40 
Fishery Bulletin 11 6(1) 
Table 2 
Prior probability density functions assigned to the parameters to reflect previous knowledge 
for the Bayesian state-space model used to incorporate environmentally forced recruitment of 
European anchovy (Engraulis encrasicolus ) in the Gulf of Cadiz, Spain. When the reliability 
of previous information was considered weak, large variance distributions were selected; such 
a situation is known as a vague prior, and parameters with a vague prior received a label of 
“vague” in this table. If there was enough information in the literature, the prior selected is 
more informative and the literature source is given in this table. The parameter pLinf is such 
that L„=minLinf +(maxLinf - minLinf)pLinf, and analogously g=ming+(maxg-ming)pg and G t 
— minsdLinf+lmaxsdLinf - minsdLinf)psdLinf 
Parameters 
Prior probability 
density function 
Comments 
\ 
-Unifl 0,2) 
Vague 
P 
~1V(0.1,0.1) 
Ruiz et al. (2009) 
Dr 
-Unifl 0,3) 
Vague, Mantyniemi et al. (2009) 
7 r 
-Beta(l,l) 
Mg\ 
-Ga mma(0. 001,0.001) 
In (F) 
~A(ln(0.09),0.04)llF>0.05| 
Giraldez et al. (2009) 
In (M) 
~Mln(0.035),0.05)l(M<0.08) 
Giraldez et al. (2009) 
N* 
~Mln(l),10000) 
Vague 
pLinf 
~Logitnorm(0,l) 
maxLinf=20 
Bellido et al. (2000) 
minLinf= 18 
Bellido et al. (2000) 
Pg 
~Logitnorm(0,l) 
maxg= 0.08 
Bellido et al. (2000) 
ming= 0.05 
Bellido et al. (2000) 
psdLinf 
~Logitnorm(0,l) 
maxsdLinf=3 
minsdLinf=0. 1 
ln(Q) 
~Mln( 2000000),500) 
h 
-Dirich ([ 1/1,2/2,... ,K/K] ) 
correspond to logical and stochastic dependencies, re¬ 
spectively. If parameter A follows a distribution depen¬ 
dent on parameter B, there is a solid arrow pointing 
from B to A. If parameter A is a function of parameter 
B, there is a dotted arrow pointing from B to A (Meyer 
and Millar, 1999). For example, in Figure 1, the rela¬ 
tionship of catches (c t ) with dead individuals (d t ) and 
the total probability of being caught ( q t ) is detailed in 
Equation 9. 
Priors 
After an extensive literature search on parameter val¬ 
ues for this particular species and area, the data were 
filtered, preprocessed, and interpreted in terms of reli¬ 
ability by those with an expert knowledge. This meth¬ 
od implied an initial inspection of the data distribution 
and the metadata. If, for example, the age structure 
from one particular data set was markedly different 
with respect to that from the Gulf of Cadiz, those data 
were excluded. Secondly, if the final filtered available 
data were of poor quality (e.g., produced with a dubious 
method), the probability density functions (PDFs) were 
built in a conservative way and at a level of reliability 
that determines the amount of information provided by 
the prior distributions (Table 2). When the reliability of 
previous information was considered weak, large vari¬ 
ance distributions were selected. In general, the use of 
the lognormal distribution was considered adequate for 
informative priors given the underlying variability and 
the scarcity of such data. The source of information to 
derive biological and exploitation-related data was an¬ 
chovy stocks from European waters and expert-knowl¬ 
edge on those stocks. All parameters were restricted to 
positive values that were consistent with the processes 
described. For some parameters (e.g., p), the PDF was 
modeled according to previous research, whereas for 
others, such as natural and fishing-induced mortal¬ 
ity (F and M), no reliable information was available 
for the area; hence selected information from similar 
stocks was used. 
Identical monthly distributions for F were chosen 
on the assumption of a mean annual F of 1.1 corre¬ 
sponding to age-1 fish in the close-by Alboran Sea stock 
(Giraldez et al. 7 ). The genetic structure of Alboran Sea 
7 Giraldez, A., P. Torres, L. F. Quintanilla-Hervas, J. M. Bel- 
lido-Millan, F. Alemany, and M. Iglesias. 2009. Anchovy 
(Engraulis encrasicolus) stock assessment in the GFCM 
geographical sub-area GSA 01, Northern Alboran Sea, 18 p. 
