Oecologia (2004) 138: 485–504 DOI 10.1007/s00442-003-1464-4 METHODS Miquel Àngel Rodríguez-Arias . Xavier Rodó A primer on the study of transitory dynamics in ecological series using the scale-dependent correlation analysis Received: 6 July 2003 / Accepted: 12 November 2003 / Published online: 31 January 2004 # Springer-Verlag 2004 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. Keywords Ecological series . Transitory dynamics . Discontinuities . Ecological interactions . Environmental forcing The study of transitory dynamics in ecological series The analysis of temporal and spatial ecological series has typically focused on the detection and extraction of permanent signals (trends and stable oscillations) and on the explanation of the remaining residuals (Platt and Denman 1975; Chatfield 1989; Legendre and Fortin 1989). Trends, stable cycles, and structured residuals are the signature of permanent ecological processes such as those encountered in population dynamics, ecological interactions, or studies of environmental forcings (Butler 1953; Steele 1978; Broomhead and King 1986; Powell and Steele 1995). Transitory signals Sometimes important signatures laid by a process inter- acting with a variable of interest, hereafter referred to as signals, can be non-permanent because ecological pro- cesses do not remain constant and might be subject to changes. Figure 1 shows the natural series we will study. The three series display stable oscillations corresponding to the annual cycle in North Sea zooplankton (Fig. 1A, B) and to an internal population cycle in the blowflies experiment (Fig. 1C), but also they contain a large fluctuating behavior raising non-permanent features. Co- pepod populations show, apparently at random, periods of high and low summer abundance peaks (Fig. 1A, B). The annual cycle of total copepod abundance changed gradually after 1960 (Fig. 1A), while the abundance of Calanus decreased considerably during the period of study (Fig. 1B) and, after 1970, even failed sometimes to develop the annual cycle. Similarly, blowfly populations (Fig. 1C) display a clear cycle the first year, behave at random the next 10 months, and afterwards recover a periodic-like dynamics at the end of the experiment (Stokes et al. 1988). Signals manifest in ecological series only when the forcing process (the driver) exceeds the minimum intensity threshold that originates a response in the system. The M. À. Rodríguez-Arias . X. Rodó (*) Climate Research Laboratory, Parc Científic de Barcelona, Universitat de Barcelona c/Baldiri Reixach, 4-6 (Torre D), 08028 Barcelona, Catalonia, Spain e-mail: xrodo@pcb.ub.es M. À. Rodríguez-Arias Systems Ecology Group, Institutt for fiskeri-og marinbiologi, Universiteten i Bergen, Høyteknologisenteret, Thormøhlens Gate 55, P.O. Box 7800, 5020 Bergen, Norway