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Marine Ecology Progress Series

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MEPS 359:11-23 (2008)  -  DOI:

Analysing multiple time series and extending significance testing in wavelet analysis

Tristan Rouyer1,2,*, Jean-Marc Fromentin1, Nils Chr. Stenseth2,3, Bernard Cazelles4,5

1IFREMER, Centre de Recherche Halieutique Méditerranéenne et Tropicale, Avenue Jean Monnet, BP 171, 34203 Sète cedex, France
2Centre for Ecological and Evolutionary Synthesis (CEES), Department of Biology, University of Oslo, PO Box 1066, Blindern, 0316 Oslo, Norway
3Institute of Marine Research, Department of Coastal Zone Studies, Flødevigen Research Station, 4817 His, Norway
4CNRS UMR 7625, École Normale Supérieure (ENS), 46 rue d’Ulm, 75230 Paris cedex 05, France
5IRD, UR 079, GEODES Centre IRD Ile de France, 32 avenue Henri Varagnat, 93143 Bondy cedex, France

ABSTRACT: In nature, non-stationarity is rather typical, but the number of statistical tools allowing for non-stationarity remains rather limited. Wavelet analysis is such a tool allowing for non-stationarity but the lack of an appropriate test for statistical inference as well as the difficulty to deal with multiple time series are 2 important shortcomings that limits its use in ecology. We present 2 approaches to deal with these shortcomings. First, we used 1/ƒβ models to test cycles in the wavelet spectrum against a null hypothesis that takes into account the highly autocorrelated nature of ecological time series. To illustrate the approach, we investigated the fluctuations in bluefin tuna trap catches with a set of different null models. The 1/ƒβ  models approach proved to be the most consistent to discriminate significant cycles. Second, we used the maximum covariance analysis to compare, in a quantitative way, the time–frequency patterns (i.e. the wavelet spectra) of numerous time series. This approach built cluster trees that grouped the wavelet spectra according to their time–frequency patterns. Controlled signals and time series of sea surface temperature (SST) in the Mediterranean Sea were used to test the ability and power of this approach. The results were satisfactory and clusters on the SST time series displayed a hierarchical division of the Mediterranean into a few homogeneous areas that are known to display different hydrological and oceanic patterns. We discuss the limits and potentialities of these methods to study the associations between ecological and environmental fluctuations.

KEY WORDS: Non-stationarity · Multivariate time series · Wavelet clustering · Wavelet significance testing · Surrogates · Maximum covariance analysis

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Cite this article as: Rouyer T, Fromentin JM, Stenseth NC, Cazelles B (2008) Analysing multiple time series and extending significance testing in wavelet analysis. Mar Ecol Prog Ser 359:11-23.

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