Rincon et al.: A Bayesian model with dual-time resolution for estimating abundance of Engraulis encrasicolus 
45 
Figure 4 
Modeled mean population size of second-stage juveniles (number of individuals that are 3 
months old in month t, B t ( 3)), divided by the size of the initial population (i.e., B t (3)/N*) of 
European anchovy (Engraulis encrasicolus) in the Gulf of Cadiz, Spain, during 1996-2004 
(black circles) and juvenile data from Drake et al. (2007) that were not used in the model 
of our study (solid lines). 
CPUE, and acoustics), as well as those that are not (ju¬ 
veniles and length frequencies). Table 3 shows the ca¬ 
pacity of the models to reproduce the yearly evolution 
of juveniles. The dual-resolution performs better than 
the monthly model to estimate juvenile abundance in 
five out of the 8 years and the overall MSE is also bet¬ 
ter (1.57 vs. 1.83, respectively). In addition, the differ¬ 
ence between CPUE residuals for both models is very 
small and can be thought of as an improvement of the 
current model over the former, considering that CPUE 
is the main source of data of the model in Ruiz et al. 
(2009) and the high variance defined in Equation 10. 
This high variance is permissible with some data im¬ 
perfections such as those identified by ICES, for exam¬ 
ple, for CPUE in year 1998. These data imperfections 
are assimilated by this Bayesian exercise with greater 
flexibility than would have been achieved through de¬ 
terministic modeling. Another difference between the 
present model and the Ruiz et al. (2009) model is the 
intimate connection between landings and N t defined 
by Equation 9. This connection decreases the role of 
CPUE in abundance estimation when compared with 
the Ruiz et al. (2009) model, a model that does not in¬ 
clude reported landings data in the observation model 
and relies mainly on CPUE. 
Another enhancement of the current model is the 
possibility of calculating catches as a model output 
which is a preliminary condition for constructing a 
forecast model for management purposes. Albeit the 
small RMSE for observed and estimated catches (5 mil¬ 
lion corresponding to 3.84% of the maximum value of 
observed catches) can be a consequence of the process 
simplification induced by the assumption of constant 
fishing-induced mortality, it shows the goodness of fit 
of the model in a plausible “What if’ scenario: What 
Table 3 
Seasonal performance of 2 models used to incorporate 
an environmentally forced recruitment of European 
anchovy (Engraulis encrasicolus) in the Gulf of Cadiz, 
Spain: the dual-time resolution model of this study and 
the monthly resolution model of Ruiz et al. (2009). Val¬ 
ues are the expected value of the quadratic loss (mean 
squared error [MSE]) between predicted and observed 
juvenile abundance for each of the years when the lat¬ 
ter available. Predictions and observations were stan¬ 
dardized with the mean and variance of the yearly 
model outputs (for 8 years) before MSE was calculated. 
Year 
Current 
model 
Model from 
Ruiz et al.(2009) 
Difference 
1997 
3.3099 
9.4143 
-6.1044 
1998 
0.0721 
0.2029 
-0.1309 
1999 
4.0713 
2.7520 
1.3193 
2000 
2.7627 
0.3107 
2.4520 
2001 
1.2112 
0.0184 
1.1928 
2002 
0.9918 
1.1475 
-0.1557 
2003 
0.2155 
1.4419 
-1.2264 
2004 
0.0016 
0.1662 
-0.1646 
if catches are proportional to the population, and that 
scenario is not far from reality according to the re¬ 
sults from the previously developed Bayesian model. 
Although a proportionality between catches and abun¬ 
dance is not necessarily observed and is the subject 
of hot debate (Pauly et al., 2013), this proportionality 
is frequently observed in short-lived small pelagic fish 
(Lloret et ah, 2004). 
