Lo et al.: Application of the continuous egg sampler to estimation of the daily egg production of Sardmops sagax 
563 
With these data, an embryonic mortality was modeled by 
an exponential curve (Eq. 5) (Lo et al., 1996). The mortality 
curve was fitted to eggs/0.05 m 2 in each age class and num- 
bers of yolksac larvae/0.05 m 2 with an assigned age based 
on observed mean water temperature. The estimates of the 
intercept (P 0 : ) and the instantaneous mortality rate from 
the mortality curve were obtained by a nonlinear regres- 
sion of S+ nonlinear regression function (nls()). 
The exponential embryonic mortality curve is 
P t = P 01 exp(-zt), (5) 
where P t = a weighted average of eggs - yolksac larvae 
/0.05m 2; and 
t - the mean age (d) for each of 6 half-day age 
groups of eggs and yolksac larvae. The weights 
are total CUFES sampling time (minutes) for 
each transect (Eq. 4). 
Daily egg production in the low-density 
stratum ( P Q 2 ) 
Because no CalVET samples were taken in the low-den- 
sity stratum, we estimated daily egg production (P 0 2 ) in 
that stratum as the product of the egg production in the 
high-density stratum (P 01 ) and the ratio (q) of egg/min in 
the low-density stratum to that in the high density stra- 
tum from the CUFES samples. Here we assumed that q 
is the same no matter whether it was computed from eggs/ 
min by the CUFES or from eggs/tow by the CalVET: 
and according to Goodman (1960), the unbiased estimate 
of var(P 0 ) is 
v(P 0 ) = v{P 01 )(w 1 + w 2 q) 2 + P^wlviq)- v{P 0 x )w 2 v(q), (9) 
& 
where w - — — — > i = 1,2, and A, - the area size. 
' Aj + Aj 
Simulation 
Bootstrap simulations were conducted to provide the pos- 
sible biases and another estimate of the standard error of 
daily egg production (P 0 ) and the instantaneous mortality 
rate (z) for each stratum and the entire survey area under 
the adaptive allocation sampling scheme. As mentioned ear- 
lier, CalVETs were taken on nine transect lines and not on 
line 8 and line 11. In the simulation, nine transects with 
CalVETs were sampled with replacement and estimation 
procedures described in previous section were followed. To 
evaluate the effect of weighting, we included weighted and 
unweighted nonlinear regression where the weight was the 
inverse of the standard error of egg production of each age 
group and yolksac larvae. One thousand iterations were 
run, and the standard deviation of 1000 estimates was the 
bootstrapped standard error of the estimates. Bias was the 
difference between the average of 1000 estimates and the 
estimate from the original data. The bias-corrected esti- 
mate was the original estimate minus the bias. 
■^ 0,2 - ^ 0,1 9 ’ 
( 6 ) Results of the 1997 CUFES and DEPM survey 
Zj m ' 
where m l = the total CUFES time (minutes) in the zth 
transect; and 
Xj x - was eggs/min in the jth stratum and ith tran- 
sect. 
The variance of q was computed according to that of a 
ratio estimator (Eq. 4). 
Daily egg production for the total survey area ( P 0 ) 
P n was computed as a weighted average of P 0 1 and P 0 2 , 
where 
D _ P 0 ,A + ^0,2^2 
A, + A-, (8) 
— P 0 jlfj + P 02 w 2 
= P 01 [i<-\+qw. 2 ] 
Daily egg production 
The daily egg production for each half-day category and 
yolksac larval production and their ages (d) were used to 
construct an embryonic mortality curve for the high-den- 
sity stratum (Eq. 5, Fig. 8, Table 3). The daily egg produc- 
tion in the high-density stratum (P 0 j) based on unweighted 
nonlinear regression was 5.04 eggs/0.05 m 2 /d (100.8 eggs/ 
m 2 /d ,CV=0.25) and egg mortality was z=0.21 (CV=0.73) 
for an area (Aj) of 66,841 km 2 (19,530 nmi 2 ) (Eq. 8, 
Fig. 9). The ratio (q) of egg density between the low- 
density stratum and high-density stratum from CUFES 
samples was 0.211 (CV=0.43) (Eq. 7). Therefore, in the 
low-density stratum, the egg production (P 02 ) was 1.064 
eggs/0.05 m 2 /d (21.28 eggs/m 2 /d, CV=0.49) for an area (A 2 ) 
of 107,255 km 2 (31,338 nmi 2 ). The estimate of the daily 
egg production for the entire survey area was 2.57/0.05 m 2 
(51.4/m 2 , CV=0.27) (Eq. 8, Table 4). The weighted nonlinear 
regression produced estimates slightly different from those 
with unweighted nonlinear regression: P 0 x =4.76/0.05 m 2 
(59.2/m 2 , CV=0.18), z = 0.35(CV=0.14), and the P 0 for the 
entire survey area was 2.43/0.05 m 2 (48.6/m 2 , CV=0.21). 
The bootstrap estimate of P 0 (5.10) was similar to the 
original estimate P 0 (5.04) in the high-density stratum. 
The standard error ofP 0 (1.6) from the bootstrap analysis 
was higher than the estimate from the original data (1.28). 
The bias of P 0 (0.06) was negligible because the ratio 
