364 
Fishery Bulletin 1 10(3) 
ment model, first the length-weight relationship was 
determined by using the typical nonlinear allometric 
relationship: 
W a = a 1 + e. (4) 
Here, length /, a, and [i are parameters estimated by 
procedures for nonlinear least squares. This equation 
was combined with the length-at-age model to construct 
the weight-at-age model. The weight-at-age model was 
log-transformed to the following equation because the 
data had a multiplicative error structure: 
InW =lnW + /3 ln(l-e'-* ,a ‘ ,0, ) + £, (5) 
where £ = a normally distributed error term. 
Because of high parameter correlation with only one 
dependent variable, the allometric parameter /3 was 
fixed, determined from the length-weight relationship. 
The 3 remaining parameters, W^, k, and t 0 were esti- 
mated by a nonlinear procedure (Quinn and Deriso, 
1999). 
Two age-weight, models were fitted to each sex to test 
whether sablefish weight-at-age differed by region. The 
full model used separate growth curves fitted to each 
of the 6 regions, and the reduced model relied on one 
growth curve fitted to pooled data. Equation 3 was used 
to compare the full model against the reduced model at 
a significance level of a=0.05 (Sigler et al., 1997; Quinn 
and Deriso, 1999). 
Biological and oceanographic explanations 
for observed changes 
Several hypotheses have been formulated to explain the 
possible change in growth of sablefish in Alaska: inter- 
specific competition with healthy arrowtooth flounder 
( Atheresthes stomias) populations, intraspecific density- 
dependent processes, and changing environmental con- 
ditions (Hanselman et ah, 2006; Maloney and Sigler, 
2008). We explored the possibility that temporal growth 
changes can be attributed to density-dependent effects 
or to environmental factors, including winter sea-sur- 
face temperature (SST), summer SST, and the Pacific 
Decadal Oscillation (PDO) index. 
To test for intra- and interspecific density-depen- 
dence, linear regressions were performed between each 
of the response variables (the growth parameter k, 
mean length at age 4, and mean length at age 6), and 
each of the explanatory variables (biomass values for 
age-2 sablefish, age-4+ sablefish, and age-4+ arrowtooth 
flounder). Biomass estimates were obtained from the 
2008 Alaskan sablefish stock assessment (Hanselman 
et ah, 2007) and 2008 Alaska arrowtooth flounder stock 
assessment (Turnock and Wilderbuer, 2007). Growth 
estimates were taken from data pooled across the en- 
tire series, 1981-2004, for all regions, fitted to the von 
Bertalanffy growth curve. Significance was determined 
using a level of a=0.05, and then the coefficients of 
determination ( r 2 ) were used to assess the explanatory 
power of the model. 
To discern the effect of density-dependence while sa- 
blefish were in the juvenile stage, abundance estimates 
for sablefish and arrowtooth flounder were lagged by 2, 
3, and 4 years. This calculation was made to compare 
the growth rate and size of sablefish at age 4 and age 6 
with the abundance of sablefish and arrowtooth floun- 
der exposed to while young of the year (YOY), and at 
age 1, age 2, and age 3. 
To examine the influence of environment on growth, 
linear regressions were performed between each of the 
response variables (mean length at age 4 and mean 
length at age 6), and each of the explanatory vari- 
ables (winter SST, summer SST, and an index used to 
quantify the PDO). Because YOY and juvenile sable- 
fish are more susceptible to surface temperatures and 
are considered to be more susceptible to oceanographic 
variability than are adults, we lagged the SST by 2, 3, 
and 4 years to compare the size of an age 4 sablefish 
with the SST exposed to while as a YOY, and at age 1, 
and age 2, and we lagged the SST by 4, 5, and 6 years 
to compare the size of an age 6 sablefish with the SST 
exposed to as a YOY, and at age 1 and age 2. 
Monthly values of the PDO index were obtained from 
the Joint Institute for the Study of Atmosphere and 
Oceans (Mantua et al., 1997; http://jisao.washington. 
edu/pdo/PDO. latest, accessed January 2008; http:// 
www.beringclimate.noaa.gov/data/index.php, accessed 
January 2008), which incorporated data from the Unit- 
ed Kingdom’s Meteorological Office’s (UKMO) Historical 
SST Dataset and Reynolds’ Optimally Interpolated SST. 
SST values for the Bering Sea (http://www.beringcli- 
mate.noaa.gov/data/BCresult.php, accessed January 
2008) and the GOA (Kaplan et al., 1998; http://www. 
esrl.noaa.gov/psd/data/timeseries/, accessed January 
2008) were taken from a data set of SST anomalies, 
Kaplan Extended SST V2, provided by the Physical 
Sciences Division of NOAA’s Earth System Research 
Laboratory, Boulder, Colorado. 
Management implications 
We examined the sensitivity of the current stock assess- 
ment model to the use of the new growth information 
from our study. The AFSC models the Alaskan sable- 
fish population with statistical catch-at-age methods. 
It uses a penalized maximum likelihood function to 
estimate parameters simultaneously to obtain the best 
fit between predicted and observed data. Data in the 
sablefish stock assessment model include catch, several 
abundance indices, and age and length data from the 
longline survey and from the fishery. For details of the 
assessment model, see Hanselman et al. (2010). 
This assessment model in its current form uses age- 
length conversion matrices, not empirical age-length 
keys, to describe the probability that a fish of a giv- 
en age is of a certain length. This model uses these 
age-length conversion matrices to predict lengths. The 
weight-at-age is input as a fixed vector for the whole 
