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Relationships between the environmental variables and BFT catches were then

investigated in time domain through regression and correlation. Linear regressions were

performed on each pair of BFT/environmental time series that overlapped on a

sufficiently long period (i.e., 80 years minimum). To summarise the results of the

regressions, we could not perform a meta-analysis (e.g. Myers et al., 2001), because of

the non-independence between analyses (i.e., various BFT time series being regressed

against a same climate time series). Therefore, we simply plotted the p-values of the

regressions using the boxplots (S-Plus, 1999), so that we could get an indication of the

distribution of the probabilities. To deal with serial correlation due to long-term

fluctuations, we also fitted linear models using the generalised least squares (GLS, S-

Plus, 1999; Venables and Ripley, 1999). GLS model is a regression in which errors are

allowed to be correlated and/or have unequal variance. Here, errors were specified to

follow an autoregressive process of degree p, that was determined using the partial

autocorrelation function and the goodness of fit of an ARIMA model (Box and Jenkins,

1976; S-Plus, 1999).

Performing linear models on each pair of BFT/environmental time series induces

multiple testing, i.e. the probability of the type I error becomes larger than the nominal

value α (e.g. Legendre and Legendre, 1998). To correct for this, we performed

correlation analyses and applied the Holm’s procedure for non-independent tests to

compute adjusted probabilities values (which may be larger than 1, see Holm, 1979).

Since some time series were not normally distributed, we used the non-parametric

Spearman correlation coefficient (Zar, 1984). Correlation was tested using a Monte

Carlo procedure (10,000 simulations).

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