Lo et al.: Application of the continuous egg sampler to estimation of the daily egg production of Sardinops sagax 
557 
124“ 122“ 120“ 118“ 116“ 
38" N 
36“ 
34“ 
32“ 
■ i i 
124“ 122“ 120” 118“ 116“W 
Figure 2 
Sardine eggs/minute from CUFES samples and survey pattern in cruise 9703, 
11 March-6 April 1997, with two strata: a high-density stratum (open area) and 
a low-density stratum (shaded area). 
the DEPM. P 0 is only one of six parameters used in esti- 
mating biomass with the DEPM. In the DEPM, biomass is 
related to egg production using the model B s = P^A /(R/ W f ) 
SF, where B s - biomass for area A, P 0 - the daily egg pro- 
duction at age 0 day per unit sea surface area; W f - the 
average female weight; S = the fraction of females spawn- 
ing per day; F =batch fecundity; and R - the fraction of 
the biomass that is female (Alheit, 1993; Hunter and Lo, 
1997). The denominator, (R/W^)SF, is the number of eggs/ 
biomass in grams and is also called the daily specific fe- 
cundity. In the 1994 survey all parameters were estimated 
but in the 1997 survey we estimated only P 0 and A and 
used historical data for the other parameters (Hill et al. 1 ). 
Variograms of sardine density (eggs/minute) 
As the first step in developing a DEPM survey design for 
the CUFES, we used geostatistical techniques (Cressie, 
1 Hill, Kevin, T. M. Yaremko, L. D. Jacobson, N. C. H. Lo, and 
D. A. Hannan. 1998. Stock assessment and management 
recommendations for Pacific sardine ( Sardinops sagax ) in 
1997. Marine region. Admin. Rep. 98-5, Cal. Dep. of Fish and 
Game, 8604 La Jolla Shores Dr., La Jolla, CA 92037. 
1991; Barange and Hampton, 1997; and Fletcher and 
Sumner, 1999) to describe the spatial structure of the egg 
distribution and estimated the major diameters of sardines 
egg patches from the 1996 survey. We applied variogram 
models (Cressie, 1991; Petitgas, 1993) to CUFE samples (in 
units of eggs/minute) grouped into three age groups: 1-day 
(4-27 h), 2-day (28-51 h), and 3-day (52-75 h). 
Variogram (y(h)) is defined as the variance of difference 
between values that are h units apart and is a function of 
variance and covariance: 
2y(h) = var[w(x) - u(x + h )] 
= 2(var(u) - co v(/i)) if var[w(x)] = var[«(x + h)], 
where u(x) = the eggs/min at location x; 
u(x+h) = the eggs/min at the location h (nmi) away 
from x; 
var(u) = the variance; and 
co v(/i) = the covariance of eggs/min that are h (nmi) 
apart. 
y(h) is the semivariogram. For simplicity, we refer to y(h) 
as the variogram. We used S+SpatialStats (Kaluzny et al., 
