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Eastern Atlantic and Mediterranean bluefin tuna populations    1303

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