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.
Keywords Spatial analysis - Variance decomposition - Boundary detection - Spruce budworm