Echave et at: Interdecadal change in growth of Anoplopoma fimbria in the northeast Pacific Ocean 
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In the first sampling design, fish samples from the 
Japan-U.S. cooperative survey (1981-93) were strati- 
fied by length (5 fish were aged per centimeter length 
per sex per area). The sex and fork length (FL) of all 
collected fish were recorded. No assessment of weight 
was performed. 
A change of sampling method took place in 1996 in 
the NMFS domestic longline survey. A random sub- 
sample of fish was collected (if the first hook of a skate 
contained a sablefish, it was sampled) to acquire age 
and weight data (Hanselman et al., 2010). A “skate” 
is a unit of gear that is 100 m long and contains 45 
hooks. As before, fork-length measurements and sex of 
all fish brought aboard were recorded. Age was deter- 
mined from otoliths stored in 50% ethanol by using the 
break and burn technique (Beamish and Chilton, 1982; 
Nielsen and Johnson, 1983). 
Length-at-age analysis 
Mean length-at-age was calculated from the age-length 
data in 3 ways by 3 different strata: 1) by sex, region, 
and survey period, 2) by sex and survey period, and 3) 
by sex and region. Data were split between the 2 sexes 
because it was already known that male and female 
sablefish have different growth rates (Sasaki, 1985) 
and because the current sablefish assessment model is 
split by sex. Data were split into 2 periods by using the 
shift in sampling design: 1981-93 and 1996—2004 (no 
otoliths were collected in 1994 and 1995). Fish aged 
31 years and older were pooled into a 31+ age category 
(Hanselman et al., 2010). Only the 6 regions sampled 
consistently across the entire time series (Southeast, 
Kodiak, Chirikof, Shumagin, EBS, Al; Fig. 1) were used 
in regional comparisons. 
Estimates of mean length-at-age produced by simple 
averaging with length-stratified data are biased. This 
bias is caused by aging smaller and larger specimens 
more often than would be aged under a random sam- 
pling design. The mean size-at-age for early age groups 
is too small, and the mean size-at-age for the oldest 
age groups is too large (Goodyear, 1995; Sigler et al., 
1997; Bettoli and Miranda, 2001). As a result, we de- 
termined that size estimates used in the assessment 
of the sablefish population in Alaska have been too 
large. To account for stratification, the length-frequency 
distribution from the survey catch data was used in 
combination with the length-stratified age samples to 
create bias-corrected age-length estimates for 1981-93 
(Goodyear, 1995; Sigler et al., 1997). The following 
equation was used (Bettoli and Miranda, 2001): 
Here, L a = the estimated mean length at age a; 
l = the median of the length group j; 
N- = the number of fish in the yth length group; 
n- = the number of fish subsampled for age deter- 
mination in the yth length group; and 
n a j = the number of fish in age group a in the 
subsample from theyth length group. 
Sablefish growth was modeled with the von Berta- 
lanffy (VB) age-length model, which was fitted by non- 
linear least squares weighted by sample size, 
L a = LJl-e~ hla ~ lJ ) + £ a . (2) 
Here, = the average maximum length; 
K" = the mean growth coefficient; 
t Q = the mean theoretical age a fish would have 
been at zero length; and 
e a = an additive normally distributed error term. 
Standard errors, correlation estimates, and 95% con- 
fidence intervals for growth curve parameters were 
estimated by the Hessian method of second partial 
derivatives (Quinn and Deriso, 1999). 
Individual parameters of growth models were com- 
pared using the univariate Fisher-Behrens test. Likeli- 
hood ratio tests (LRTs) were carried out to determine 
whether growth curves differed between the 2 sur- 
vey periods, among regions, or both survey period and 
region (Kimura, 1980; McDevitt, 1990; Sigler et al., 
1997). The LRT for comparing nested models was log- 
transformed and calculated as follows: 
-Nln(RSS F / RSS r )~ x 2 - (3) 
Here, N = the total number of observations 
(of length-at-age); and 
RSS f and RSS r = the estimated residual sum of 
squares ( RSS ) of the full ( F ) 
and reduced (R) models, respec- 
tively (Kimura, 1980; Quinn and 
Deriso, 1999). 
The degrees of freedom for the test are the difference in 
the number of parameters between the full and reduced 
models. The increase in the RSS between each of the 
reduced models and the full model was used to test for 
temporal and spatial effects. This increase also was used 
to further test for differences among pairs of regions and 
between survey periods within each region if a regional 
or temporal effect was discovered. 
Weight-at-age analysis 
Weight-at-age curves were fitted to data by sex and 
region strata. Sasaki (1985) reported sablefish weight 
estimates; however, no weight data were collected before 
1996 in the domestic longline survey; therefore, no tem- 
poral changes were investigated. Because weight data 
were collected only from random samples, no correc- 
tion for stratification was needed. Fish of ages >31 
were pooled into a 31+ age category (Hanselman et al., 
2010). To determine weight-at-age for the stock assess- 
