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A primer on the study of transitory dynamics in ecological series using the scale-dependent correlation analysis

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Abstract

Here we describe a practical, step-by-step primer to scale-dependent correlation (SDC) analysis. The analysis of transitory processes is an important but often neglected topic in ecological studies because only a few statistical techniques appear to detect temporary features accurately enough. We introduce here the SDC analysis, a statistical and graphical method to study transitory processes at any temporal or spatial scale. SDC analysis, thanks to the combination of conventional procedures and simple well-known statistical techniques, becomes an improved time-domain analogue of wavelet analysis. We use several simple synthetic series to describe the method, a more complex example, full of transitory features, to compare SDC and wavelet analysis, and finally we analyze some selected ecological series to illustrate the methodology. The SDC analysis of time series of copepod abundances in the North Sea indicates that ENSO primarily is the main climatic driver of short-term changes in population dynamics. SDC also uncovers some long-term, unexpected features in the population. Similarly, the SDC analysis of Nicholson’s blowflies data locates where the proposed models fail and provides new insights about the mechanism that drives the apparent vanishing of the population cycle during the second half of the series.

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Acknowledgements

We thank S. Pueyo, J.J. Camarero, J. Piera, F. Bartomeus, and X. de Pedro at the Department of Ecology (Universitat de Barcelona, UB) for their fruitful discussions during the development of the SDC method. We gratefully acknowledge M. Pascual, R. Solow, E. Ranta, C. Osenberg, A. Steward-Oaten, and two anonymous reviewers for their useful comments on preliminary versions of this manuscript. We also especially thank Parc Científic de Barcelona (UB), Servei Meteorològic de Catalunya, CIRIT (ACES98 29/7), Moelco (Research branch), and BATMARE (Marie Curie Training Site at the Institutt for fiskeri- og marinbiologi, Universiteten i Bergen, EVK3-CT-2000-57129) for support, funding, and computing facilities. NAO and ENSO indices were kindly provided by the Climate Analysis Section, NCAR, Boulder, Colo., USA (Hurrel 1995). Nicholson’s blowflies and North Sea zooplankton series can be found, respectively, at the URLs of the Monash University and the Sir Alister Hardy Foundation for Ocean Sciences (SAHFOS). Wavelet software (http://paos.colorado.edu/research/wavelets/) was provided by C. Torrence and G.P Compo.

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  1. Climate Research Laboratory, Parc Científic de Barcelona, Universitat de Barcelona c/Baldiri Reixach, 4-6 (Torre D), 08028, Barcelona, Catalonia, Spain

    Miquel Àngel Rodríguez-Arias & Xavier Rodó

  2. Systems Ecology Group, Institutt for fiskeri-og marinbiologi, Universiteten i Bergen, Høyteknologisenteret, Thormøhlens Gate 55, P.O. Box 7800, 5020 , Bergen, Norway

    Miquel Àngel Rodríguez-Arias

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Rodríguez-Arias, M.À., Rodó, X. A primer on the study of transitory dynamics in ecological series using the scale-dependent correlation analysis. Oecologia 138, 485–504 (2004). https://doi.org/10.1007/s00442-003-1464-4

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