Chapter 6
Canonical Ordination
6.1 Objectives
Simple (unconstrained) ordination analyses one data matrix and reveals its major
structure in a graph constructed with a reduced set of orthogonal axes. It is therefore
a passive form of analysis, and the user interprets the ordination results a posteriori,
as described in Chap. 5. Canonical ordination, on the contrary, associates two or
more data sets in the ordination process itself. Consequently, if one wishes to extract
structures of a data set that are related to (or can be interpreted by) another data set,
and/or formally test statistical hypotheses about the significance of these relationships, canonical ordination is the way to go.
Canonical ordination methods can be classified into two groups depending on the
role played by the two matrices involved: symmetric and asymmetric.
Practically, you will:
• learn how to choose among various canonical ordination techniques: asymmetric
[redundancy analysis (RDA), distance-based redundancy analysis (db-RDA),
canonical correspondence analysis (CCA), linear discriminant analysis (LDA),
principal response curves (PRC), co-correspondence analysis (CoCA)] and symmetric [canonical correlation analysis (CCorA), co-inertia analysis (CoIA) and
multiple factor analysis (MFA)];
• explore methods devoted to the study of the relationships between species traits
and environment;
• compute them using the correct options and properly interpret the results;
• apply these techniques to the Doubs River and other data sets;
• explore particular applications of some canonical ordination methods, for
instance variation partitioning and multivariate analysis of variance by RDA;
• write your own RDA function.
© Springer International Publishing AG, part of Springer Nature 2018
D. Borcard et al., Numerical Ecology with R, Use R!,
https://doi.org/10.1007/978-3-319-71404-2_6
203
Canonical Ordination
6.1 Objectives
Simple (unconstrained) ordination analyses one data matrix and reveals its major
structure in a graph constructed with a reduced set of orthogonal axes. It is therefore
a passive form of analysis, and the user interprets the ordination results a posteriori,
as described in Chap. 5. Canonical ordination, on the contrary, associates two or
more data sets in the ordination process itself. Consequently, if one wishes to extract
structures of a data set that are related to (or can be interpreted by) another data set,
and/or formally test statistical hypotheses about the significance of these relationships, canonical ordination is the way to go.
Canonical ordination methods can be classified into two groups depending on the
role played by the two matrices involved: symmetric and asymmetric.
Practically, you will:
• learn how to choose among various canonical ordination techniques: asymmetric
[redundancy analysis (RDA), distance-based redundancy analysis (db-RDA),
canonical correspondence analysis (CCA), linear discriminant analysis (LDA),
principal response curves (PRC), co-correspondence analysis (CoCA)] and symmetric [canonical correlation analysis (CCorA), co-inertia analysis (CoIA) and
multiple factor analysis (MFA)];
• explore methods devoted to the study of the relationships between species traits
and environment;
• compute them using the correct options and properly interpret the results;
• apply these techniques to the Doubs River and other data sets;
• explore particular applications of some canonical ordination methods, for
instance variation partitioning and multivariate analysis of variance by RDA;
• write your own RDA function.
© Springer International Publishing AG, part of Springer Nature 2018
D. Borcard et al., Numerical Ecology with R, Use R!,
https://doi.org/10.1007/978-3-319-71404-2_6
203