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1308 C. Ravier and J.-M. Fromentin
Tunisia, Sicily and Sardinia (Table 1). These five
areas were gathered within two main areas, the area
around Gibraltar, and the eastern end of the western
Mediterranean. The most productive traps were on the
southern coasts of Spain and Portugal (Figure 1). They
caught 4300 tuna per year (median value). The most
productive trap was ‘‘Barbate’’ which caught about
16 000 tuna annually, and the least productive was
‘‘Ramalhete’’, which caught about 1100 bluefin tuna
annually. Some traps at the eastern end of the western
Mediterranean were also productive; the median annual
catches (for the period 1880–1930) were about 6200 tuna
for the Tunisian trap ‘‘Sidi Daoud’’, 3800 and 3000 tuna
for the Sardinian ‘‘Porto Scuso’’ and ‘‘Isola Piana’’
respectively, and 3000 and 5200 tuna for the Sicilian
‘‘Formica’’ and ‘‘Favignana’’ respectively.
Amplitude of fluctuations
Trap catches displayed remarkable temporal fluctua-
tions: coefficients of variation of the 54 series of trap
catches ranged from 0.49 to 1.33 (Table 1). The ampli-
tude of variation between periods of low (1690–1710,
1790–1810, 1910–1930) and high abundance (1630–1650,
1750–1770, 1870–1890) was large, with factors of 2–4 on
Tunisian, Sicilian, and Sardinian traps and 4–7 on
Portuguese traps (Figure 5). For example, mean annual
catches of the ‘‘Formica’’ trap were only 1000 tuna in
periods of low abundance and up to 3500 tuna during
periods of high abundance.
Patterns of periodicity
Quick visual inspection of the series of trap catches
indicated periodic fluctuations of about a century; they
are clearly outlined by Eigen Vector Filtering (Figure 5). son, smoothing time-series of random numbers would
On the three longest series (Sicilian traps ‘‘Formica’’,
‘‘Favignana’’, and ‘‘Bonagia’’), years of high annual
catches (1630–1650, 1750–1770, 1870–1890) alternated
with years of low annual catches (1690–1710, 1790–
1810, 1910–1930), with a period of about 100–120 years.
The other long time-series (‘‘Porto Scuso’’, ‘‘Isola
Piana’’, ‘‘Porto Paglia’’, ‘‘Medo das Casas’’) also dis-
played pseudo-cyclic variation of about 100–120 years,
with a peak at the end of the 19th century, which was
common to all traps.
More careful inspection revealed a shorter cycle
of about 15–25 years superimposed on the 100-year
fluctuations (Figure 5). This secondary periodicity was
further investigated by spectral analysis on the 12 series Sicilian time-series declined in parallel, then increased up
more than 80 years long (from ten different traps,
‘‘Favignana’’ and ‘‘Formica’’ being split up in two parts
because of missing values). To summarize the patterns of
periodicity, a PCA was performed on these 12 series of
spectral densities. The first principal axis encompassed
67% of the variance, so it captured the bulk of the
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0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Frequency (year–1)
Figure 6. Plot of the first principal component of the PCA,
computed on the spectral densities of the 12 time-series >80
years long. This axis encompassed 67% of the total variance
and depicted a main peak at around 0.035–0.07 year 1, i.e. a
cycle of about 15–30 years.
variability. It displayed a peak for frequencies around
0.05 year 1 (0.035–0.07 year 1) i.e. periods
around 20 years (30–15 years; Figure 6). All 12 series
were highly positively correlated with this axis (r>0.7),
confirming the cycle to be common to all the series. The
two following axes explained only 11 and 8% of the total
variability, respectively, and detected short-term fluctua-
tions. Hence, temporal variability may be decomposed
into three main components: (i) pseudo-cyclic fluctua-
tions of about 100–120 years, (ii) cycles around 20 years,
and (iii) annual fluctuations.
Importance of the trends
The percentage of variance explained by medium- to
long-term fluctuations (d15 years) was high for most of
the series (Table 1). The trends represented an average of
51% of the total variance in the series, and about 68%
when the series were longer than 80 years (for compari-
lead to a trend explaining 20–30% of the total variance).
As expected, the percentage of variance attributable to
the low frequency is related to the length of the series;
the longer the series, the greater the percentage of
variance. Although, the year-to-year fluctuations
appeared non-negligible (Figure 5), they remained sec-
ondary in comparison to the long- and medium-term
fluctuations.
Synchrony of the series
Simple graphical observation of the time-series shows
synchrony between the long-term fluctuations of the
different traps (Figure 5). From 1620 to 1700, the three
to 1750 before declining again until 1800. The time-
series covering the 19th and 20th centuries also dis-
played synchrony, with low catches in the early 19th
century, then an increasing trend from 1850 through the
end of the 19th and into the early 20th centuries.