NELSON and AHRENHOLZ: CHARACTERISTICS OF GULF MENHADEN 



Fig. 6). The maximum recruitment level of 588,236 

 t is equal to about 18.5 billion recruits. The optimum 

 spawning stock biomass of 336,011 t is equal to 

 about 3.2 billion spawners, assuming the age distri- 

 bution for the spawning stock is average. The func- 

 tion for biomass accounts for changes in age struc- 

 ture of the spawning stock and since age-2 fish 

 consistently represent over 90% of the spawners, 

 differences between plots of numbers and biomass 

 (Figs. 5, 6) are minor. 



Spawning stock size has generally remained with- 

 in a range of potentially good recruitment and has 

 not undergone years of extreme highs or lows (Figs. 

 5, 6). Trends indicating a steady decrease or increase 

 in stock size and recruitment are not apparent, al- 

 though the general increased level of recruitment 

 in recent years may be part of a cyclic recruitment 

 fluctuation that is found in many stocks. 



YIELD-PER-RECRUIT 



We applied what is essentially a Ricker type yield- 

 per-recruit model that was initially developed to 

 evaluate a multiple-gear fishery (M-GE AR) and later 

 modified to accommodate a multiple-area fishery (M- 

 AREA) (Lenarz et al. 1974; Epperly et al. 1979 4 ). 

 Yield is summed by time intervals, and individual 

 weights and estimates of natural and fishing mor- 

 tality can be inserted for each interval (Ricker 1975). 

 An option developed by Epperly et al. (fn. 4) allows 



4 Epperly, S. P., W. H. Lenarz, L. T. Massey, and W. R. Nelson. 

 1979. A generalized computer program for yield per recruit 

 analysis of a migrating population with area specific growth and 

 mortality rates. Unpubl. manuscr., 14 p. Southeast Fisheries 

 Center Beaufort Laboratory, National Marine Fisheries Service, 

 NOAA, Beaufort, NC 28516. 



for calculation of biomass within intervals by either 

 exponential or arithmetic means. We applied the 

 model in its simpliest form: one set of growth data 

 because the stock was not divided into subareas, con- 

 stant natural mortality rate, and the exponential 

 growth mode for biomass calculation. The year was 

 divided into quarters to simulate the seasonal nature 

 of the fishery (Table 8). Quarterly fishing mortality 

 rates were developed from the cohort analysis. 

 Estimates were obtained for periods of low popula- 

 tion size and high fishing mortality (1964-68), high 

 population size and low fishing mortality (1974-77), 

 and "average" population size and mortality 

 (1964-77) (Table 8). Age of entry into the fishery was 



Table 8.— Input array of quarterly length (mm), weight (g), and 

 fishing mortality rates (F) used in the calculation of yield-per-recruit 

 of gulf menhaden under average fishing conditions (1964-77), years 

 of low stock size (1964-68), and years of high stock size (1974- 

 77). 



Age 



0.50 

 0.75 

 1.00 

 1.25 

 1.50 

 1.75 

 2.00 

 2.25 

 2.50 

 2.75 

 3.00 

 3.25 

 3.50 

 3.75 

 4.00 

 4.25 

 4.50 

 4.75 



Months 



W 



F 

 (64-77) 



F 



(64-68) 



July-Sept. 



Oct.-Dec. 



Jan. -Mar. 



Apr.-June 



July-Sept. 



Oct.-Dec. 



Jan. -Mar. 



Apr.-June 



July-Sept. 



Oct.-Dec. 



Jan.-Mar. 



Apr.June 



July-Sept. 



Oct.-Dec. 



Jan.-Mar. 



Apr.-June 



July-Sept. 



Oct.-Dec. 



84.7 

 103.5 

 120.2 

 135.1 

 148.2 

 160.0 

 170.4 

 179.6 

 187.8 

 195.1 

 201.6 

 207.3 

 212.4 

 216.9 

 221.0 

 224.5 

 227.7 

 230.5 



10.1 



19.5 



31.8 



46.6 



63.2 



81.0 



99.5 



118.2 



136.8 



154.9 



172.3 



188.9 



204.5 



219.1 



232.7 



245.2 



256.7 



267.2 



0.0013 

 0.0003 

 0.0002 

 0.1850 

 0.4437 

 0.0299 

 0.0002 

 0.4478 

 1.2213 

 0.1448 

 0.0003 

 0.4500 

 1 .2722 

 0.1106 

 0.0000 

 0.1605 

 1.6501 



0.0018 

 0.0001 

 0.0004 

 0.2677 

 0.6315 

 0.0264 

 0.0000 

 0.5652 

 1 .5858 

 0.0594 

 0.0000 

 0.5407 

 1.5752 

 0.0133 

 0.0000 

 0.3085 

 2.3018 



F 



(74-77) 



0.0008 

 0.0005 

 0.0000 

 0.1244 

 0.3593 

 0.0329 

 0.0000 

 0.3683 

 0.8253 

 0.0852 

 0.0000 

 0.2966 

 1 .0670 

 0.1557 

 0.0000 

 0.0488 

 0.0480 



CO 

 CO 



< r 



800r 



600 



68 



76 



600 



SPAWNING BIOMASS (metric tons X 10 3 ) 



Figure 6— Ricker spawner-recruit relationship for biomass of spawners and recruits at age 1, 

 estimated as of 1 January, for the 1964-76 gulf menhaden year classes. 



319 



