36 
Fishery Bulletin 11 6(1) 
Table 1 
List of symbols used in the specification of the Bayesian state-space model, a kind of probabilistic model that describes the 
probabilistic dependence between latent state variables and the observed measurements, used to incorporate an environ¬ 
mentally forced recruitment for European anchovy ( Engraulis encrasicolus) in the Gulf of Cadiz, Spain. TL=total length. 
Symbol 
Description 
Indexes 
k and I 
Size class, k,l= 1,...,6 
t 
Month, t=l,...,222 
j 
Week, . 7 = 1 ,...,4 
i 
Age (months), specified only for individuals between 3 and 5 months old 
Data 
T ] 
t 
Sea-surface temperature during week j in month t (°C) 
w> 
Number of days that strong easterlies have blown during week j in month t 
D t 
Discharges from Alcala del Rio dam at month t (hm 3 ) 
CPUE t 
Catch per unit of effort at month t (tons/fishing trip) 
A t 
Stock abundance from acoustic surveys in month t (numbers) 
c t 
Catch in numbers at month t 
Parameters 
A 
Parameter for the effect of easterlies 
P 
Parameter for the effect of discharges 
Cr 
Coefficient of variation of recruitment process 
Q 
Monthly catchability (fish caught per unit of effort) 
Asymptotic length (cm TL) 
Standard deviation for the size of large individuals (cm TL) 
g 
Monthly somatic growth rate 
F 
Monthly fishing mortality 
M 
Monthly natural mortality 
N* 
Initial population (numbers) 
r/** 
Inverse of the number of fish in a school (numbers/s) 
Oa 
Standard deviation for acoustic surveys 
It 
Column vector of size-class frequencies after recruitment at time t 
Fixed parameters 
minLinf, maxLinf 
Bounds for L„ in cm TL (see Table 2) 
minsdLinf, maxscLLinf Bounds for <7 L in cm TL (see Table 2) 
ming, maxg 
Bounds for the expected somatic growth rate (see Table 2) 
W k 
Weight (g) for a fish in size class k (a=00029, 6=3.3438) 
fee 
Number of eggs per gram spawned by a female fec= 450 eggs/g 
sexr 
Proportion of females in the population, sexr=0.5 
matk 
Maturity at length k. If fish in size class k is mature (>11.2 cm TL) is equal to 1, or, 0 otherwise 
Other parameters 
B t (i) 
Number of anchovies between i and 7 + 1 months old at time t 
N t 
Population of individuals more than 5 months old (numbers) in the stock at month t 
Rt 
Recruits at month t (numbers) 
d t 
Death of fish at month t (numbers) 
s t 
Proportion of the population that survives to the next month t+1 
Pt 
Survival probability 
<7t 
Proportion of caught fish to dead fish at month t 
Table 1 and a formal graphical representation is pro¬ 
vided in Figure 1 (an informal and illustrative diagram 
is available from the following website). 
Process model 
We present below a weekly resolution model to explain 
mathematically the dynamics of anchovy eggs and lar¬ 
vae in the Gulf of Cadiz. The model includes the effect 
of the environment on these early life history stages 
and it is designed to be embedded in a GPDM that 
runs with longer time steps. 
Environmentally forced recruitment According to the 
anchovy spawning dynamics described in Motos et al. 
(1996) and Garcia and Palomera (1996), it is reason¬ 
able to consider that the production of anchovy eggs 
in the Gulf of Cadiz occurs when there is a sea-sur¬ 
face temperature (SST) increase of at least one degree 
(°C) between consecutive months and the temperature 
