Landscape Ecology

, Volume 25, Issue 6, pp 873–887 | Cite as

Identifying significant scale-specific spatial boundaries using wavelets and null models: spruce budworm defoliation in Ontario, Canada as a case study

  • Patrick M. A. JamesEmail author
  • Richard A. Fleming
  • Marie-Josée Fortin
Research Article


We combine wavelet analysis and multiple null models to identify significant spatial scales of pattern and spatial boundaries in historical spruce budworm defoliation in Ontario, Canada. Previous analyses of budworm defoliation in Ontario over the last two outbreaks have suggested three distinct zones of defoliation. We asked the following three questions: (1) is there statistical support for the existence of these three zones? (2) Are the locations of these boundaries consistent between outbreak periods? And (3) how does boundary identification depend on the spatial null model used? Defoliation data for the two outbreak periods (1941–1965 and 1966–2001), and the combined period (1941–2001) were analyzed using a 1D continuous wavelet transform. Boundaries were identified through comparison of wavelet power spectra of each outbreak period to reference distributions based on three different spatial null models: (1) a complete spatial randomness model, (2) an autoregressive model, and (3) a Gaussian random field model. The Gaussian random field model identified coarser scales of pattern than the autoregressive model. Locally, the Gaussian random field model found significant boundaries similar to those previously described, whereas the autoregressive model only did so for the first outbreak. These results indicate that the coarse scale spatial factors that influenced defoliation were more consistent between outbreaks relative to fine scale factors, and that previously described boundaries were strongly driven by the first outbreak. Wavelet analysis combined with spatial null models provides a powerful tool for identifying non-arbitrary scales of structure and significant spatial boundaries in non-stationary ecological data.


Spatial analysis Variance decomposition Boundary detection Spruce budworm 



Funding was provided by an NSERC-PGS and CFS-NSERC supplement to PMAJ and a NSERC Discovery grant to MJF. We thank Ron Fournier, Tony Hopkin (CFS), Taylor Scarr (OMNR), and the rest of Ontario’s Forest Health Survey for providing the survey data. We thank Jean-Noel Candau and Tim Burns (CFS) for help with data processing and Steve Walker for comments on an earlier version. We also thank three anonymous reviews for their comments that improved the quality of this paper. Wavelet software was originally provided by C. Torrence and G. Compo, and is available at URL:


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Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  • Patrick M. A. James
    • 1
    • 4
    Email author
  • Richard A. Fleming
    • 2
  • Marie-Josée Fortin
    • 3
  1. 1.Faculty of ForestryUniversity of TorontoTorontoCanada
  2. 2.Canadian Forest Service, Great Lakes Forestry CentreSault Ste. MarieCanada
  3. 3.Department of Ecology and Evolutionary BiologyUniversity of TorontoTorontoCanada
  4. 4.Department of Biological SciencesUniversity of AlbertaEdmontonCanada

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