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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.