Advertisement

Canonical Ordination

  • Daniel Borcard
  • François Gillet
  • Pierre Legendre
Chapter
Part of the Use R! book series (USE R)

Abstract

Canonical ordination associates two or more data sets in the ordination process itself. Consequently, if one wishes to extract structures of a data set that are related to (or can be interpreted by) another data set, and/or formally test statistical hypotheses about the significance of these relationships, canonical ordination is the way to go. in this chapter, you will learn how to choose among various canonical ordination techniques: asymmetric (RDA, db-RDA, CCA, LDA, PRC and CoCA) and symmetric (CCorA, CoIA and MFA); explore methods devoted to the study of the relationships between species traits and environment; compute them using the correct options and properly interpret the results; apply these techniques to the Doubs River and other data sets; explore particular applications of some canonical ordination methods, for instance variation partitioning and multivariate analysis of variance by RDA; and write your own RDA function.

Bibliography

  1. Abdi, H., Williams, L.J., Valentin, D.: Multiple factor analysis: principal component analysis for multitable and multiblock data sets. WIREs Comput Stat. 5, 149–179 (2013)CrossRefGoogle Scholar
  2. Anderson, M.J.: Distinguishing direct from indirect effects of grazers in intertidal estuarine assemblages. J. Exp. Mar. Biol. Ecol. 234, 199–218 (1999)CrossRefGoogle Scholar
  3. Anderson, M.J.: Distance-based tests for homogeneity of multivariate dispersions. Biometrics. 62, 245–253 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  4. Beamud, S.G., Diaz, M.M., Baccala, N.B., Pedrozo, F.L.: Analysis of patterns of vertical and temporal distribution of phytoplankton using multifactorial analysis: acidic Lake Caviahue, Patagonia, Argentina. Limnologica. 40, 140–147 (2010)CrossRefGoogle Scholar
  5. Benjamini, Y., Hochberg, Y.: Controlling the false discovery rate: a practical and powerful approach to multiple testing. J R Stat Soc B. 57, 289–300 (1995)MathSciNetzbMATHGoogle Scholar
  6. Bernier, N., Gillet, F.: Structural relationships among vegetation, soil fauna and humus form in a subalpine forest ecosystem: a Hierarchical Multiple Factor Analysis (HMFA). Pedobiologia. 55, 321–334 (2012)CrossRefGoogle Scholar
  7. Blanchet, F.G., Legendre, P., Borcard, D.: Forward selection of explanatory variables. Ecology. 89, 2623–2632 (2008a)CrossRefGoogle Scholar
  8. Borcard, D., Legendre, P., Drapeau, P.: Partialling out the spatial component of ecological variation. Ecology. 73, 1045–1055 (1992)CrossRefGoogle Scholar
  9. Carlson, M.L., Flagstad, L.A., Gillet, F., Mitchell, E.A.D.: Community development along a proglacial chronosequence: are above-ground and below-ground community structure controlled more by biotic than abiotic factors? J. Ecol. 98, 1084–1095 (2010)CrossRefGoogle Scholar
  10. Choler, P.: Consistent shifts in Alpine plant traits along a mesotopographical gradient. Arct. Antarct. Alp. Res. 37, 444–453 (2005)CrossRefGoogle Scholar
  11. Dolédec, S., Chessel, D.: Co-inertia analysis: an alternative method to study species-environment relationships. Freshw. Biol. 31, 277–294 (1994)CrossRefGoogle Scholar
  12. Dolédec, S., Chessel, D., ter Braak, C.J.F., Champely, S.: Matching species traits to environmental variables: a new three-table ordination method. Environ. Ecol. Stat. 3, 143–166 (1996)CrossRefGoogle Scholar
  13. Dray, S., Legendre, P.: Testing the species traits-environment relationships: the fourth-corner problem revisited. Ecology. 89, 3400–3412 (2008)CrossRefGoogle Scholar
  14. Dray, S., Pettorelli, N., Chessel, D.: Matching data sets from two different spatial samplings. J. Veg. Sci. 13, 867–874 (2002)CrossRefGoogle Scholar
  15. Dray, S., Chessel, D., Thioulouse, J.: Co-inertia analysis and the linking of ecological data tables. Ecology. 84, 3078–3089 (2003)CrossRefGoogle Scholar
  16. Dray, S., Choler, P., Doledec, S., Peres-Neto, P.R., Thuiller, W., Pavoine, S., ter Braak, C.J.F.: Combining the fourth-corner and the RLQ methods for assessing trait responses to environmental variation. Ecology. 95, 14–21 (2014)CrossRefGoogle Scholar
  17. Escofier, B., Pagès, J.: Multiple factor analysis (AFMULT package). Comput Stat Data Anal. 18, 121–140 (1994)CrossRefzbMATHGoogle Scholar
  18. Escoufier, Y.: The duality diagram: a means of better practical applications. In: Legendre, P., Legendre, L. (eds.) Developments in Numerical Ecology, NATO ASI Series Series, Series G: Ecological Sciences, vol. 14, pp. 139–156. Springer, Berlin (1987)Google Scholar
  19. Ezekiel, M.: Methods of Correlational Analysis. Wiley, New York (1930)zbMATHGoogle Scholar
  20. Faith, D.P., Minchin, P.R., Belbin, L.: Compositional dissimilarity as a robust measure of ecological distance. Vegetatio. 69, 57–68 (1987)CrossRefGoogle Scholar
  21. Geffen, E., Anderson, M.J., Wayne, R.K.: Climate and habitat barriers to dispersal in the highly mobile gray wolf. Mol. Ecol. 13, 2481–2490 (2004)CrossRefGoogle Scholar
  22. Hill, M.O., Smith, A.J.E.: Principal component analysis of taxonomic data with multi-state discrete characters. Taxon. 25, 249–255 (1976)CrossRefGoogle Scholar
  23. Holm, S.: A simple sequentially rejective multiple test procedure. Scand. J. Stat. 6, 65–70 (1979)MathSciNetzbMATHGoogle Scholar
  24. Josse, J., Pagès, J., Husson, F.: Testing the significance of the RV coefficient. Comput Stat Data Anal. 53, 82–91 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  25. Laliberté, E., Paquette, A., Legendre, P., Bouchard, A.: Assessing the scale-specific importance of niches and other spatial processes on beta diversity: a case study from a temperate forest. Oecologia. 159, 377–388 (2009)CrossRefGoogle Scholar
  26. Lamentowicz, M., Lamentowicz, L., van der Knaap, W.O., Gabka, M., Mitchell, E.A.D.: Contrasting species-environment relationships in communities of testate amoebae, bryophytes and vascular plants along the fen-bog gradient. Microb. Ecol. 59, 499–510 (2010)CrossRefGoogle Scholar
  27. Le Dien, S., Pagès, J.: Analyse factorielle multiple hiérarchique. Revue de statistique appliquée. 51, 47–73 (2003)Google Scholar
  28. Lear, G., Anderson, M.J., Smith, J.P., Boxen, K., Lewis, G.D.: Spatial and temporal heterogeneity of the bacterial communities in stream epilithic biofilms. FEMS Microbiol. Ecol. 65, 463–473 (2008)CrossRefGoogle Scholar
  29. Legendre, P., Anderson, M.J.: Distance-based redundancy analysis: testing multi-species responses in multi-factorial ecological experiments. Ecol. Monogr. 69, 1–24 (1999)CrossRefGoogle Scholar
  30. Legendre, P., Gallagher, E.D.: Ecologically meaningful transformations for ordination of species data. Oecologia. 129, 271–280 (2001)CrossRefGoogle Scholar
  31. Legendre, P., Legendre, L.: Numerical Ecology, 3rd English edn. Elsevier, Amsterdam (2012)Google Scholar
  32. Legendre, P., Galzin, R., Harmelin-Vivien, M.L.: Relating behavior to habitat: solutions to the fourth-corner problem. Ecology. 78, 547–562 (1997)Google Scholar
  33. Legendre, P., Oksanen, J., ter Braak, C.J.F.: Testing the significance of canonical axes in redundancy analysis. Methods Ecol. Evol. 2, 269–277 (2011)CrossRefGoogle Scholar
  34. McArdle, B.H., Anderson, M.J.: Fitting multivariate models to community data: a comment on distance-based redundancy analysis. Ecology. 82, 290–297 (2001)CrossRefGoogle Scholar
  35. McCune, B.: Influence of noisy environmental data on canonical correspondence analysis. Ecology. 78, 2617–2623 (1997)CrossRefGoogle Scholar
  36. Miller, J.K.: The sampling distribution and a test for the significance of the bimultivariate redundancy statistic: a Monte Carlo study. Multivar. Behav. Res. 10, 233–244 (1975)CrossRefGoogle Scholar
  37. Oksanen, J., Blanchet, F. G., Friendly, M., Kindt, R., Legendre, P., McGlinn, D., Minchin, P. R., O’Hara, R. B., Simpson, G. L., Solymos, P., Stevens, M. H. H., Szoecs, E., Wagner, H. vegan: Community Ecology Package. R package version 2.5-0. (2017)Google Scholar
  38. Peres-Neto, P.R., Legendre, P., Dray, S., Borcard, D.: Variation partitioning of species data matrices: estimation and comparison of fractions. Ecology. 87, 2614–2625 (2006)CrossRefGoogle Scholar
  39. Pillai, K.C.S., Hsu, Y.S.: Exact robustness studies of the test of independence based on four multivariate criteria and their distribution problems under violations. Ann. Inst. Stat. Math. 31, 85–101 (1979)MathSciNetCrossRefzbMATHGoogle Scholar
  40. Robert, P., Escoufier, Y.: A unifying tool for linear multivariate statistical methods: the RV-coefficient. Appl. Stat. 25, 257–265 (1976)MathSciNetCrossRefGoogle Scholar
  41. ter Braak, C.J.F.: Canonical correspondence analysis: a new eigenvector technique for multivariate direct gradient analysis. Ecology. 67, 1167–1179 (1986)CrossRefGoogle Scholar
  42. ter Braak, C.J.F.: The analysis of vegetation-environment relationships by canonical correspondence analysis. Vegetatio. 69, 69–77 (1987)CrossRefGoogle Scholar
  43. ter Braak, C.J.F.: Partial canonical correspondence analysis. In: Bock, H.H. (ed.) Classification and Related Methods of Data Analysis, pp. 551–558. North-Holland, Amsterdam (1988)Google Scholar
  44. ter Braak, C.J.F.: Fourth-corner correlation is a score test statistic in a log-linear trait–environment model that is useful in permutation testing. Environ. Ecol. Stat. 24, 219–242 (2017)MathSciNetCrossRefGoogle Scholar
  45. ter Braak, C.J.F., Schaffers, A.P.: Co-correspondence analysis: a new ordination method to relate two community compositions. Ecology. 85, 834–846 (2004)CrossRefGoogle Scholar
  46. ter Braak, C., Cormont, A., Dray, S.: Improved testing of species traits–environment relationships in the fourth corner problem. Ecology. 93, 1525–1526 (2012)CrossRefGoogle Scholar
  47. van den Brink, P.J., ter Braak, C.J.F.: Multivariate analysis of stress in experimental ecosystems by Principal Response Curves and similarity analysis. Aquat. Ecol. 32, 163–178 (1998)CrossRefGoogle Scholar
  48. van den Brink, P.J., ter Braak, C.J.F.: Principal response curves: analysis of time-dependent multivariate responses of biological community to stress. Environ. Toxicol. Chem. 18, 138–148 (1999)CrossRefGoogle Scholar
  49. Le, S., Josse, J., Husson, F.: FactoMineR: an R package for multivariate Analysis. J Stat Soft. 25, 1–18 (2008).CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Daniel Borcard
    • 1
  • François Gillet
    • 2
  • Pierre Legendre
    • 1
  1. 1.Département de sciences biologiquesUniversité de MontréalMontréalCanada
  2. 2.UMR Chrono-environnementUniversité Bourgogne Franche-ComtéBesançonFrance

Personalised recommendations