977) developed a multiple regression model to 

 explain observed deviations from the Ricker 



model attributable to several annually varying 

 environmental parameters, primarily Ekman 

 transport, which would affect the oceanic larval 

 stage. 



The spawner-recruitment data (Table 7) were 

 fitted with both the Ricker and Beverton-Holt 

 models using a nonlinear least squares method 

 (Marquardt's (1963) algorithm). Both models fit 

 the data poorly (Fig. 12). The Beverton-Holt 

 model is slightly better than the Ricker model if 

 residual sum of squares is used as a goodness of fit 

 criterion. The Beverton-Holt residual is only 

 slightly less than that about a mean value, which 

 assumes no relationship between numbers of 

 spawners and numbers of recruits. Residual sum 

 of squares in the Ricker model was slightly 

 greater than results for the mean. 



POTENTIAL AND ACTUAL YIELD 

 Production Models 



The application of production models to the At- 

 lantic menhaden purse seine fishery is hampered 

 on theoretical grounds by two major conditions: 

 1) the fishery has not been operating under equi- 

 librium conditions, and 2) fishing effort is not 

 proportional to fishing mortality (F). The catcha- 

 bility coefficient {q ) is inversely related to popula- 

 tion size (Schaaf 1975b). Schaaf and Huntsman 

 (1972) and Schaaf (1979) circumvented this latter 

 problem by adjusting effort to a base year. 



The effects of this problem were reduced in this 

 analysis by using an estimate of population F for 

 the independent variable instead of adjusting ef- 

 fort (Nelson and Ahrenholz 1986). To estimate a 

 population rate of fishing mortality (Fpop), esti- 

 mates of the population sizes (excluding 0-age 

 fish) at the beginning of each fishing season from 

 1955 to 1979 were reconstructed from annual 

 VPA estimates. These were in turn divided into 

 the estimated catch in numbers (excluding age 0), 

 to obtain an estimate of population rate of ex- 

 ploitation (C/pop). By trial and error, estimates of 

 Fpop were obtained for each fishing season from 



Food =U Z/(1 

 P"P pop 



e-^), 



assuming 



M = 0.45 



- F^K" " po ^ 



(Table 8). 



A Graham-Schaefer curve was fitted to the 

 catch and population fishing mortality data by 

 Marquardt's (1963) algorithm. This procedure 

 produced an MSY (maximum sustainable yield) 

 estimate of 414,000 t at Fpop = 0.574. Recent pop- 

 ulation fishing mortality values have been 

 slightly above and below this value, and yield has 



585 



