Environmental and Ecological Statistics

, Volume 3, Issue 2, pp 143–166 | Cite as

Matching species traits to environmental variables: a new three-table ordination method

  • S. Dolédec
  • D. Chessel
  • C. J. F. ter Braak
  • S. Champely


This paper addresses the question of studying the joint structure of three data tablesR,L andQ. In our motivating ecological example, the central tableL is a sites-by-species table that contains the number of organisms of a set of species that occurs at a set of sites. At the margins ofL are the sites-by-environment data tableR and the species-by-trait data table Q. For relating the biological traits of organisms to the characteristics of the environment in which they live, we propose a statistical technique calledRLQ analysis (R-mode linked toQ-mode), which consists in the general singular value decomposition of the triplet (R t D I LD J Q,D q ,D p ) whereD I ,D J ,D q ,D p are diagonal weight matrices, which are chosen in relation to the type of data that is being analyzed (quantitative, qualitative, etc.). In the special case where the central table is analysed by correspondence analysis,RLQ maximizes the covariance between linear combinations of columns ofR andQ. An example in bird ecology illustrates the potential of this method for community ecologists.


Correspondence analysis three-table ordination randomization tests RLQ analysis species-traitenvironment relationships statistical graphics 


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Copyright information

© Chapman & Hall 1996

Authors and Affiliations

  • S. Dolédec
    • 1
  • D. Chessel
    • 1
  • C. J. F. ter Braak
    • 2
  • S. Champely
    • 3
  1. 1.Laboratoire d'Ecologie des Eaux Douces et des Grands Fleuves, URA CNRS No 1974Université Lyon 1Villeurbanne CedexFrance
  2. 2.DLO-Institute for Forestry and Nature Research and DLO-Agricultural Mathematics GroupWageningenThe Netherlands
  3. 3.Institut Universitaire de Technologie STIDMetzFrance

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