# Add weighted average projection of species
spe.wa <- wascores(spe.b.pcoa$points[, 1:2], spe)
text(spe.wa, rownames(spe.wa), cex = 0.7, col = "red")
# A posteriori projection of environmental variables
(spe.b.pcoa.env <- envfit(spe.b.pcoa, env))
# Plot significant variables with a user-selected colour
plot(spe.b.pcoa.env, p.max = 0.05, col = 3)
Hint Observe the use of two vegan functions, ordiplot() and scores(), to
produce the ordination plot. vegan provides many special functions to handle
outputs of its own analytical functions. Also, type ?cca.object to learn about
the internal structure of the vegan output objects.
5.5.3 Application of PCoA to the Doubs Data Set Using pcoa()
There is another way to draw a double projection. It is based on correlations of the
environmental variables with the PCoA ordination axes (see Legendre and Legendre
2012 p. 499). A PCoA computed on a matrix of Euclidean distances produces
eigenvectors corresponding to what would be obtained in a scaling 1 PCA biplot
of the same data. This representation can be drawn by using functions pcoa() and
biplot.pcoa(), both available in the package ape.
Here is how these functions work. In our example, PCoA is run on a Euclidean
distance matrix computed on a Hellinger-transformed species abundance matrix; the
result of these two operations is a Hellinger distance matrix. In such a case, it is
actually better (simpler and faster) to run a PCA directly on the transformed species
data, but here the idea is to allow a comparison with the PCA run presented in Sect.
5.3.3. Two biplots are proposed, with projection of the raw and standardized species
abundances. Compare the result below (Fig. 5.11) with the biplot of the PCA scaling
1 result in Fig. 5.4 (left).
spe.h.pcoa <- pcoa(dist(spe.h))
# Biplots
par(mfrow = c(1, 2))
# First biplot: Hellinger-transformed species data
biplot.pcoa(spe.h.pcoa, spe.h, dir.axis1 = -1)
abline(h = 0, lty = 3)
abline(v = 0, lty = 3)
# Second biplot: standardized Hellinger-transformed species data
spe.std <- scale(spe.h)
biplot.pcoa(spe.h.pcoa, spe.std, dir.axis1 = -1)
abline(h = 0, lty = 3)
abline(v = 0, lty = 3)
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5 Unconstrained Ordination
spe.wa <- wascores(spe.b.pcoa$points[, 1:2], spe)
text(spe.wa, rownames(spe.wa), cex = 0.7, col = "red")
# A posteriori projection of environmental variables
(spe.b.pcoa.env <- envfit(spe.b.pcoa, env))
# Plot significant variables with a user-selected colour
plot(spe.b.pcoa.env, p.max = 0.05, col = 3)
Hint Observe the use of two vegan functions, ordiplot() and scores(), to
produce the ordination plot. vegan provides many special functions to handle
outputs of its own analytical functions. Also, type ?cca.object to learn about
the internal structure of the vegan output objects.
5.5.3 Application of PCoA to the Doubs Data Set Using pcoa()
There is another way to draw a double projection. It is based on correlations of the
environmental variables with the PCoA ordination axes (see Legendre and Legendre
2012 p. 499). A PCoA computed on a matrix of Euclidean distances produces
eigenvectors corresponding to what would be obtained in a scaling 1 PCA biplot
of the same data. This representation can be drawn by using functions pcoa() and
biplot.pcoa(), both available in the package ape.
Here is how these functions work. In our example, PCoA is run on a Euclidean
distance matrix computed on a Hellinger-transformed species abundance matrix; the
result of these two operations is a Hellinger distance matrix. In such a case, it is
actually better (simpler and faster) to run a PCA directly on the transformed species
data, but here the idea is to allow a comparison with the PCA run presented in Sect.
5.3.3. Two biplots are proposed, with projection of the raw and standardized species
abundances. Compare the result below (Fig. 5.11) with the biplot of the PCA scaling
1 result in Fig. 5.4 (left).
spe.h.pcoa <- pcoa(dist(spe.h))
# Biplots
par(mfrow = c(1, 2))
# First biplot: Hellinger-transformed species data
biplot.pcoa(spe.h.pcoa, spe.h, dir.axis1 = -1)
abline(h = 0, lty = 3)
abline(v = 0, lty = 3)
# Second biplot: standardized Hellinger-transformed species data
spe.std <- scale(spe.h)
biplot.pcoa(spe.h.pcoa, spe.std, dir.axis1 = -1)
abline(h = 0, lty = 3)
abline(v = 0, lty = 3)
190
5 Unconstrained Ordination