MacNair et at: Age, growth, and mortality of Paralichthys californicus 
591 
ing the Gauss-Newton method in the program NLIN from 
SAS (1990). Outliers were removed when the von Ber- 
talanffy growth function was fitted to the data. Outliers 
were data points that clearly stood apart in scatter plots 
of individual total length versus age. Means and standard 
deviations of observed length-at-age, and the theoretical 
von Bertalanffy growth function (VBGF) were plotted for 
females and males by region. 
Hotelling’s T 2 test (Bernard, 1981) compared growth pa- 
rameters between male and female halibut in each region. 
This test was also used to determine if growth in southern 
California was different from growth in central California, 
for each sex separately. 
The estimated annual survival rate, S, was calculated 
for males and females separately by region by using Rob- 
son and Chapman’s method (1961). Total annual mortal- 
ity, A, was calculated by using the complement of annual 
survival, A = 1 - S. The instantaneous mortality rate, Z, 
was estimated by using -ln(S) (Ricker, 1975). All statistical 
analyses were performed at the 0.05 level of significance. 
Results 
In our preliminary analysis, a subsample of whole otoliths 
from 80 fish were read and then sectioned to determine 
the best method for reading otoliths for age determina- 
tion. In Figure 3 is a plot of the mutually determined ages 
from sectioned and whole otoliths, along with a 45 degree 
line and a linear regression. No significant difference was 
found between ages from whole and sectioned otoliths 
when using all 80 fish (paired Wilcoxon test, P=0.21), and 
when using only older fish (8 years and older) (paired Wil- 
coxon test, P=0.11). 
Also, as part of the preliminary analysis, in the compari- 
son of averaged ages with mutually determined ages for 
the estimation of halibut age, we found no significant dif- 
ferences for both whole (paired Wilcoxon test, mean dif- 
ferenced. 15, P=0.23) and sectioned ototliths (paired Wil- 
coxon test, mean differenced. 16, Pd. 06). Therefore, ages 
were estimated for each individual by calculating an aver- 
age of four independent readings from whole or sectioned 
otoliths because an average of several readings is consid- 
ered a more reliable measurement than a single reading 
(Fleiss, 1986). 
The total number of trawls conducted by strata and re- 
gion are listed in Table 1. The original intent was to per- 
form 50 trawls at each depth stratum for both southern 
and central California. However, substrate obstructions 
and other problems limited the number of successful tows 
at most strata. A total of 58 trawls were successfully com- 
pleted in stratum 1 in southern California. 
Because most of the halibut were collected in a single 
stratum (stratum 1), comparisons among strata were not 
made (Table 1). In southern California, a total of 916 indi- 
viduals were collected from stratum 1 (84% of total), 167 
individuals from stratum 2, and only 14 individuals from 
stratum 3. In central California, a total of 254 individuals 
were collected from stratum 1 (92% of total), 22 individu- 
als from stratum 2, and none from stratum 3. 
Figure 3 
A scatter plot of mutually determined ages 
for sectioned otoliths and whole otoliths. The 
dotted line is the linear regression through 
the origin (slope is 0.947); solid line is the 45 
degree line. 
For southern California, pairs of whole otoliths from 
1109 individuals were initially examined to estimate age. 
Twenty-two pairs of whole otoliths were unreadable, six 
pairs had no discernible opaque and translucent zones, 
and sixteen pairs had large variations in the four age 
readings (SD >1.5). These 22 pairs of whole otoliths were 
sectioned to determine age. Of these, two were eliminated 
because of large variations in the four age readings (SD 
>1.5). An additional ten were eliminated as outliers be- 
cause lengths were anomalously small or large for the es- 
timated age when the von Bertalanffy growth function 
was fitted to the data. Thus, a total of 1097 individuals 
were used to evaluate age and growth for halibut in south- 
ern California. The sample consisted of 69% males (761 in- 
dividuals) and 31% females (336 individuals). Tables 2 and 
3 provide counts of total length versus age for males and 
females, respectively, in southern California. 
In central California, pairs of whole otoliths from 292 
individuals were initially examined to estimate age. Oto- 
liths from 28 halibut had no discernible opaque and trans- 
lucent zones and 49 had large variations in the four age 
readings (SD >1.5), resulting in a total of 77 otoliths that 
were sectioned to estimate age. Of these, fourteen otolith 
pairs were eliminated because of large variations in read- 
ings (SD >1.5). An additional two became outliers that 
were removed when the von Bertalanffy growth function 
was fitted to the data. Thus, a total of 276 individuals were 
used to evaluate age and growth for halibut in central 
California. The sample consisted of 53% (147 individuals) 
males and 47% (129 individuals) females. Counts of total 
length versus age for males and females, respectively, in 
central California are shown in Tables 4 and 5. 
Within-reader index of average percent error for whole 
otoliths ranged from 8.1%< to 13.2%. For sectioned otoliths, 
