section of the river, i.e. the group discharge and hardness, which are highly correlated with the distance from the source, and the group of variables linked to
eutrophication, i.e. phosphate, ammonium concentration and biological oxygen
demand. Positively correlated with these two groups is nitrate concentration. Nitrate
and pH have nearly orthogonal arrows, indicating a correlation close to 0. pH
displays a shorter arrow, showing its lesser importance for the ordination of the
sites in the ordination plane. A plot of axes 1 and 3 would emphasize its contribution
to axis 3.
This example shows how useful a biplot representation can be in summarizing the
main features of a data set. Clusters and gradients of sites are obvious, as are the
correlations among the variables. The correlation biplot (scaling 2) is far more
informative than the visual examination of a correlation matrix among variables;
the latter can be obtained by typing cor(env)).
Technical remark: vegan allows its output object to be plotted by the low-level
plotting function plot(env.pca). However, the use of this function provides
PCA plots where sites as well as variables are represented by points. This is
misleading, since the points representing the variables are actually the apices (tips)
of vectors that must be drawn as arrows for the plot to be interpreted correctly. For
further information about this function, type ?plot.cca.
5.3.2.4 Projecting Supplementary Variables into a PCA Biplot
Supplementary variables can be added to a PCA plot through the function
predict(). This function uses the ordination result to compute the ordination
scores of new variables as a function of their values in the sites. The data frame
containing the supplementary items must have the exact same row names as the
original data.
Let us compute a PCA of the Doubs environment data, but without the two last
variables, oxy and bod, then “predict” the position of the new variables in the
ordination plot as an exercise:
5.3 Principal Component Analysis (PCA)
161