Rincon et al.: A Bayesian model with dual-time resolution for estimating abundance of Engraulis encrasicolus 
43 
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Figure 2 
Posterior distributions (solid lines) for the parameters of the model used to incorporate an en¬ 
vironmentally forced recruitment of European anchovy ( Engraulis encrasicolus) in the Gulf of 
Cadiz, Spain. Parameters were the following: population size at the first time step (AT), natural 
mortality (M), fishing-induced mortality iF), effect of strong winds (A), effect of monthly dis¬ 
charges (p), coefficient of variation of recruits (C R ), inverse of the number of fish in a school (f]**), 
Naperian logarithm of monthly catchability log(Q), inverse of the variance for acoustic surveys 
1 / asymptotic length (L„), and somatic growth rate (g ). Dotted lines indicate the prior dis¬ 
tributions, except for parameters L„ and g, for which they represent upper and lower bounds. 
small pelagic populations (Erzini, 2005; Freon et al., 
2005). However, attempts to include the environment 
in Bayesian models of recruitment (Ruiz et al., 2009) 
are hampered by the short time-scale response of early 
stages to environmental forcing. 
The dual-time resolution implemented in this study 
overcomes this handicap. We were able to integrate 
within the same model the traditional formulations 
and parameters of fishery management (e.g., von Ber- 
talanffy growth function, Baranov catch equation, M, 
F ) with advanced tools in oceanographic research (e.g., 
remote sensing) and to perform this merging in a con¬ 
sistent manner with existing data from observations 
made in the field (e.g., CPUE, landings,or acoustic 
data). 
The proposed dual time resolution does not create 
a significant numerical burden for the computational 
effort demanded by a model fully formulated under 
monthly resolution. The weekly forcing of early stages 
is implicitly resolved through the M\ terms (Eq. 1) and 
the whole MCMC sampling is resolved at monthly time 
steps. The computational time required by a monthly 
resolved model is already very high (311 hours in our 
case with a super-computing center, see also Ruiz et 
