Combining the fourth-corner and the RLQ methods for assessing trait responses to environmental variation. Dray, S.; Choler, P.; Dolédec, S.; Peres-Neto, P., R.; Thuiller, W.; Pavoine, S.; and ter Braak, C., J. Ecology, 95(1):14-21, 2014.
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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.
@article{
 title = {Combining the fourth-corner and the RLQ methods for assessing trait responses to environmental variation},
 type = {article},
 year = {2014},
 keywords = {alps,fourth-corner matrix,functional ecology,permutation procedures,rlq tables,trait-environment relationship},
 pages = {14-21},
 volume = {95},
 websites = {http://www.esajournals.org/doi/abs/10.1890/13-0196.1},
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 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–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.},
 bibtype = {article},
 author = {Dray, Stéphane and Choler, P and Dolédec, Sylvain and Peres-Neto, P R and Thuiller, Wilfried and Pavoine, Sandrine and ter Braak, Cajo J.F.},
 journal = {Ecology},
 number = {1}
}
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