FISHERY BULLETIN: VOL. 75, NO. 1 



B 



Pa 



F r  K 



(7) 



where B = biomass of adults in the stock 



F r = mean relative fecundity of females 



(eggs produced per gram female per 



year) 

 K = the proportion of adults that are 



females 

 P a is defined in Equation (5). 



Estimates ofP a , F r , and if were obtained for round 

 herring in the Gulf of Mexico. 



An estimate of K was derived from examination 

 of 71 gonads of adult round herring trawled from 

 the Gulf of Mexico by the National Marine 

 Fisheries Service. The estimate of F r also was ob- 

 tained from these specimens. Fecundity was esti- 

 mated by the gravimetric method (Holden and 

 Raitt 1974). Modes of yolked oocytes were as- 

 sumed to be spawned during an annual spawning 

 cycle. This assumption was supported by the pres- 

 ence of only a single mode of unyolked oocytes in 

 six females collected during months when no 

 spawned eggs were collected in plankton tows. 

 Fecundity was estimated in a sample of eight 

 near-ripe females. Procedures used to estimate 

 round herring fecundity are like those outlined for 

 scaled sardine, Harengula jaguana, by Martinez 

 and Houde (1975). 



Three techniques were used to estimate adult 

 biomass. All give estimates of annual spawning 

 (P a ) that are based on the same egg catches, stan- 

 dardized per unit area of sea surface. Thus, the 

 three estimates of biomass for each spawning sea- 

 son are not independent; but, because each 

 technique has unique assumptions, the spawning 

 estimates are different, and it was useful to calcu- 

 late biomass by each procedure for comparison 

 purposes. The three techniques are outlined by 

 Sette and Ahlstrom (1948), Simpson (1959), and 

 Saville(1956, 1964). 



The method first used by Sette and Ahlstrom 

 (1948) and subsequently by Ahlstrom (1954, 

 1959a) is based on obtaining an estimate of annual 

 spawning by the techniques that I have outlined in 

 Equations (2), (3), (5), and (7). It assumes that the 

 abundance of eggs at a station is equal over the 

 entire area represented by that station. Moreover, 

 it assumes that egg abundance at the time of col- 

 lection is the same on each day of the cruise period 

 and also for one-half the days since the preceding 

 cruise, or since the beginning date of the spawning 



season plus one-half the days until the next cruise 

 or the number of days until the end of the spawn- 

 ing season. 



Simpson's ( 1959) method was modified to obtain 

 round herring annual spawning estimates. He ob- 

 tained his estimates of spawning during each 

 cruise by summing areas within contours of egg 

 abundance. I used Equation (3) to obtain cruise 

 estimates. The annual spawning estimate (P a ) 

 was obtained by plotting the daily spawning esti- 

 mate for each cruise (PJdi) against the middate of 

 the cruise (Simpson 1959). The area under the 

 resulting polygon was obtained by planimeter and 

 was equated to annual spawning. Because Equa- 

 tion (3) was used to obtain cruise spawning esti- 

 mates, Sette and Ahlstrom's (1948) and Simpson's 

 (1959) methods give results that converge, the two 

 annual spawning estimates differing only by some 

 number of eggs spawned near the beginning and 

 near the end of the spawning season. The Sette 

 and Ahlstrom technique will always give a some- 

 what larger estimate of annual spawning for 

 species like round herring that have a well-defined 

 spawning season, but identical estimates will re- 

 sult for species that spawn year round. 



The third method (Saville 1956, 1964) assumes 

 that spawning follows some known distribution 

 during the season. Spawning is approximately 

 normally distributed throughout the season for 

 many fishes. Thus, cruises that fall within the 

 spawning season represent part of the area under 

 the normal curve. If the peak spawning date is 

 known (even approximately) each cruise can be 

 equated to some percentage of the area under a 

 standard normal curve. Then each cruise spawn- 

 ing estimate (P, ) can be used to obtain an annual 

 spawning estimate (P a ): 



P,t t 

 x, d, 



(8) 



where x, = the proportion of the area under the 

 normal curve represented by cruise i 

 t, = the number of days included in cruise i 

 dj = the duration (days) of the egg stage 

 during cruise i. 



Saville (1956, 1964) did not discuss use of the 

 technique if more than a single cruise is included 

 in the spawning season, but because each cruise 

 can provide an independent estimate of annual 

 spawning, it was possible to get as many as three 

 estimates of round herring annual egg production 

 within a spawning season. 



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