HOUDE: ABUNDANCE AND POTENTIAL YIELD OF ROUND HERRING 



were located closest to the coast (Figure 1). An 

 estimate of the variance in egg abundance under a 

 square meter of sea surface (s y ) was obtained from 

 the log 10 ((CjZjVvj) + 0.1 egg catch at each station 

 during a cruise (Cushing 1957). The log 10 variance 

 estimate so obtained was backtransformed to ob- 

 tain the untransformed estimate of variance. The 

 variance estimate for a cruise was calculated 

 using the estimator given by Taft (1960) that as- 

 sumes random sampling. It is: 



7 = 1 



A 2 <t* 



(4) 



where S P . = variance estimate on the abundance 



r i. 



of eggs spawned during the period 

 represented by cruise i 



D, = the number of days represented by 

 cruise i, defined as the days included 

 in the cruise plus one-half the days 

 since the previous cruise and one- 

 half the days to the next cruise 

 (Sette and Ahlstrom 1948). When a 

 cruise took place shortly after the 

 assumed date of the beginning of the 

 round herring spawning period (15 

 October) or near the end of the 

 spawning season (31 May), the 

 number of days from the inclusive 

 cruise days to the beginning or end 

 of the season was used in estimating 

 D, 



Ay = the area (m 2 ) represented by thejth 

 station in the ith cruise 



dy = the duration (days) of the egg stage 

 from spawning until hatching. The 

 best estimate of d u for round herring 

 is 2.0 days, based on observed egg 

 stages in catches during the surveys 

 and this value was used in all abun- 

 dance and variance calculations 



sfj = the variance estimate for the 

 number of eggs present under 1 m 2 of 

 sea surface for cruise i 



k, = the number of stations included in 

 the variance estimate for cruise i. 



Sampling was not random in the eastern Gulf 

 surveys. Also, egg catches were not normally or 

 log-normally distributed, nor did the distribution 

 of catches fit contagious distributions like the 

 negative binomial. Thus, the variance estimates 

 that I have obtained are not the best estimates, but 



they may be reasonable approximations (Saville 

 1964) for variance in the area represented by the 

 cruises. Variation in spawning that occurs over 

 time (i.e., day to day variation) has not been ac- 

 counted for, which is the usual situation in 

 ichthyoplankton abundance surveys (Saville 

 1964). 



An estimate of the abundance of eggs spawned 

 over the entire spawning season is: 



Pa - 1 



P,D, 



(5) 



i = \ 



where P a = the total number of eggs spawned in 

 an annual spawning season 

 r = the number of cruises upon which the 

 estimate of annual spawning is based 

 Pi, D,, and d, are defined in Equation (4). 



An estimate of variance on the number of eggs 

 spawned annually was obtained, assuming that 

 sampling was random using the formula given by 

 Taft (1960): 



= Isl 



(6) 



i = l 



where Sp 



the variance estimate on the number 

 of eggs spawned annually 

 r is defined in Equation (5) 

 Sp is defined in Equation (4). 



This variance estimate, like that for individual 

 cruise abundance estimates, is not entirely satis- 

 factory because the assumptions of random sam- 

 pling and normally distributed catches do not hold. 

 Also, as in the cruise variance estimates (Equa- 

 tion (4)), it was not possible to obtain an estimate 

 of variance in abundance due to day to day varia- 

 bility, thus leaving variation in time unaccounted. 

 Taft has shown that this can be a large source of 

 error and that annual spawning estimates will not 

 be more precise than individual cruise estimates 

 when variation in time is not considered. 



Biomass Estimating Procedure 



An estimate of adult biomass of a fish stock can 

 be obtained if the annual spawning (number of 

 eggs), sex ratio, and relative fecundity (eggs pro- 

 duced per gram adult female per year) are known 

 (Saville 1964; Ahlstrom 1968). Biomass of adults 

 is: 



65 



