Hint Here you could also produce a clustering and overlay its result on the CA plot.
The first axis opposes the lower section of the stream (sites 19–30) to the upper
portion. This is clearly a strong contrast, which explains why the first eigenvalue is
so high. Many species appear close to sites 19–30, indicating that they are more
abundant downstream. Many of them are actually absent from the upper part of the
river. The second axis contrasts the 10 upstream sites with the intermediate ones.
Both groups of sites, which display short gradients on their own, are associated
with characteristic species. The scaling 2 biplot shows how small groups of species
are distributed among the sites. One can see that the grayling (Thth), the bullhead
(Cogo) and the varione (Teso) are found in the intermediate group of sites
(11–18), while the brown trout (Satr), the Eurasian minnow (Phph) and the
stone loach (Babl) are found in a longer portion of the stream (approximately
sites 1–18).
Observe how scalings 1 and 2 produce different plots. Scaling 1 shows the sites at
the (weighted) centres of mass of the species. This is appropriate to interpret site
proximities and find gradients or groups of sites. The converse is true for the scaling
2 biplot, where one can look for groups or replacement series of species. In both
cases, interpretation of the species found near the origin of the graph should be done
with care. This proximity could mean either that the species is at its optimum in the
mid-range of the ecological gradients represented by the axes, or that it is present
everywhere along the gradient.
5.4.2.2 Projection of Supplementary Sites or Species in a CA Biplot
Supplementary sites or species can be projected into a CA biplot using function
predict()of stats. For a CA computed with vegan’s function cca(), this
function computes the positions of supplementary sites in an appropriate manner
(weighted averages); this is not the case for a PCA computed with rda() (Sect.
5.3.2.4). The data frame containing the supplementary items must have the exact
same row names (for supplementary variables) or column names (for supplementary
objects) as the data set that has been used to compute the CA. The examples below
show (1) a CA with three sites removed, followed by the passive projection of these
three sites, and (2) the same with three species.
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5 Unconstrained Ordination
The first axis opposes the lower section of the stream (sites 19–30) to the upper
portion. This is clearly a strong contrast, which explains why the first eigenvalue is
so high. Many species appear close to sites 19–30, indicating that they are more
abundant downstream. Many of them are actually absent from the upper part of the
river. The second axis contrasts the 10 upstream sites with the intermediate ones.
Both groups of sites, which display short gradients on their own, are associated
with characteristic species. The scaling 2 biplot shows how small groups of species
are distributed among the sites. One can see that the grayling (Thth), the bullhead
(Cogo) and the varione (Teso) are found in the intermediate group of sites
(11–18), while the brown trout (Satr), the Eurasian minnow (Phph) and the
stone loach (Babl) are found in a longer portion of the stream (approximately
sites 1–18).
Observe how scalings 1 and 2 produce different plots. Scaling 1 shows the sites at
the (weighted) centres of mass of the species. This is appropriate to interpret site
proximities and find gradients or groups of sites. The converse is true for the scaling
2 biplot, where one can look for groups or replacement series of species. In both
cases, interpretation of the species found near the origin of the graph should be done
with care. This proximity could mean either that the species is at its optimum in the
mid-range of the ecological gradients represented by the axes, or that it is present
everywhere along the gradient.
5.4.2.2 Projection of Supplementary Sites or Species in a CA Biplot
Supplementary sites or species can be projected into a CA biplot using function
predict()of stats. For a CA computed with vegan’s function cca(), this
function computes the positions of supplementary sites in an appropriate manner
(weighted averages); this is not the case for a PCA computed with rda() (Sect.
5.3.2.4). The data frame containing the supplementary items must have the exact
same row names (for supplementary variables) or column names (for supplementary
objects) as the data set that has been used to compute the CA. The examples below
show (1) a CA with three sites removed, followed by the passive projection of these
three sites, and (2) the same with three species.
178
5 Unconstrained Ordination