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Eastern Atlantic and Mediterranean bluefin tuna populations
Sella, 1929; Rodriguez-Roda, 1964; Farrugio, 1981).
However, a few traps caught juveniles (<35 kg), which
do not, unlike the spawners, have similar patterns of
annual migration. In order to be consistent, only the
data on traps fishing spawners were retained for this
analysis. The literature often distinguished between
spawners caught in May during their entrance into the
Mediterranean and spawners caught in July during the
return trip, but for our purposes, the sum of these two
was taken in computing the annual catch.
More than a hundred time-series were gathered, but
only the 54 that were at least 20 years long were finally
used for the analysis (Table 1). Because of missing
values, a few time-series had to be split into several parts kernel filter was used. Further, because it appeared that
(Figure 3). The oldest time-series of trap catches went
back to 1599 for Sicily (‘‘Favignana’’, ‘‘Formica’’), to
1797 for Portugal (‘‘Medo das Casas’’), to 1825 for
Sardinia (‘‘Saline’’, ‘‘Porto Scuso’’, ‘‘Porto Paglia’’,
‘‘Isola Piana’’), and to 1863 for Tunisia (‘‘Sidi Daoud’’).
About one-third of the time-series were more than 50
years long, six spread over more than a century, but 42%
of them were no longer than 30 years. Most of the
Portuguese, Sicilian, Sardinian, and Tunisian series
extended from the second part of the 19th century to the
early 20th century. Spanish and Moroccan series consti-
tuted a particular and problematic case insofar as, unlike
others, they mainly covered the 20th century and started
in 1910 or 1930. For that reason, they only overlapped
Italian, Tunisian, and Portuguese time-series for a few
years (Figure 3).
Methods
The methodological procedure is shown graphically in
Figure 4. The data were log-transformed (natural
logarithm) to stabilize the variance (Sen and Srivastava,
1990). Such a transformation is biologically reasonable
because population dynamics are largely governed by
multiplicative processes (Williamson, 1972). As men-
tioned above, about 8% of the catches were published as
number of barrels or weight. For consistency, the series
in weight or barrels were converted to number of fish,
using simple linear regressions or generalized linear
models over the periods for which catches were
expressed in both number and weight or barrels. The
goodness of fit was always highly satisfactory; the
multiple r2 ranged between 0.75 and 0.97 and the p-value
was always <0.0002.
Time-series were also plagued by some missing values
(lack of data for one or a few successive years either
because the trap was temporarily not set for reasons
such as war, lack of workers, bad environmental con-
ditions, and/or credits, or because records were lost). As
most numerical analyses require time contiguity, missing
values were estimated either from additional infor-
1303
mation available during that period, such as data in
barrels or in weight (see above), or from time-series
modelling. For the latter, empirical analysis was carried
out to determine (1) the most appropriate numerical
method of filling in missing values (while not distorting
the underlying relationships in the data) and, (2) the
number of successive missing values that could be
estimated satisfactorily. Different smoothing methods
(moving average, splines and kernel; S-Plus, 1999) and
autoregressive models (ARIMA; Box and Jenkins, 1976)
were used and compared in terms of performance. When
a significant autoregressive signal was detected, the
ARIMA model was selected on the basis of differences
between estimated and true values, but otherwise a
estimates were reliable up to three continuous missing
values, we restricted completion of missing values to
one, two or three contiguous ones. Finally, 31 of the 54
time-series were considered for the analyses. In 50% of
these, the interpolated values represented 1–5% of the
total observations and only one time-series had >10%
interpolated values (i.e. 14.8%; see also Table 1).
Geographical clustering
To determine homogeneous regions, we classified on the
geographic distance matrix (straight line, km) between
traps. We used a hierarchical classification with flexible
clustering (Lance and Williams, 1967) and grouped the
traps on the criterion of Euclidean distance. This clus-
tering technique successively fuses traps into groups and
groups into larger clusters, starting with the highest
mutual similarity (lowest distance in km), then gradually
lowering the similarity level at which groups are formed.
Filtering
To investigate the general trends of the various time-
series, data were smoothed by Eigen Vector Filtering
(EVF; Colebrook, 1978; Ibanez and Dauvin, 1988). The
method consists of constructing, for each time-series, an
autocovariance matrix by shifting the series between one
and five years (a smoothing window of five years allows
for retention only of medium- to long-term fluctuations,
i.e. >15–20 years). A Principal Components Analysis
(PCA; Hotelling, 1933; Jackson 1986; Legendre and
Legendre, 1998) is then conducted on the autocovari-
ance matrix and the first component of the PCA gives
the trend of that series. In addition to other smoothing
methods (splines, polynomial models, kernel filter,
LOESS, or moving average), the EVF evaluates the
quantitative importance of the trend, which is given by
the percentage of variance explained by the first axis of
the PCA.