unconstrained (residual) variances, excluding the conditioned (i.e., removed)
variance.
We can now test the partial RDA and, if it is significant, draw triplots of the first
pair of axes (Fig. 6.3).
anova(spechem.physio2,
permutations = how(nperm = 999),
by = "axis"
)
# Partial RDA triplots (with fitted site scores)
# Scaling 1
triplot.rda(spechem.physio,
site.sc = "lc",
scaling = 1,
cex.char2 = 0.8,
pos.env = 3,
mar.percent = 0
)
# Scaling 2
triplot.rda(spechem.physio,
site.sc = "lc",
scaling = 2,
cex.char2 = 0.8,
pos.env = 3,
mult.spe = 1.1,
mar.percent = 0.04
)
# Test of the partial RDA, using the results with the formula
# interface to allow the tests of the axes to be run
anova(spechem.physio2, permutations = how(nperm = 999))
Hint See the hints in Sect. 6.3.3 about the two ways of coding formulas containing
covariables.
As could be expected, the results of this partial analysis differ somewhat from the
previous results, but not fundamentally. Although there are interesting features to
discuss about the amounts of variance explained, we will postpone this aspect until
we have seen a quick and elegant manner to compute the adjusted R
2 of partial
analyses, by means of variation partitioning (Sect. 6.3.2.8). On the triplots, the
explanatory variables show the same relationships to one another, but some of
them [hardness (har) and nitrates (nit)] are less important to explain the fish
community structure, as shown by their shorter vectors. This may be due to the fact
that these two variables are well correlated with the positions of the sites along the
6.3 Redundancy Analysis (RDA)
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