Page 5 - 10.1.1.498.8230
P. 5
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-