Canonical correspondence analysis and related multivariate methods in aquatic ecology

TL;DR: After pointing out the key assumptions underlying CCA, the paper focuses on the interpretation of CCA ordination diagrams and some advanced uses, such as ranking environmental variables in importance and the statistical testing of effects are illustrated on a typical macroinvertebrate data-set.

Abstract: Canonical correspondence analysis (CCA) is a multivariate method to elucidate the relationships between biological assemblages of species and their environment. The method is designed to extract synthetic environmental gradients from ecological data-sets. The gradients are the basis for succinctly describing and visualizing the differential habitat preferences (niches) of taxa via an ordination diagram. Linear multivariate methods for relating two set of variables, such as twoblock Partial Least Squares (PLS2), canonical correlation analysis and redundancy analysis, are less suited for this purpose because habitat preferences are often unimodal functions of habitat variables. After pointing out the key assumptions underlying CCA, the paper focuses on the interpretation of CCA ordination diagrams. Subsequently, some advanced uses, such as ranking environmental variables in importance and the statistical testing of effects are illustrated on a typical macroinvertebrate data-set. The paper closes with comparisons with correspondence analysis, discriminant analysis, PLS2 and co-inertia analysis. In an appendix a new method, named CCA-PLS, is proposed that combines the strong features of CCA and PLS2.