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Fishery Bulletin 1 14(2) 
Sea temperature Sea temperature data for the eastern 
North Pacific Ocean were available from NOAA’s Earth 
System Research Laboratory’s Physical Sciences Divi- 
sion website (website, accessed April 2012). The NCEP/ 
NCAR re-analyzed SST data set was used (Kalnay et al., 
1996) to derive average monthly SST for a region east 
of 157. 5°W and north of 52.4°N. Averages were comput- 
ed for 3 grids of equal area (52.4°N-48.6°Nxl48.1°W- 
157. 5°W, 52.4 0 N-48.6°Nxl48.1°W-138.7°W, and 
58. l 0 N-52.4°Nxl48.1°W-138.7°W ) and the 3 areas 
were then averaged for each year from 1972 to 2004. 
An index was constructed from the average of the 
monthly SST from July 1 through Oct 31 to encompass 
the warmest months of the year. 
Pacific Decadal Oscillation index The PDO was calcu- 
lated as the leading principle component of the Reyn- 
olds optimally interpolated monthly SST anomalies 
poleward from 20°N (Zhang et al., 1997). Data were 
available from the website of Steven Hare and Nathan 
Mantua at the University of Washington Joint Institute 
for the Study of the Atmosphere and Ocean (Hare and 
Mantua, 2000). The mean winter PDO was calculated 
as the average of the monthly Dec (in year t- 1), Jan (in 
year t), and Feb (in year t) PDO values. The correlation 
coefficient between the winter PDO and the summer 
SST time series was not statistically significant. 
Analytical techniques 
Scatter and line plots were used to assess temporal 
variation in the average length at maturity and growth 
during each life stage by stock. For the models, each 
time series was scaled and centered by subtracting the 
mean and dividing by the standard deviation. This al- 
lowed for interpretation of the model coefficients as the 
number of standard deviations of change in growth for 
each 1 standard deviation change in the predictor vari- 
able. For example, a coefficient of -0.500 (0.500) indi- 
cates a 50% decrease (increase) in 1 standard deviation 
of the dependent variable (growth) with an increase of 
1 standard deviation in the predictor variable (abun- 
dance, length, or climate). 
We used a transfer function-noise model introduced 
for fisheries by Noakes et al. (1987) to explain varia- 
tion in growth. The growth dynamic model was a re- 
gression equation with an error correction equation. 
The regression equation based on a generalized least 
squares (GLS) method was used to describe growth as 
a function of chum and pink salmon abundance and 
body length at the start of the growing season. The 
error correction model was used to capture additional 
variation in growth due to multicollinearity among cli- 
mate and salmon production. The GLS regression equa- 
tion was given as 
SW i t - ^{Abundance t ) + ^(Abundance t ) 2 
+ P 3 Le?igth t _i + e t , (3) 
where t = year or season; 
SW i t - growth variable at stage i in year t; 
stage i = la, lb, lc, 2, 3, 4; 
Abundance t = a chum and/or pink salmon abundance 
index in year t\ 
Length t _i = the length of the fish at the end of the pre- 
vious growing season; 
P = the coefficient; and 
£ t - the residuals. 
The process encompasses contemporaneous and seri- 
ally correlated sample, observation, and model specifi- 
cation error. To test for domeshaped or asymptotic rela- 
tionships between growth and abundance and climate, 
we added variables for the square of the abundance. 
Degrees of freedom were calculated for the GLS model 
( n-k ) from the number of observations in a time series 
(n) and the number of coefficients in model (k). 
The error correction equation (Eq. 4) was used to 
extract signal from the noisy residuals from the regres- 
sion equation (Eq. 3). A vector autoregression (VAR) 
equation was used to relate contemporaneous values 
of the regression model residuals with lagged values of 
the regression model residuals and lagged values of cli- 
mate indices. In a system of two equations, the single 
VAR equation for two variables was given as 
L = Li t -£t_i + ... + B i e £ t _j + ... + Bp e £f_p 
+ B l x X t _i + ... + B, x X t _j + B px X t _ p + e t , (4) 
where X t = a climate index; 
£ t = a vector time series of the growth dynamic 
equation residuals for the two equations; 
B, ; = coefficients to be estimated; 
X, = a vector of climate indices in time t\ 
p = the maximal lag length; and 
e t = the residuals. 
For the equation, the maximum likelihood estimator 
for the matrix coefficient B was B = V'Z'(Z'Z) -1 where 
Z was a matrix composed of the elements of £ and X. 
Because the estimated coefficients of the VAR were 
conditional on the residuals of the growth model and 
because the estimated coefficients of the growth mod- 
el were inefficient when serial correlation was pres- 
ent, it was necessary to iterate with equations 3 and 
4 until the coefficient estimates of the both equations 
converged to stable values. The degree of freedom for 
the GLS and VAR integrated model were (n-m-/?-p-m), 
where p was the number of lag years and m was the 
number of time series in the VAR equation. We limited 
the maximum lag to 4 years to account for the possible 
direct or indirect effect of generation cycles on growth. 
To test the performance of the models, data were 
partitioned into two sets ( in-sample set and reserved 
observations set). The insample set was used for coef- 
ficient estimation and model specification. The reserved 
observations set was used for model validation. The in- 
sample set consisted of the first approximately 80% of 
the observations. The remaining 20% of the observa- 
tions, reserved observations, were reserved to generate 
outofsample predictions by using coefficients obtained 
for the insample model. Various software programs 
were used in the exploration of the time series, the 
