title: Combining the fourth-corner and the RLQ methods for assessing trait responses to environmental variation.
abstract: Assessing trait responses to environmental gradients requires the simultaneous analysis of the information contained in three tables: L (species distribution across samples), R (environmental characteristics of samples), and Q (species traits). Among the available methods, the so-called fourth-corner and RLQ methods are two appealing alternatives that provide a direct way to test and estimate trait-nvironment relationships. Both methods are based on the analysis of the fourth-corner matrix, which crosses traits and environmental variables weighted by species abundances. However, they differ greatly in their outputs: RLQ is a multivariate technique that provides ordination scores to summarize the joint structure among the three tables, whereas the fourth-corner method mainly tests for individual trait-environment relationships (i.e., one trait and one environmental variable at a time). Here, we illustrate how the complementarity between these two methods can be exploited to promote new ecological knowledge and to improve the study of trait-environment relationships. After a short description of each method, we apply them to real ecological data to present their different outputs and provide hints about the gain resulting from their combined use.
authors.forename: Stéphane
authors.initials: S
authors.lastname: Dray
authors.forename: Philippe
authors.initials: P
authors.lastname: Choler
authors.forename: Sylvain
authors.initials: S
authors.lastname: Dolédec
authors.forename: Pedro R
authors.initials: PR
authors.lastname: Peres-Neto
authors.forename: Wilfried
authors.initials: W
authors.lastname: Thuiller
authors.forename: Sandrine
authors.initials: S
authors.lastname: Pavoine
authors.forename: Cajo J F
authors.initials: CJ
authors.lastname: ter Braak
mesh_terms: D000222:Adaptation, Physiological / Q000502:physiology*; D000531:Altitude; D017753:Ecosystem; D008954:Models, Biological; D064209:Phytochemicals; D010944:Plants / Q000145:classification*; D012914:Snow
chemical_list: D064209:Phytochemicals