Lopez et al.: A model for estimating biomass of fish species associated with fish aggregating devices 
173 
the summary statistics of the absolute 
errors (Table 2). 
Results 
Accuracy of estimated tuna biomass 
To evaluate the accuracy of both our 
methods and those of the manufac- 
turer, corrected tuna biomass esti- 
mates obtained by each method were 
compared with the biomass estimates 
from the purse-seine catch on these 21 
DFADs. The r and r 2 and the main sta- 
tistics of the errors for each corrected 
biomass estimates obtained through 
the different correction functions are 
shown in Table 2. Results showed that 
all the methods performed similarly, 
significantly improving the accuracy 
of prediction values compared with 
the manufacturer’s method. Despite 
the similar values obtained for all the 
corrected predicted biomasses from 
the different regression models, the 
GAM corrected model was selected as 
the potential main model selection of 
this study on the basis of its statisti- 
cal robustness and consistency (Wood, 
2006). Table 3 and Figure 6 show the 
final biomass estimates and the box- 
plot of the distribution of the error for 
the manufacturer’s method and the 
GAM-corrected method developed by 
the authors. Maximum biomass esti- 
mation error ranged from -69 to 101 
t (median and standard deviation [SD] 
of -4 ±33.9 t) for the manufacturer’s 
method and from -30.12 to 24.80 t 
(with a median and SD of 1.23 ±13.74 
t) for the GAM corrected method. 
Thus, the original error variability 
(SD=33.9) was significantly reduced 
by -60% (SD=13.74) and the ranges 
of underestimation and overestimation 
were diminished by -55% and -75%, 
respectively. Additionally, the original 
r and r 2 values were also considerably 
improved from 0.50 and 0.25 to 0.90 
and 0.82, respectively. 
Nontuna biomass estimates 
Because the crew was conducting regu- 
lar fishing trips with no observer, we 
could not use catch data on in situ 
nontuna species to test the accuracy of 
the predicted biomass for this group. 
However, the average value of non- 
0 5 10 15 20 
Predicted biomass (t) 
Figure 5 
Regressions obtained through different methods (generalized additive model 
[GAM], generalized linear model [GLM], and polynomials of order 2 [POL] 
and 3 [POL3] ) between uncorrected predicted biomass and absolute errors 
for the 21 samples collected by a commercial Spanish purse seiner in the 
central and eastern Atlantic Ocean between 2009 and 2011. Specific equa- 
tions used in the present study are provided in the Defining an error func- 
tion section. Regressions were used to correct and adjust the uncorrected 
biomass to the real catch. 
Table 2 
Summary statistics (med=median; min=minimum; max=maximum; 
SD=standard deviation) of the absolute errors (in metric tons [t] ) for 
the final biomass estimations corrected through different regression 
models (GLM=generalized linear model; POL=polynomial of order 2; 
POL3=polynomial of order 3; GAM=generalized additive model) and the 
corresponding coefficients of correlation (r) and determination (r 2 ), when 
the statistics were compared with real catches. 
Error 
Before 
correction 
Manu- 
facturer 
GLM 
POL 
POL3 
GAM 
med (t) 
-18.57 
-4 
-1.18 
0.54 
2.18 
1.23 
min (t) 
-130 
-69 
-31.67 
-30.80 
-34.43 
-30.12 
max (t) 
-6 
101 
35.23 
23.68 
22.30 
24.80 
SD (t) 
28.22 
33.87 
16.77 
13.96 
13.38 
13.74 
Parameter 
r 
0.85 
0.50 
0.85 
0.90 
0.91 
0.90 
r 2 
0.73 
0.25 
0.73 
0.81 
0.83 
0.82 
