Ecologically meaningful transformations for ordination of species data

Abstract

This paper examines how to obtain species biplots in unconstrained or constrained ordination without resorting to the Euclidean distance [used in principal-component analysis (PCA) and redundancy analysis (RDA)] or the chi-square distance [preserved in correspondence analysis (CA) and canonical correspondence analysis (CCA)] which are not always appropriate for the analysis of community composition data. To achieve this goal, transformations are proposed for species data tables. They allow ecologists to use ordination methods such as PCA and RDA, which are Euclidean-based, for the analysis of community data, while circumventing the problems associated with the Euclidean distance, and avoiding CA and CCA which present problems of their own in some cases. This allows the use of the original (transformed) species data in RDA carried out to test for relationships with explanatory variables (i.e. environmental variables, or factors of a multifactorial analysis-of-variance model); ecologists can then draw biplots displaying the relationships of the species to the explanatory variables. Another application allows the use of species data in other methods of multivariate data analysis which optimize a least-squares loss function; an example is K-means partitioning.

Keywords: Biplot diagram; Canonical correspondence analysis; Correspondence analysis; Principal-component analysis; Redundancy analysis.