Page 9 - Lloreta_alii_2001

METHODS

The total annual trap catches are given in number of tuna and were log-

transformed (natural logarithm) to stabilise the variance (Sen and Srivastava, 1990). To

test for relationships between BFT and environmental data, we first computed spectral

analyses to compare patterns of variability in the frequency domain. Spectral analysis

transforms each time series into a sum of sine and cosine functions of different period

lengths (Wei, 1990). The raw periodogram is the usual way to summarise this

decomposition and we calculated it using the fast Fourier transform algorithm (Matlab

6.5, 2002). However, it is a poor statistical descriptor of the spectral density since it has

a large variance and it is not consistent (Bjørnstad et al., 1996; Priestley, 1981). We

therefore used a Parzen smoothing window (Priestley, 1981) and compared the

smoothed spectra. Spectral analysis can only be applied on continuous time series (i.e.,

without missing values) displaying constant intervals. All the time series have constant

annual intervals, but 5 BFT time series (i.e., Medo das Casas, Favignana, Formica,

Bonagia and Saline) are impaired with large gaps (see Figure 2). For these series, we

applied spectral analysis over the longest continuous period (being at least 80 years

long, Tables 1). Spectral analysis also assumes stationary (time independence of the

mean and variance of the series, Priestley, 1981). Most of the series used in this study

were stationary, but 5 of them presented a general upward trend (e.g. Cadix temperature

time series). Approximate stationarity is commonly obtained by the first order

difference, but this procedure suppresses medium to long-term variations. As we

focused on long-term variations, we decided to perform spectral analyses on raw data,

although this procedure was not totally consistent from a statistical viewpoint for these

5 time series. However, our purpose is simply descriptive and not inferential.

10