596 
Fishery Bulletin 95(3), 1997 
Fig. 4A). First, the survey area was divided into 36 subar- 
eas (Fig. 4A). The longitude of the centroid for age group 
a, X a , was estimated by using 
^ n 
-2 V 
+ 0.5o; 
- 
x = M v A j 
where ^ J ^ 'au 
11 j 
and C ai j = catch rate (eggs/m 2 ) for age group a at the ith 
station in subarea j; 
M n/ = mean catch rate for age group a in subarea j; 
n } = number of stations in subarea j; 
A ; = area of subarea j\ and 
x = longitude of center of subarea j. 
The latitudes of the centroids were calculated similarly. 
These calculations use the approximation that, for each 
age group, the centroid of eggs within a subarea is at the 
center of the subarea. 
Appendix 3: Egg production model and 
estimation 
This appendix describes the calculation of daily egg pro- 
duction, N Q , and CV given in Table 4 and shown in Figure 
6. It is assumed that 
where o a is the standard error of log (N a ), given by 
cr o = [log(l + c 0 2 )]V 
By definition, Z must be positive. However, in the boot- 
strap procedure described next, it sometimes happened 
that the maximum likelihood estimate of Z was negative 
(because, by chance, simulated egg abundance estimates 
increased with age). When this happened, Z was forced to 
be zero, so that 
E a =N o(*«-*«-i)- 
The following bootstrap procedure was used to estimate 
the degree of uncertainty in the estimates of N 0 and Z. 
1 the maximum likelihood estimates of N 0 and Z were 
used to calculate the expected egg abundances, E a , 
using the formula above; 
2 new egg abundance estimates, N , were simulated by 
using lognormal distributions with expected values, 
E , and CV’s, c ; 
a 7 7 a 7 
3 maximum likelihood estimates of N 0 and Z were cal- 
culated from the simulated values of N , and 
a 7 
4 steps 2 and 3 were repeated 1,000 times. 
1 the rate of egg production was constant (both from day 
to day and within each day) in the period immediately 
preceding and during the plankton survey, 
2 egg mortality was constant over the same period and 
independent of age, and 
3 the egg abundance estimates, N a , of Table 3 are unbi- 
ased and lognormally distributed with CV’s, c a , as given 
in Table 3. 
The resulting 1,000 values of N 0 and Z are the bootstrap 
distributions for these parameters; the 0.025 and 0.975 
quantiles of these distributions were taken as bounding 
the 95% confidence intervals for each parameter. The CV’s 
of these distributions are taken as estimates of the CV’s of 
the maximum likelihood estimates of N Q and Z. 
Under these assumptions, E a , the expected value of N a , is 
given by 
E a =[ N 0 e-“dt = ^-(e- z ‘°-'-e- z ‘°) j 
where N 0 = the daily egg production (eggs/day); 
Z = the daily instantaneous egg mortality (per 
day); and 
(t a _ i, t a ) - the range of ages (day) in age group a. 
The mean age of eggs of age group a (used in Fig. 6) is 
given by 
— r tN 0 , 
E a .L 0 
, 1 (t„ 6 
f z ‘dt = - + IV 
N 0 and Z were estimated by maximum likelihood, ie. by 
maximizing the likelihood, L, which is given by (ignoring 
constants) 
Appendix 4: Analysis of ovarian samples 
Ovaries frozen onboard were thawed in the laboratory, 
weighed, and then one of the two slit open. A subsample of 
about 5 g was scraped from the full length of one ovary 
from each fish, because preliminary analyses had indicated 
there was some variation in egg density from different 
parts of the ovary. The subsample was then placed into 
1M KOH for a period of 5-15 minutes depending on the 
ovarian stage. Maturing oocytes (stage 3) were bound more 
tightly in the matrix than advanced stages, and therefore 
needed a longer KOH treatment to separate individual 
oocytes. Stage-3 oocytes generally retained a medium or- 
ange color after KOH treatment, and thus needed no fur- 
ther treatment after separation. However, the more trans- 
parent stage-4, stage-5, and stage-8 oocytes were stained 
with Semichon’s carmine. The subsample was then washed 
through a 0.7-mm mesh sieve that was found to be of a 
suitable mesh size to retain oocytes with a diameter greater 
than about 1.2 mm. Primary, early vitellogenic, and atretic 
oocytes, as well as small fragments of matrix and tissue 
