NELSON and AHRENHOLZ: CHARACTERISTICS OF GULF MENHADEN 



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 POPULATION SIZE (billions) 



Figure 4— Catchability coefficients calculated from population fishing mor- 

 talities (open circles, dashed line), and from cohort annual weighted mean fish- 

 ing mortalities (dots, solid line) plotted on population number estimated as of 

 4 April, for the 1964-77 fishing seasons (see Table 5). 



Table 6.— 1 January estimates of number of spawners, number of eggs produced by the spawn- 

 ing stock, biomass of the spawning stock, and number and biomass of recruits at age 1 for gulf 

 menhaden. Preliminary estimates in parentheses. 



anffy growth function presented earlier. Thus, 

 length-at-age estimates are taken as constants, and 

 differences in among year estimates of egg produc- 

 tion are due to differences in both total numbers and 

 age composition of the spawning stock (Table 6). 

 Similarly, the weight-length relationship was used 

 in conjunction with the mean length-at-age esti- 

 mates to obtain weight-at-age estimates for com- 

 putation of spawning and recruitment biomass (Table 

 6). 



Least-square regressions of second and third 

 degree polynomials were run with numbers of re- 

 cruits on number of spawners to determine the 



general shape of the spawner-recruit relationship. 

 Dome-shaped functions provided the least residual 

 sum of squares, indicating that a Ricker-type curve 

 (Ricker 1975) is appropriate A Ricker-type function 

 has been applied to Atlantic menhaden data (Nelson 

 et al. 1977), and the same criteria appear to apply 

 to gulf menhaden data, i.&, that there is a size- 

 dependent fecundity relationship and that adult 

 menhaden are filter feeders which are known to in- 

 gest their own eggs. Additionally, the calculation of 

 an index of density dependence, as detailed by 

 Cushing (1971) (log e recruitment regressed on log e 

 spawning stock), provides a slope of 0.159. This slope, 



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