Dray S., Choler P., Dolédec S., Peres-Neto P.R., Thuiller W., Pavoine S., ter Braak C.J. (2014). Combining the fourth-corner and the RLQ methods for assessing trait responses to environmental variation. Ecology, 95(1):14--21.

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–environment 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.

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