par(mfrow = c(1, 2))
# Scaling 1: species scoresscaled to the relative eigenvalues,
# sites are weighted averages of the species
plot(spe.cca,
scaling = 1,
display = c("sp", "lc", "cn"),
main = "Triplot CCA spe ~ env3 - scaling 1"
)
# Default scaling 2: site scores scaled to the relative
# eigenvalues, species are weighted averages of the sites
plot(spe.cca,
display = c("sp", "lc", "cn"),
main = "Triplot CCA spe ~ env3 - scaling 2"
)
In CCA as in RDA, the introduction of explanatory variables calls for additional
interpretation rules for the triplots. Here are the essential ones:
• Scaling 1 À (1) Projecting an object at right angle on a quantitative explanatory
variable approximates the position of the object along that variable. (2) An object
found near the point representing the centroid of a class of a qualitative
explanatory variable is more likely to possess that class of the variable. (3) Distances among centroids of qualitative explanatory variables, and between centroids and individual objects, approximate χ
2 distances.
• Scaling 2 À (1) The optimum of a species along a quantitative environmental
variable can be obtained by projecting the species at right angle on the variable.
(2) A species found near the centroid of a class of a qualitative environmental
variable is likely to be found frequently (or in larger abundances) in the sites
possessing that class of the variable. (3) Distances among centroids, and between
centroids and individual objects, do not approximate χ
2 distances.
The scaling 1 triplot focuses on the distance relationships among sites, but the
presence of species with extreme scores renders the plot difficult to interpret beyond
trivialities (Fig. 6.11a). Therefore, it may be useful to redraw it without the species
(Fig. 6.12 left):
# CCA scaling 1 biplot without species (using lc site scores)
plot(spe.cca,
scaling = 1,
display = c("lc", "cn"),
main = "Biplot CCA spe ~ env3 - scaling 1"
)
Here the response of the fish communities to their environmental constraints is
more apparent. One can see two well-defined groups of sites, one linked to high
elevation and very steep slope (sites 1–7 and 10) and another with the highest
oxygen contents (sites 11–15). The remaining sites are distributed among various
conditions towards more eutrophic waters. Remember that this is a constrained
ordination of the fish community data, not a PCA of the site environmental variables.
258
6 Canonical Ordination
# Scaling 1: species scoresscaled to the relative eigenvalues,
# sites are weighted averages of the species
plot(spe.cca,
scaling = 1,
display = c("sp", "lc", "cn"),
main = "Triplot CCA spe ~ env3 - scaling 1"
)
# Default scaling 2: site scores scaled to the relative
# eigenvalues, species are weighted averages of the sites
plot(spe.cca,
display = c("sp", "lc", "cn"),
main = "Triplot CCA spe ~ env3 - scaling 2"
)
In CCA as in RDA, the introduction of explanatory variables calls for additional
interpretation rules for the triplots. Here are the essential ones:
• Scaling 1 À (1) Projecting an object at right angle on a quantitative explanatory
variable approximates the position of the object along that variable. (2) An object
found near the point representing the centroid of a class of a qualitative
explanatory variable is more likely to possess that class of the variable. (3) Distances among centroids of qualitative explanatory variables, and between centroids and individual objects, approximate χ
2 distances.
• Scaling 2 À (1) The optimum of a species along a quantitative environmental
variable can be obtained by projecting the species at right angle on the variable.
(2) A species found near the centroid of a class of a qualitative environmental
variable is likely to be found frequently (or in larger abundances) in the sites
possessing that class of the variable. (3) Distances among centroids, and between
centroids and individual objects, do not approximate χ
2 distances.
The scaling 1 triplot focuses on the distance relationships among sites, but the
presence of species with extreme scores renders the plot difficult to interpret beyond
trivialities (Fig. 6.11a). Therefore, it may be useful to redraw it without the species
(Fig. 6.12 left):
# CCA scaling 1 biplot without species (using lc site scores)
plot(spe.cca,
scaling = 1,
display = c("lc", "cn"),
main = "Biplot CCA spe ~ env3 - scaling 1"
)
Here the response of the fish communities to their environmental constraints is
more apparent. One can see two well-defined groups of sites, one linked to high
elevation and very steep slope (sites 1–7 and 10) and another with the highest
oxygen contents (sites 11–15). The remaining sites are distributed among various
conditions towards more eutrophic waters. Remember that this is a constrained
ordination of the fish community data, not a PCA of the site environmental variables.
258
6 Canonical Ordination