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Fishery Bulletin 113(2) 
season, the standardized CPUE was averaged and used 
as an index of stock abundance. We averaged all the 
CPUE data in each month and in the entire fishing 
season as the monthly and annual CPUE, respectively. 
As a result of the high variability of the abundance be- 
tween years, and because the variance might vary with 
the annual mean, the CPUE values were log-trans- 
formed to dampen variation before statistical modeling. 
Environmental data 
Our environmental data included subsurface seawa- 
ter temperatures (at a depth of 5 m), bottom seawater 
temperatures, the Southern Oscillation index (SOI), 
and the AAO index. All the environmental data were 
downloaded from databases at various websites. Sea- 
water temperature data within the study area were 
obtained from the International Research Institute for 
Climate and Society (IRI) ); we used the version 
of this data set that was re-analyzed by Carton and 
Giese (2008) by using Simple Ocean Data Assimilation 
(SODA) with a spatial resolution of 0.5° longitude by 
0.5° latitude. Time series of seawater temperature data 
were available until 2007. The SOI and AAO index 
were downloaded from the NOAA Climate Prediction 
Center website (SOI: AAO index: ) and 
were available for the period from 1984 through 2010. 
Subsurface and bottom seawater temperature data 
from 2 reference locations, south (50°S, 60°W) and 
north (36°S, 53°W), were used to represent the envi- 
ronmental conditions of the northern and southern 
fishing grounds on the Patagonian shelf. The northern 
location was near the inferred hatching zone (Waluda 
et a!., 2001a) and where paralarvae of Argentine short- 
fin squid have been found during July and December 
(Haimovici et al., 1998). The southern location was po- 
sitioned almost at the center of the heavy fishing area 
where squid have been found to be densely distributed 
(Arkhipkin and Middleton, 2002; Chen et al., 2007a; 
Haimovici et al., 1998; Sacau et al., 2005; Waluda et 
al., 2004). Monthly seawater temperatures at the 2 
reference locations were calculated by averaging the 
water temperatures, from the IRI database, at 4 sur- 
rounding data points. 
Data analysis 
We used an autocorrelation analysis to determine 
whether any intrinsic (previous abundance) factors af- 
fected squid abundances (Pierce and Boyle, 2003). A 
correlation analysis performed with Pearson’s correla- 
tion coefficient was used to assess which environmental 
variables were correlated with natural log-transformed 
CPUE (logU). Time lags can exist between environ- 
mental conditions and abundances (Chen et al., 2007a; 
Waluda et al., 1999 ); therefore, to look for potential ef- 
fects of time lags, the logU data were tested for envi- 
ronmental variables with models having no time lag 
with the current fishing season, having a lag of the 
previous year (lag 1) of the fishing season, and hav- 
ing a lag of the previous 2 years (lag 2) of the fishing 
season. Because the fishing season begins in November, 
the current fishing year in this research was defined 
from the previous November to the current October of 
a given year. 
Generalized linear model (GLM) analysis was used 
to extract empirical relationships between logU and 
environmental variables. The effects of environmental 
variables at the 3 time lags were incorporated into the 
GLM models. The model form is given by the following 
equation: 
logU t = intercept -i - E 1)t .j + E 2 ,t-j + ••■+ + C 
e ~ N(0, a 2 ), 
where logC/t = the natural log-transformed annual 
CPUE in year t (log (U) ~ Nip, o 2 )); 
•Ei,t-j = the environmental variable i in the year 
t with year lag j. 
The backward stepwise procedure was used to identify 
a useful subset of predictors. We used P-value, coef- 
ficient of multiple determination ( R 2 ), and Akaike’s in- 
formation criterion (AIC) to select variables. The vari- 
ables were added if P- values were <0.15 and removed 
if P- values were >0.15. To avoid over-fitting or unduly 
complex models, we included variables only if they add- 
ed 5% or more to the R 2 (Pierce and Boyle, 2003). We 
also calculated the AIC to select optimal model 8 - 
The variance inflation factor (VIF) test was used 
to exam any multiple colinearity between variables. 
The variables for which the VIF value was >2 were 
removed from the model. To verify the stability of the 
variables in the GLM models, a progressed time series 
data set from 1998 through 2007 was used to build the 
GLM models year after year. The baseline GLM model 
was built with fishing data from 1986 through 1998; 
then, the next year’s fishing and environmental data 
were added, and a new GLM model was built to in- 
clude them. This process was repeated with data until 
2007. The software used to develop these analyses was 
R (vers. 3.1.1; R Core Team, 2014) and the rms package 
(Harrell, 2014). 
Results 
Abundance i ndex patterns 
The range of average CPUE in each year between 1986 
and 2010 was 2.2-27.0 tons per vessel per day (t-v _1 - 
d -1 ), with an average of 11.3 t/vd. The annual CPUE 
peaked in 1999 and 2008, and decreased quickly after 
both peaks (Fig. 2). Autocorrelation analysis of logt/ 
showed no significant correlation between years. It 
indicated that catch had no interannual interactions 
(Fig. 3). The monthly CPUE- data between 1986 and 
2010 indicated that the entire fishing season was from 
November through September, and the main fishing pe- 
riod was January- June (Fig. 4). There were few catches 
in September and none in October. The monthly CPUE 
