Ligas et al. : Modeling the growth of recruits of Merluccius mer/uccius in the northwestern Mediterranean Sea 
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TL (cm) 
Figure 2 
Length-frequency distribution of European hake ( Merluccius merluccius) ob- 
tained from 13 stations sampled in the Ligurian Sea and northern Tyrrhenian 
Sea in June 2011 during the Mediterranean International [bottom] Trawl Survey 
(MEDITS). Lengths for fish <18 cm in total length (TL) are shown in size classes 
of 0.5 cm TL. 
to define the length-age relationship with covariates, 
the following equation was used: 
Length = a + f\(Age) + (bottom T) + fgidensity) 
+ f 4 depth) + f 5 (SST) + fglwind) + fq( chl-aj 
+ fg(depth:density)+ factor(Area) + £,, (1) 
where bottom T, density, and depth = the bottom temper- 
ature, European hake recruit density, and depth 
from each station, respectively; and SST, wind , 
and chl-a = sea-surface temperature, scalar wind 
speed and chlorophyll-a concentration averaged 
over the period of January-March 2011. 
To evaluate possible differences in recruit growth 
patterns, the area (Ligurian Sea or Tyrrhenian Sea) 
was included in the analysis and treated as a fac- 
tor (Area). Following the findings by Bartolino et al. 
(2008b), which included observation of a stable pattern 
of depth preference by juvenile European hake, the in- 
teraction between depth and fish density (fg) was also 
included in the GAM. 
Two forms of this model were constructed. With the 
first, a continuous variable of density was assumed; this 
first form was compared with a second model in which 
density was treated as a 3-level factor: low (<2000 in- 
dividuals km -2 ), medium (2000-4000 individuals km -2 ) 
and high (>4000 individuals km -2 ). Then, the fit of 
these models was compared. Analysis of variance was 
used to test for a significant difference in model fit, and 
the model with the lowest Akaike’s information crite- 
rion (AIC) was selected as the best model, which is the 
model that best fits the set of data. 
The degree of collinearity between explanatory vari- 
ables was tested with plots of paired variables (pair- 
plots), a matrix of scatter plots that show the bivariate 
relationships of variables, and variance inflation fac- 
tor (VIF) values (Zuur et al., 2009). Variables with a 
high Pearson’s correlation coefficient (r) (>0.8, absolute 
value) and a high VIF value (>3) were considered cor- 
related, and one of the pair was removed. A backward 
stepwise model selection procedure based on analysis 
of variance and on the AIC was used to identify the 
most parsimonious model with the greatest explanato- 
ry power. The significance of each variable in the GAM 
was determined by means of analysis of variance (F- 
test). The levels of constraints ( k ) for splines were re- 
duced from a maximum, but still achieving convergence 
to 1. The level of constraint for the number of splines 
that were used in the final analysis was selected by a 
comparison of AIC scores. Model residuals were tested 
for assumptions of homogeneity and normality (Zuur 
et al., 2009). A multiple linear regression model that 
used the final selected explanatory variables also was 
compared with the GAM model by using analysis of 
variance and AIC. Data exploration and analyses were 
carried out with the package R, vers. 2.15.2, and the 
associated mgcv package (R Core Team, 2012). An as- 
sumed significance level of 5% was used in all statisti- 
cal analyses. 
