Landscape Ecology

, Volume 17, Issue 7, pp 637–646 | Cite as

Hierarchical, Multi-scale decomposition of species-environment relationships

  • Samuel A. Cushman
  • Kevin McGarigal


We present an adaptation of existing variance partitioning methods todecompose species-environment relationships in hierarchically-structured,multi-scaled data sets. The approach translates a hierarchical, multi-scaleconceptual model into a statistical decomposition of variance. It uses a seriesof partial canonical ordinations to divide the explained variance inspecies-environment relationships into its independent and confoundedcomponents, facilitating tests of the relative importance of factors atdifferent organizational levels in driving system behavior. We discuss themethod in the context of an empirical example based on forest bird communityresponses to multiple habitat scales in the Oregon Coast Range, USA. Theexamplepresents a two-tiered decomposition of the variation in the bird community thatis explainable by a series of habitat factors nested within three spatialscales(plot, patch, and landscape). This method is particularly suited for theproblems of hierarchically structured landscape data. The explicit multi-scaleapproach is a major step forward from conducting separate analyses at differentscale levels, as it allows comprehensive analysis of the interaction of factorsacross scales and facilitates ecological interpretation in theoretical terms.

Canonical correspondence analysis Hierarchy Partial canonical ordination Species-environment relationships Variance decomposition 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Allen T.F.H. and Starr T.B. 1982. Hierarchy: Perspectives for Ecological Complexity. University of Chicago Press, Chicago, Illinois, USA.Google Scholar
  2. Anderson M.J. and Gribble N.A. 1998. Partitioning the variation among spatial, temporal and environmental components in a multivariate data set. Australian Journal of Ecology 23: 158–167.Google Scholar
  3. Anderson M.J. and Legendre P. 1999. An empirical comparison of permtuation methods for tests of partial regression coefficients in a linear model. J. Stat. Comput. Sim. 62: 271–303.MathSciNetGoogle Scholar
  4. Borcard D. and Legendre P. 1994. Environmental control and spatial structure in ecological communities: an example using oribatid mites (Acari, Orbiatei). Environ. Ecol. Stat. 1: 37–53.CrossRefGoogle Scholar
  5. Borcard D., Legendre P. and Drapeau P. 1992. Partialling out the spatial component of ecological variation. Ecology 73: 1045–1055.Google Scholar
  6. Kotliar N.B. and Wiens J.A. 1990. Multiple scales of patchiness and patch structure: a hierarchical framework for the study of heterogeneity. Oikos 59: 253–260.Google Scholar
  7. Legendre P. and Borcard D. 1994. Rejoiner. Environ. Ecol. Stat. 1: 57–61.CrossRefGoogle Scholar
  8. Legendre P. and Legendre L. 1998. Numerical Ecology. 2nd edn. Elsevier, Amsterdam, The Netherlands.Google Scholar
  9. Liu Q.H. and Brakenhielm S. 1995. A statistical approach to decompose ecological variation. Water, Air, and Soil Pollution 1–4: 61–87.Google Scholar
  10. McGarigal K. and Cushman S.A. 2002. Comparative evaluation of experimental approaches to the study of habitat fragmentation effects. Ecological Applications.Google Scholar
  11. McGarigal K., Cushman S.A. and Stafford S. 2000. Multivariate Statistics for Wildlife and Ecology Research. Springer Verlag, New York, New York, USA.Google Scholar
  12. McGarigal K. and Marks B.J. 1995. FRAGSTATS: spatial pattern analysis program for quantifying landscape structure. Gen. Tech. Rep. PNW-GTR-351., Portland, Oregon, USA.Google Scholar
  13. McGarigal K. and McComb W.C. 1995. Relationships between landscape structure and breeding birds in the Oregon Coast Range. Ecological Monographs 65: 235–260.Google Scholar
  14. O’Neill R.V., DeAngelis D.L., Waide J.B. and Allen T.F.H. 1986. A Hierarchical Concept of Ecosystems. Princeton University Press, Princeton, New Jersy, USA.Google Scholar
  15. Schneider D.C. 1994. Quantitative Ecology: Spatial and Temporal Scaling. Academic Press, San Diego, California, USA.Google Scholar
  16. ter Braak C.J.F. 1986. Canonical correspondence analysis: a new eigenvector technique for multivariate direct gradient analysis. Ecology 67: 1167–1179.Google Scholar
  17. ter Braak C.J.F. 1987. The analysis of vegetation-environment relationships by canonical correspondence analysis. Vegetatio 75: 159–160.Google Scholar
  18. ter Braak C.J.F. 1988. Partial canonical correspondence analysis. In: Bock H.H. (ed.), Classification and Related Methods of Data Analysis., Amsterdam, North-Holland, The Netherlands, pp. 551–558.Google Scholar
  19. ter Braak C.J.F. 1992. Permutation vs. bootstrap significance tests in multiple regression and ANOVA. In: Jockel K.H., Rothe G. and Sendler W. (eds), Bootstrapping and Related Techniques. Springer-Verlag, Berlin, Germany, pp. 79–85.Google Scholar
  20. ter Braak C.J.F. and Prentice I.C. 1988. A theory of gradient analysis. Adv. Ecol. Res. 18: 271–317.Google Scholar
  21. ter Braak C.J.F. and Smilauer P. 1998. CANOCO Reference Manual and User’s Guide to Canoco for Windows: Software for Canonical Community Ordination (Version 4). Microcomputer Power, Ithaca, New York, USA.Google Scholar
  22. Wiens J.A. 1989. Spatial scaling in ecology. Functional Ecology 3: 385–397.Google Scholar
  23. Whittaker J. 1984. Model interpretation from the additive elements of the likelihood function. Appl. Statistics 33: 52–64.Google Scholar

Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • Samuel A. Cushman
    • 1
  • Kevin McGarigal
    • 1
  1. 1.Department of Natural Resources ConservationUniversity of MassachusettsAmherstUSA

Personalised recommendations