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logCPUE and used its canonical link function (identity), 
meaning that a proportional rate of change between the 
set of explanatory variables and logCPUE was expected, 
and we evaluated each model’s residuals to verify com- 
pliance with assumptions. To avoid confounding effects, 
we tested multicollinearity in explanatory variables 
through tests of correlation and analysis of variance 
inflating factors. We used only variables with variance 
inflating factors <3 (Zuur et al., 2009). Model formula- 
tions were tested according to our previous knowledge 
of the system. Stepwise addition of terms was con- 
ducted, and we kept only variables that reduced the 
Akaike information criterion (AIC) by at least 2 units 
and that had a significant increase of explained deviance 
(Marin-Enriquez et al., 2020). Also, variables with effec- 
tive degrees of freedom greater than 8 were excluded 
because they are considered highly nonlinear and dif- 
ficult to interpret (Zuur et al., 2009). The model with 
the lowest AIC was considered the best (Burnham and 
Anderson, 2004). Equal fishing power for the entire fleet 
was assumed. 
Variability of length and sex composition The length and sex 
composition of the catch of Pacific hake were assessed by 
using a 2-step approach. First, using GAMs, we repeated 
the analysis previously described to identify significant 
explanatory variables and the nature of the relationship. 
For this purpose, we used only tows for which biometrics 
were recorded (n=469) and estimated the mean SL and 
sex ratio for each one. An index of the natural logarithms 
of sex ratios (logSR) and mean SL were used as response 
variables of the GAMs. 
The second step involved a detailed analysis of the dis- 
tribution of SL in catch related to the factors of sex and 
maturity stage (juvenile or adult) by using a 2-way analy- 
sis of variance with interaction. For significant effects, we 
included the year factor to evaluate temporal consistency. 
A Tukey’s honestly significant difference test was carried 
out to identify level-specific differences. 
Also, we performed a set of chi-square tests to exam- 
ine significant departures from the null hypothesis of an 
equal sex ratio (ratio of the number of males to the num- 
ber of females: 1:1) according to Zar (1999). 
Biometric relationships The length—weight relationship 
(LWR) was estimated by fitting a power model: 
TW =a(SL)?, (2) 
where TW = the total weight (in grams); 
a = the intercept; and 
b = the slope (allometric coefficient). 
Models were fit hierarchically to each data set for Pacific 
hake caught in this study, starting with the full data 
set and continuing with data sets for each sex, maturity 
stage, and year. Parameter optimization for each model 
was conducted by minimizing the residual sum of squares 
(RSS). Statistical differences in the LWR by sex, maturity 
stage, and year were assessed by a series of “extra sum 
of squares” tests (Ritz and Streibig, 2008) defined by the 
following equation: 
_ (RSS(Bo) = RSS, (B,)) / fo - df) (3) 
RSS, / df, 
F 
where F = the Fisher’s parameter; 
df = the degrees of freedom; 
By = the nested model; and 
B, = subset of each model. 
To describe the relationships of TL and fork length (FL) to 
SL, we used linear regression models: 
y=a+b(SL), (4) 
where y = TL or FL. 
Pearson’s correlation coefficient (7) was used to evalu- 
ate the level of association of each pair of variables. The 
existence of differences between males and females for 
each relationship was determined by using analysis of 
covariance. 
All data and statistical analyses were carried out by 
using a significance level of 0.05, Microsoft Excel” 2016 
(Microsoft Corp., Redmond, WA), and statistical software R, 
vers. 3.6.1 (R Core Team, 2019). 
Results 
Catch rate standardization 
Year and the interaction of month and year were the 
most important variables (explained 10.69% of total 
deviance). Also, nonlinear effects (explained by smooth- 
ers) were found between tow speed, mesh size of trawl 
net, depth of tow, and hour of the day of tow in logCPUE 
(Table 1). The final model explained 19.9% of the total 
deviance. Levels of CPUE were higher during tows with 
speeds of 3.50—4.70 km/h (1.89-2.54 kt) and declined 
inversely with speed (Fig. 3A). Tows of trawl nets with 
mesh sizes of 7.62—8.16 cm (3.00—3.25 in) had the highest 
CPUE values, followed by tows of nets with mesh sizes 
of 9.80—10.00 cm (Fig. 3B). Values of CPUE remained 
mostly stable with depth. However, lower CPUE levels 
were observed for tows at depths >280 m, with a conse- 
quent increase in the uncertainty (Fig. 3C). The highest 
CPUE values were recorded during the morning from 
0800 to 1000 with a significant decrease beginning after 
1400 (Fig. 3D). 
Estimated mean CPUE was the highest in 2015 with 
633 kg/h (95% confidence interval [CI]: 484-830 kg/h) and 
the lowest in 2016 with 199 kg/h (95% CI: 158-250 kg/h), and 
estimates indicate less variability for 2017 (529 kg/h [95% 
CI: 368-773 kg/h]), 2018 (379 kg/h [95% CI: 310-464 kg/h]), 
? Mention of trade names or commercial companies is for identi- 
fication purposes only and does not imply endorsement by the 
National Marine Fisheries Service, NOAA. 
