An added bonus of CA.newr() is the possibility to display the cumulative fit of
species and sites in terms of R
2 . The maximum value is 1. These fits help identify the
axes to which the species or sites contribute the most. For instance:
# Cumulative fit of species
spe.CA.PL$fit$cumulfit.spe
# Cumulative fit of sites
spe.CA.PL$fit$cumulfit.obj
The cumulative fit for species shows, for instance, that Phph is well fitted by axis
1 only (0.865) whereas Cogo is very well fitted by axes 1 and 2 together (0.914). On
the other hand, Lele has no contribution to axes 1 and 2 but gets half of its fit
(0.494) on axis 3. The same exercise can be done for the sites.
This information could be used for graphical purposes, e.g. to display only the
sites or species whose cumulative fit is at least 0.5 on axis 2. Another application
would involve the selection of several axes for a further analysis, retaining only
enough to reach a cumulative fit of 0.8 for 80% of the sites (these figures are arbitrary
and given as an example).
5.4.4 Arch Effect and Detrended Correspondence Analysis
(DCA)
Long environmental gradients often support a succession of species. Since the
species that are controlled by environmental factors tend to have unimodal distributions, a long gradient may encompass sites that, at opposite ends of the gradient,
have no species in common; thus, their dissimilarity has the maximum possible
value
4 (or their similarity is 0). But if one starts at any one point along the gradient
and walks slowly towards an end, successive sites grow more and more different
from the starting point until the maximum value of D is reached. Therefore, instead
of a straight line, the gradient is represented as an arch on a pair of CA axes. Several
detrending techniques have been proposed to counter this effect and straighten up
gradients in ordination diagrams, leading to detrended correspondence analysis
(DCA):
• Detrending by segments combined with nonlinear rescaling: axis I is divided into
an arbitrary number of segments and, within each one, the mean of the object
scores along axis 2 is made equal to zero. The arbitrarily selected number of
4 The maximum value of the chi-square distance is
ffiffiffiffiffiffiffiffiffiffi
2y þþ
p
, where y ++ is the sum of all frequencies in
the table. This value is only obtained when there is a single species with abundance 1 in each of the
two sites producing this maximum value, and these two species each have a total abundance of 1 in
the data table. See Legendre and Legendre (2012, pp. 308–309) for details.
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5 Unconstrained Ordination
species and sites in terms of R
2 . The maximum value is 1. These fits help identify the
axes to which the species or sites contribute the most. For instance:
# Cumulative fit of species
spe.CA.PL$fit$cumulfit.spe
# Cumulative fit of sites
spe.CA.PL$fit$cumulfit.obj
The cumulative fit for species shows, for instance, that Phph is well fitted by axis
1 only (0.865) whereas Cogo is very well fitted by axes 1 and 2 together (0.914). On
the other hand, Lele has no contribution to axes 1 and 2 but gets half of its fit
(0.494) on axis 3. The same exercise can be done for the sites.
This information could be used for graphical purposes, e.g. to display only the
sites or species whose cumulative fit is at least 0.5 on axis 2. Another application
would involve the selection of several axes for a further analysis, retaining only
enough to reach a cumulative fit of 0.8 for 80% of the sites (these figures are arbitrary
and given as an example).
5.4.4 Arch Effect and Detrended Correspondence Analysis
(DCA)
Long environmental gradients often support a succession of species. Since the
species that are controlled by environmental factors tend to have unimodal distributions, a long gradient may encompass sites that, at opposite ends of the gradient,
have no species in common; thus, their dissimilarity has the maximum possible
value
4 (or their similarity is 0). But if one starts at any one point along the gradient
and walks slowly towards an end, successive sites grow more and more different
from the starting point until the maximum value of D is reached. Therefore, instead
of a straight line, the gradient is represented as an arch on a pair of CA axes. Several
detrending techniques have been proposed to counter this effect and straighten up
gradients in ordination diagrams, leading to detrended correspondence analysis
(DCA):
• Detrending by segments combined with nonlinear rescaling: axis I is divided into
an arbitrary number of segments and, within each one, the mean of the object
scores along axis 2 is made equal to zero. The arbitrarily selected number of
4 The maximum value of the chi-square distance is
ffiffiffiffiffiffiffiffiffiffi
2y þþ
p
, where y ++ is the sum of all frequencies in
the table. This value is only obtained when there is a single species with abundance 1 in each of the
two sites producing this maximum value, and these two species each have a total abundance of 1 in
the data table. See Legendre and Legendre (2012, pp. 308–309) for details.
182
5 Unconstrained Ordination