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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

Abstract

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 

Notes

Acknowledgements

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: http://atoc.colorado.edu/research/wavelets/.

References

  1. Bailey TC, Gatrell AC (1995) Interactive spatial data analysis. Longman Scientific and Technical, Essex, UKGoogle Scholar
  2. Bellier E, Monestiez P, Durbec J-P, Candau J-N (2007) Identifying spatial relationships at multiple scales: principal coordinates of neighbour matrices (PCNM) and geostatistical approaches. Ecography 30:385–399Google Scholar
  3. Blais JR (1983) Trends in the frequency, extent, and severity of spruce budworm outbreaks in eastern Canada. Can J For Res 13:539–547CrossRefGoogle Scholar
  4. Borcard D, Legendre P (2002) All-scale spatial analysis of ecological data by means of principal coordinates of neighbour matrices. Ecol Model 153:51–68CrossRefGoogle Scholar
  5. Bradshaw RHW, Spies T (1992) Characterizing canopy gap structure in forests using wavelet analysis. J Ecol 80:205–215CrossRefGoogle Scholar
  6. Bruce A, Gao HY (1996) Applied wavelet analysis with S-plus. Springer-Verlag, New YorkGoogle Scholar
  7. Candau J-N, Fleming R (2005) Landscape-scale spatial distribution of spruce budworm defoliation in relation to bioclimatic conditions. Can J For Res 35:2218–2232CrossRefGoogle Scholar
  8. Candau J-N, Fleming RA, Hopkin A (1998) Spatiotemporal patterns of large-scale defoliation caused by the spruce budworm in Ontario since 1941. Can J For Res 28:1733–1741CrossRefGoogle Scholar
  9. Cazelles B, Chavez M, De Magny GC, Guégan JF, Hales S (2007) Time-dependent spectral analysis of epidemiological time-series with wavelets. J R Soc Interface 4:625–636CrossRefPubMedGoogle Scholar
  10. Cazelles B, Chavez M, Berteaux D, Ménard F, Vik JO, Jenouvrier S, Stenseth N (2008) Wavelet analysis of ecological time series. Oecologia 156:287–304CrossRefPubMedGoogle Scholar
  11. Cooke BJ, Nealis VG, Regniere J (2007) Insect defoliators as periodic disturbances in northern forest ecosystems. In: Johnson EA, Miyanishi K (eds) Plant disturbance ecology: the process and the response. Elsevier, Amsterdam, pp 487–525Google Scholar
  12. Cressie NA (1993) Statistics for Spatial Data. Wiley, New YorkGoogle Scholar
  13. Csillag F, Kabos S (2002) Wavelets, boundaries, and the spatial analysis of landscape pattern. Ecoscience 9:177–190Google Scholar
  14. Dale MRT, Mah M (1998) The use of wavelets for spatial pattern analysis in ecology. J Veg Sci 9:805–814CrossRefGoogle Scholar
  15. Daubechies I (1992) Ten lectures on wavelets. Society for industrial and applied mathematics, Philadelphia, PAGoogle Scholar
  16. Diggle PJ, Ribeiro PJ (2006) Model-based geostatistics. Springer, New YorkGoogle Scholar
  17. Dungan JL, Perry JN, Dale MRT, Legendre P, Citron-Pousty S, Fortin MJ, Jakomulska A, Miriti M, Rosenberg MS (2002) A balanced view of scale in spatial statistical analysis. Ecography 25:626–640CrossRefGoogle Scholar
  18. Elkie PC, Rempel RS (2001) Detecting scales of pattern in boreal forest landscapes. For Ecol Manag 147:253–261CrossRefGoogle Scholar
  19. Fajardo A, McIntire EJB (2007) Distinguishing microsite and competition processes in tree growth dynamics: an a priori spatial modeling approach. Am Nat 169:647–661CrossRefPubMedGoogle Scholar
  20. Fortin M-J, Dale MRT (2005) Spatial analysis. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  21. Fortin M-J, Jacquez GM (2000) Randomization tests and spatially autocorrelated data. Bull ESA 81:201–206Google Scholar
  22. Goovaerts P, Jacquez GM (2005) Detection of temporal changes in the spatial distribution of cancer rates using local Moran’s I and geostatistically simulated spatial neutral models. J Geograph Syst 7:137–159CrossRefGoogle Scholar
  23. Gray DR, Régnière J, Boulet B (2000) Analysis and use of historical patterns of spruce budworm defoliation to forecast outbreak patterns in Quebec. For Ecol Manag 127:217–231CrossRefGoogle Scholar
  24. Halley JM (1996) Ecology, evolution and 1/f-noise. Trends Ecol Evol 11:33–37CrossRefGoogle Scholar
  25. Holling CS (1992) Cross-scale morphology, geometry, and dynamics of ecosystems. Ecol Monogr 62:447–502CrossRefGoogle Scholar
  26. Howse GM (1995) Forest insect pests in the Ontario region. In: Armstrong JA, Ives WGH (eds) Forest insect pests in Canada. Canadian Forest Service, Ottawa, ON, pp 41–58Google Scholar
  27. Jacquez GM, Maruca S, Fortin M-J (2000) From fields to objects: a review of geographic boundary analysis. J Geogr Syst 2:221–241CrossRefGoogle Scholar
  28. Keitt TH (2000) Spectral representation of neutral landscapes. Landscape Ecol 15:479–494CrossRefGoogle Scholar
  29. Keitt TH, Urban DL (2005) Scale-specific inference using wavelets. Ecology 86:2497–2504CrossRefGoogle Scholar
  30. Kembel SW, Dale MRT (2006) Within-stand spatial structure and relation of boreal canopy and understory vegetation. J Veg Sci 17:783–790CrossRefGoogle Scholar
  31. Levin SA (1992) The problem of pattern and scale in ecology. Ecology 73:1943–1967CrossRefGoogle Scholar
  32. Levin SA (2000) Multiple scales and the maintenance of biodiversity. Ecosystems 3:498–506CrossRefGoogle Scholar
  33. McCullough DG, Werner RA, Neumann D (1998) Fire and insects in northern and boreal forest ecosystems of North America. Annu Rev Entomol 43:107–127CrossRefPubMedGoogle Scholar
  34. McLeod AI, Zhang Y (2008) Improved subset autoregression: with R package. J Stat Softw 28. URL: http://www.jstatsoft.org/v28/i02/
  35. Mi X, Ren H, Ouyang Z, Wei W, Ma K (2005) The use of the Mexican Hat and the Morlet wavelets for detection of ecological patterns. Plant Ecol 179:1–19CrossRefGoogle Scholar
  36. Morris DW (2003) Toward an ecological synthesis: a case for habitat selection. Oecologia 136:1–13CrossRefPubMedGoogle Scholar
  37. Percival DP (1995) On estimation of the wavelet variance. Biometrika 82:619–631CrossRefGoogle Scholar
  38. Percival DB, Walden AT (2000) Wavelet methods for time series analysis. Cambridge University Press, New YorkGoogle Scholar
  39. R Development Core Team (2008) R: a language and environment for statistical computing. Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0, URL http://www.R-project.org
  40. Ribeiro PJ Jr, Diggle PJ (2001) geoR: a package for geostatistical analysis. R-NEWS 1:15–18Google Scholar
  41. Rodionov SN (2006) Use of prewhitening in climate regime shift detection. Geophys Res Lett 33:L12707CrossRefGoogle Scholar
  42. Rosenberg MS (2004) Wavelet analysis for detecting anisotropy in point patterns. J Veg Sci 15:277–284CrossRefGoogle Scholar
  43. Rouyer T, Fromentin JM, Stenseth NC, Cazelles B (2008) Analysing multiple time series and extending significance testing in wavelet analysis. Mar Ecol Prog Ser 359:11–23CrossRefGoogle Scholar
  44. Saunders SC, Chen J, Drummer TD, Crow TR, Brosofske KD, Gustafson EJ (2002) The patch mosaic and ecological decomposition across spatial scales in a managed landscape of northern Wisconsin, USA. Basic Appl Ecol 3:49–64CrossRefGoogle Scholar
  45. Schlather M (2009) RandomFields: simulation and analysis of random fields. R package version 1.3.41. URL: http://CRANR-projectorg/package=RandomFields
  46. Schroeder D, Perera AH (2002) A comparison of large-scale spatial vegetation patterns following clearcuts and fires in Ontario’s boreal forests. For Ecol Manag 159:217–230CrossRefGoogle Scholar
  47. Torrence C, Compo GP (1998) A practical guide to wavelet analysis. Bull Am Meteorol Soc 79:61–78CrossRefGoogle Scholar
  48. Turner MG (1993) A revised concept of landscape equilibrium: disturbance and stability on scaled landscapes. Landscape Ecol 8:213–227CrossRefGoogle Scholar
  49. Wackernagel H (2003) Multivariate geostatistics: an introduction with applications. Springer, BerlinGoogle Scholar
  50. Wiens JA (1989) Spatial scaling in ecology. Funct Ecol 3:385–397CrossRefGoogle Scholar

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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