Chapter 5 What are “constrained” ordinations?

Described first by Rao (1964), canonical analysis is a generic term that for several types of statistical analyses sharing a common goal, which is to identify the relationship between a multivariate response table (matrix \(Y\), generally describing the species composition of communities) and a multivariate explanatory table (matrix \(X\), generally containing environmental descriptors) by combining ordination and regression concepts.

Canonical analyses allow users to test ecological hypothesis concerning the environmental drivers of species composition. Among the diversity of canonical analysis, we will mainly focus here on Redundancy Analysis (RDA).


Rao, C. Radhakrishna. 1964. “The Use and Interpretation of Principal Component Analysis in Applied Research.” Sankhyā: The Indian Journal of Statistics, Series A (1961-2002) 26 (4): 329–58.