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

Abstract

This paper addresses the question of studying the joint structure of three data tables R, L and Q. In our motivating ecological example, the central table L 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 of L are the sites-by-environment data table R 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 called RLQ analysis (R-mode linked to Qmode), which consists in the general singular value decomposition of the triplet (RtDILDjQ,Dq,Dp) where DI, D j, Dq, ])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 of R and Q. An example in bird ecology illustrates the potential of this method for community ecologists.

Use of functional traits to assess changes in stream fish assemblages across a habitat gradient

“…We conducted an RLQ ordination analysis to analyze the relationship between species functional traits and habitat structure (Dolédec et al, 1996). This procedure links species traits to habitat variables and has been shown to be a powerful tool for identifying the set of traits that are associated with environmental changes (Hausner et al, 2003).…”

“…This procedure links species traits to habitat variables and has been shown to be a powerful tool for identifying the set of traits that are associated with environmental changes (Hausner et al, 2003). This multivariate technique is based on the ordination of three matrices (Dolédec et al, 1996): the R matrix has streams as rows, habitat variables as columns, and values for each environmental variables as entries; the L matrix has sites as rows, species as columns, and species abundances as entries; and the Q matrix has species as rows, functional morphological traits as columns, and morphological trait values as entries. We square root transformed the L matrix, which was the link between the R and Q matrices, to minimize the differences between abundant and rare species.…”

Refugia and Speciation in North American Scarlet Snakes (Cemophora)

“…Note that the model 5 is strictly equivalent to permuting simultaneously the rows of tables R and Q, as proposed by Doledec et al (1996).…”

Impact of pastoral land use on central Namibian savanna vegetation - Methods for indictor development and perspectives for their application

“…Von den Hauptkategorien, denen sich die Dolédec et al (1996). Bei der Methode handelt es sich um eine sog.…”

“…dreier Matritzen (RLQ-Analyse, Abb.5, Dolédec et al 1996) Abstract: How farmers perceive the state of their pastures is an important component of their management decision and affects natural resources in arid and semi-arid regions. In an explorative study conducted in the Rehoboth farm area of central Namibia, we addressed the question whether the judgments of commercial farmers on pasture conditions are consistent with a botanical assessment of these pastures based on measurements.…”