Rincon et al.: A Bayesian model with dual-time resolution for estimating abundance of Engraulis encrasicolus 
35 
Durant et al., 2013), but the adoption of these drivers 
for management is not widespread (Freon et al., 2005; 
Freon et al., 2009). 
Intense easterlies, stratification of the water col¬ 
umn, and the influence of the Guadalquivir river have 
been identified as the main environmental factors in¬ 
fluencing early life stages of the European anchovy 
(Engraulis encrasicolus) (Ruiz et al., 2006) in the Gulf 
of Cadiz. The synoptic time-scales of these environmen¬ 
tal forcing variables and the nature of the spawning 
process, with clear, spatially explicit components, sug¬ 
gest that egg and larval abundances can change drasti¬ 
cally within a time scale of days (Catalan et al., 2006). 
Because many environmental databases are structured 
on a weekly basis, both the natural scale of the en¬ 
vironmentally controlled recruitment process and the 
availability of data suggest that it is sensible to model 
these early stages at a weekly resolution. 
However, for small pelagic fish, fishing-induced 
mortality may become a dominant element of popula¬ 
tion dynamics after recruitment (Pinsky et al., 2011; 
Lindegren et al., 2013). Fisheries data are frequently 
structured as monthly statistics in publicly available 
databases. Moreover, the availability of landing data or 
catch per unit of effort (CPUE) data and the decreased 
sensitivity of individual fish to short-term synoptic 
events suggest that it is sensible to model postrecruit 
processes with a time resolution longer than a week. 
The change of time scale for the natural processes gov¬ 
erning the dynamics of clupeoids during ontogenetic 
development poses significant challenges for modeling 
purposes. Restricting the whole model to a resolution 
that is suitable only for postrecruits (e.g., monthly) 
would result in a model that misses the impact of 
oceanographic synoptic events on recruitment. These 
synoptic events have a time scale of the order of days 
but their potential impact can be devastating on the 
survival of eggs and larvae. Ruiz et al. (2009) param¬ 
eterized the impact of synoptic events through the im¬ 
plementation of monthly averages. However, these av¬ 
erages may hide the real impact of synoptic events. For 
instance, in spring or summer, a period of several days 
of calm and sunny weather in the Gulf of Cadiz will 
result in a warming of the sea surface, thereby trig¬ 
gering spawning of species like anchovy. If this event is 
followed by days of intense easterlies, spawning will be 
lost by the advection of eggs by oceanic currents (Ruiz 
et ah, 2006). The time-scale of these synoptic events 
(several days) cannot be resolved by the monthly aver¬ 
ages implemented in Ruiz et al. (2009). A trivial option 
would be to select the maximum resolution (e.g., week¬ 
ly) for the whole life cycle. However, this option may 
render the model numerically intractable owing to the 
large number of time steps involved. A dual resolution 
model, with shorter time steps for earlier stages, offers 
a compromise between the need to resolve the synoptic 
(3-5 September 2001, Cape Town, South Africa). GLOBEC 
Spec. Contrib. 5, 122 p. [Available from website.] 
scale that forces both eggs and larvae and the need to 
keep the numerical burden tractable. 
A dual resolution model should be able to encom¬ 
pass the change in time scales inherent with ontogenic 
development. However, the suitability of such a model 
does not imply the ability to resolve the intrinsic un¬ 
certainty that characterizes ecosystem dynamics. This 
uncertainty demands a probabilistic rather than a de¬ 
terministic approach (Ruiz and Kuikka, 2012). In fish¬ 
ery research, state-space models, a kind of probabilis¬ 
tic model that describes the probabilistic dependence 
between the latent state variables and the observed 
measurements, coupled with Bayesian Markov Chain 
Monte Carlo (MCMC) methods, provide estimates of 
abundance while measuring the uncertainty pervasive 
throughout the life-cycle of individuals. State-space 
models separate the problem into two stochastic mod¬ 
els (Meyer and Millar, 1999; Rivot et al., 2004). The 
first one, the process model, accounts for the unobserv¬ 
able stochastic variations that govern internal popula¬ 
tion dynamics. The second one, the observation model 
describes how the population state is observed and 
with what uncertainty. The linking of these two sto¬ 
chastic models provides consistent simulation of stock 
dynamics and computes uncertainty as a natural out¬ 
put (Punt and Hilborn, 1997; Millar and Meyer, 2000). 
We describe the implementation of a state-space, 
size-structured population dynamics model for ancho¬ 
vy in the Gulf of Cadiz. For this model, it is assumed 
that the environment affects early stages of the life 
cycle at different time scales, and a von Bertalanffy 
growth process provides consistent recruitment and 
length-frequency estimates. The first section of this 
article is devoted to the description of the conceptual 
framework necessary to accommodate a dual resolution 
and environmentally forced formulation into the gen¬ 
eral population dynamics model (GPDM) described in 
Mantyniemi et al. (2015). The second section describes 
the model outputs, and the third section presents a dis¬ 
cussion regarding the validation of our hypothesis and 
the effectiveness of the proposed tool. 
Materials and methods 
For this study, we implemented a Bayesian state-space 
size-structured population dynamics model. This state- 
space model included 2 stochastic models, a process 
model and an observation model. The process model 
has two modules in order to integrate both environ¬ 
mentally forced recruitment and size-structured stock 
dynamics. The first one is applied in this study to the 
environmental conditions in the Gulf of Cadiz but could 
be extended to model the dynamics of other small pe¬ 
lagic fish species whose recruitment is mainly forced by 
the environment during their earliest life stages. The 
second module describes mainly growth and mortal¬ 
ity processes. The observation model requires data on 
catch in numbers, CPUE, and acoustic surveys. The no¬ 
tation for data and model parameters is summarized in 
