Rincon et al.: A Bayesian model with dual-time resolution for estimating abundance of Engraulis encrasicolus 
41 
stock is very similar to that of the Gulf of Cadiz stock 
(Zarraonaindia et ah, 2012). Further, age 1 reflects 
the average age of most close-by stocks (Pertierra and 
Lleonart, 1996). A large standard deviation was sup¬ 
plied, so that maximum (annual) F values might reach 
the maximum F values reported in the literature for 
the aforementioned stocks (approximately F= 2/year). 
The prior distribution was constrained at the lower 
end to 0.05/month, which corresponds to approximately 
50% of the selected average F value for age 1. The PDF 
for M, for which even less data exist, was based on the 
age-specific M estimates for age-1 anchovy in the near 
Alboran Sea (Giraldez et al. 7 ). Those authors estimat¬ 
ed M according to the ProdBiom method (Abella et al., 
1997) that is based on Caddy (1991). The large vari¬ 
ance assigned to M had an upper boundary of 0.08, 
which would yield theoretical annual mortality rates 
close to M- 1/year, which is 15% higher than the M val¬ 
ue for age-0 anchovy reported from 5 years of surveys 
of an unfished anchovy stock (Gulf of Biscay; ICES 3 ). 
The bounds for growth parameters L e „, <7, , and g 
(logitnorm function) were constructed on the basis of 
a single work performed in the Gulf of Cadiz (Table 2) 
during which biological data were collected fortnightly 
for 4 years on individuals ranging in size from 4 cm TL 
to maximum length. and g extremes were estimated 
directly from that series, whereas bounds for <J, were 
considered uninformative and embraced the mean of 
the standard deviation of L«, also approximated from 
that series. 
The lower bound for A was chosen by considering 
the negative effect of winds on recruitment (Ruiz et 
al., 2006), and the upper bound was chosen on the ba¬ 
sis of a preliminary analysis, in which extreme windy 
conditions from a historical series were considered and 
that would allow a replacement rate of at least one 
recruit per female. This assumption prevents collapse 
in the absence of fishing and adverse environmental 
conditions. 
Constant values used in the model were taken from 
the literature and were based on expert knowledge, 
namely the consensus of two experts, and with the as¬ 
sumption that if data were not available from the same 
stock, they should be taken from the closest (geneti¬ 
cally and geographically) stock that experiences a simi¬ 
lar exploitation pattern. Using data collected during 4 
years in the Gulf of Cadiz (Millan, 1999), we extracted 
constant parameter values including a 1/1 sex ratio 
(sexr=0.5), an average length of maturity equal to 11.2 
cm TL (for females) to define maturity at length class k 
(mor/ k ) (see Table 1), and a=0029 and 6=3.3438 for the 
power length-weight relationship, w k = a( ) b . The 
number of eggs spawned per gram fec =450 eggs/g was 
Working paper of the GFCM-SAC-SCSA working group on 
stock assessment of small pelagic species. Centro Ocean- 
ografico de Malaga, Malaga, Spain. [Available from Centro 
Oceanografico de Malaga, Institute Espanol de Oceanografia, 
Puerto Pesquero, s/n Apdo. 285 29640, Fuengirola (Malaga), 
Spain.] 
approximated from a review on spawning traits of 22 
anchovy stocks in European waters (Somarakis et al., 
2004). 
Data 
The observation model is defined by using quarterly 
data on catch (in numbers of fish) and yearly CPUE 
from January 1988 to December 2004 extracted from 
ICES reports (ICES 2 ’ 8 ’ 910 ). CPUE data were trans¬ 
formed to monthly data with the knowledge that 
most of the anchovy landings occur during the spawn¬ 
ing season. Therefore, it was assumed that CPUE is 
known only for spawning months and is equal to the 
CPUE in the corresponding year. Acoustic estimates 
were provided by ICES (ICES 2 ) for June of years 1993 
and 2004. Length frequency of the catches for the same 
years from ICES annual reports (ICES 2 ’ 8 ’ 9 ’ 10 ) was used 
for validation. Monthly catch (in numbers) and month¬ 
ly length frequency of the catch data resulted from the 
assumption that the same amount of fish is landed ev¬ 
ery month of the quarter and that the third quarter 
has four months. This assumption results in months of 
28 days, 13 months per year approximately, and that 
the 204 months from January 1988 to December 2004 
become 222 months in the process model (7=222). 
The environmental covariates SST, discharges from 
the Alcala del Rio dam, and wind were obtained as fol¬ 
lows: SST was extracted from the advanced very high 
resolution radiometer (AVHRR) sensor data. The night¬ 
time AVHRR PATHFINDER SST v5 weekly means with 
4-km 2 pixel resolution were taken from NASA Physi¬ 
cal Oceanography Distributed Active Archive Center 
(available from website). The region of interest was ac¬ 
quired from the global image, and the arithmetic mean 
was calculated from the SST of all pixels within this 
region. Discharges were provided by Confederacion Hi- 
drografica del Guadalquivir (data available from web¬ 
site). The data correspond to the monthly accumulated 
cubic hectometers that are discharged from the dam 
each month. Wind data represent the weekly accu¬ 
mulated time (in days) that easterlies faster than 30 
km/h have been recorded at the meteorological station 
of Cadiz. 
8 ICES (International Council for the Exploration of the Sea). 
1990. Report of the working group on the assessment of the 
stocks of sardine, horse mackerel and anchovy, Copenhagen, 
20-29 June 1990. ICES CM 1990/Assess:24, 176 p. [Avail¬ 
able from ICES, H. C. Andersens Blvd. 44-46, 1553 Copen¬ 
hagen, Denmark.] 
9 ICES (International Council for the Exploration of the 
Sea). 1995. Report of the working group on the assess¬ 
ment of mackerel, horse mackerel, sardine and anchovy, 
ICES Headquarters, 21 June-1 July 1994. ICES CM 1995/ 
Assess:2, 329 p. [Available from ICES, H. C. Andersens Blvd. 
44-46, 1553 Copenhagen, Denmark.] 
10 ICES (International Council for the Exploration of the 
Sea). 2000. Report of the working group on the assess¬ 
ment of mackerel, horse mackerel, sardine and anchovy, 
ICES Headquarters, 14-23 September 2000. ICES CM 
2Q01/ACFM:06, 456 p. [Available from website.] 
