NELSON ET AL.: LARVAL TRANSPORTOFBfi£VOO/?77A TYRANNUS 



stocks greater than S m produce progressively 

 fewer recruits. There is a size-dependent fecundity 

 relationship for Atlantic menhaden (Higham and 

 Nicholson 1964), and growth rates are slower for 

 large year classes (Gene R. Huntsman, pers. com- 

 mun., Atlantic Estuarine Fisheries Center). Also, 

 adult menhaden are indiscriminate filter feeders 

 and are known to ingest their own eggs. Calcula- 

 tion of a density-dependent index for Atlantic 

 menhaden (i.e., the slope of a regression of InR on 

 InS ) yields a value of 0.238. This index falls within 

 the category described by Cushing (1971) as hav- 

 ing a slightly convex spawner-recruit curve. The 

 average fecundity of Atlantic menhaden (113,000 

 eggs per female) calculated from data used in this 

 study, also places the species in groups which 

 Cushing describes as having a dome-shaped 

 spawner-recruit curve. Accordingly, the Ricker 

 model has been used in this analysis, instead of 

 models proposed by Beverton and Holt ( 1957), and 

 others. 



Schaaf and Huntsman (1972) presented a 

 Ricker spawner-recruit curve for Atlantic 

 menhaden. The same catch data and basically the 

 same methodology were used in this study, with 

 one important modification. Instead of using the 

 estimated total number of spawning age fish as the 

 independent variable to estimate recruitment, the 

 potential number of eggs that could be produced 

 from the spawning stock was used. This annual 

 potential is influenced by the age distribution of 

 the spawners and their average size. The potential 

 number of eggs produced each year and at each age 

 (Table 2) was calculated from the estimated 

 number of age 3 and older females (1955-70), their 

 back-calculated length, and the following fecun- 



dity relation from data presented by Higham and 

 Nicholson (1964): 



ME) = 0.3149+0.0176(/) 



where E = thousands of eggs produced per female 

 at length, and 

 / = back-calculated length at age of an- 

 nulus formation for age-3 and older 

 fish. 



Another deviation from the data used on the 

 original Ricker spawner-recruit curve by Schaaf 

 and Huntsman (1972) is the calculated number of 

 recruits in the 1955-70 year classes. The numbers 

 differ between the two studies because: 1) some 

 adult menhaden were reaged following the initial 

 study which brought about slight changes in 

 estimates of year-class size, 2) the maximum 

 instantaneous fishing mortality rates were av- 

 eraged for age-specific exploitation rates for age 

 2-5 fish and were not weighted for numbers at age 

 as was done in the earlier study, and 3) the 

 exploitation rate of age-1 fish was estimated each 

 year based on the exploitation rate of age 2-5 fish 

 instead of an estimated exploitation rate of two- 

 thirds that of older fish as was done in the previous 

 study. This was necessary because shifts in fishing 

 area and effort in recent years have increased the 

 vulnerability of age-1 fish. 



The parameters of the Ricker model were es- 

 timated from a linear regression of ln(i?/S) on S. 

 Fitting the model (Figure 2) yielded an estimate of 

 S m equal to 60 x 10 12 eggs. This is equivalent to 

 531 million spawning females spread over ages 

 3-6, and would produce an average recruitment of 

 3.68 billion fish at age 1. 



TABLE 2. — Estimated number of eggs produced by spawning 

 stock of Atlantic menhaden for each year class by age, 1955-70. 



+ = less than 0.05 x 10 12 . 



20 40 60 80 100 120 140 160 ISO 



SIZE OF SPAWNING STOCK {NO OF EGGS * 10' J ) 



FIGURE 2. — Ricker spawner-recruit relationship for Atlantic 

 menhaden, 1955-70. 



29 



