7.5.2 Application to the Mite Data – Exploratory Approach
Let us use the oribatid mite data as an example. Wagner (2004) also used these data,
but in a CCA context, so that the results of the RDA below will differ from hers.
MSO can be computed using function mso() of the package vegan. This function
uses a result object produced by functions rda() or cca(), plus the table of
geographical coordinates and a value for the interval size (argument ‘grain‘) of the
distance classes of the variograms. The first example applies MSO in the exploratory
way proposed by Wagner. An MSO plot of direct ordination can show whether the
spatial structure of the response data can be explained by the explanatory (environmental) variables alone. In such a case, no detrending is necessary (H. Wagner, pers.
comm.), but the confidence interval of the variogram is only indicative since a
variogram should be computed on stationary data.
Hereunder MSO is run using the RDA result of the (Hellinger-transformed)
oribatid mite data explained by the environmental variables. The “grain” of the
variogram (size of a distance classes) is chosen to be the truncation threshold used in
the dbMEM analysis, 1.011187.
## MSO of the undetrended mite data vs environment RDA
mite.undet.env.rda <- rda(mite.h~., mite.env2)
(mite.env.rda.mso
grain = dmin,
perm = 999))
msoplot(mite.env.rda.mso, alpha = 0.05/7)
The resulting plot (Fig. 7.13) is rich in information. In the upper part of the
diagram, the dashed line with the plus signs represents the sum of the explained and
residual empirical variograms. The continuous lines represent the confidence envelopes of the variogram of the data matrix. The monotonic increase of the dashed line
is the signature of the strong linear gradient present in the data. Note, however, that
the variogram of the residuals (squares, bottom of the graph) shows no distance class
with significant spatial correlation (after a global Bonferroni correction for 7 simultaneous tests, where the rejection threshold is divided by the number of classes), and
that variogram is essentially flat. This means that the broad scale linear gradient is
well explained by the environmental variables.
However, an intriguing feature appears. When the species-environment correlations do not vary with scale, the dashed line remains within the boundaries of the
confidence envelopes (full lines). This is not the case here (see classes 1, 2 and
5, which correspond to distances 0, 1 and 4 along the abscissa), suggesting that it is
not appropriate to run a non-spatial, global species-environment analysis with the
implicit assumption that the relationships are scale-invariant. On the contrary, we
can expect the regression parameters to vary with scale, so that a global estimation is
meaningless unless one controls for the regional-scale spatial structure causing the
problem.
356
7 Spatial Analysis of Ecological Data
Let us use the oribatid mite data as an example. Wagner (2004) also used these data,
but in a CCA context, so that the results of the RDA below will differ from hers.
MSO can be computed using function mso() of the package vegan. This function
uses a result object produced by functions rda() or cca(), plus the table of
geographical coordinates and a value for the interval size (argument ‘grain‘) of the
distance classes of the variograms. The first example applies MSO in the exploratory
way proposed by Wagner. An MSO plot of direct ordination can show whether the
spatial structure of the response data can be explained by the explanatory (environmental) variables alone. In such a case, no detrending is necessary (H. Wagner, pers.
comm.), but the confidence interval of the variogram is only indicative since a
variogram should be computed on stationary data.
Hereunder MSO is run using the RDA result of the (Hellinger-transformed)
oribatid mite data explained by the environmental variables. The “grain” of the
variogram (size of a distance classes) is chosen to be the truncation threshold used in
the dbMEM analysis, 1.011187.
## MSO of the undetrended mite data vs environment RDA
mite.undet.env.rda <- rda(mite.h~., mite.env2)
(mite.env.rda.mso
grain = dmin,
perm = 999))
msoplot(mite.env.rda.mso, alpha = 0.05/7)
The resulting plot (Fig. 7.13) is rich in information. In the upper part of the
diagram, the dashed line with the plus signs represents the sum of the explained and
residual empirical variograms. The continuous lines represent the confidence envelopes of the variogram of the data matrix. The monotonic increase of the dashed line
is the signature of the strong linear gradient present in the data. Note, however, that
the variogram of the residuals (squares, bottom of the graph) shows no distance class
with significant spatial correlation (after a global Bonferroni correction for 7 simultaneous tests, where the rejection threshold is divided by the number of classes), and
that variogram is essentially flat. This means that the broad scale linear gradient is
well explained by the environmental variables.
However, an intriguing feature appears. When the species-environment correlations do not vary with scale, the dashed line remains within the boundaries of the
confidence envelopes (full lines). This is not the case here (see classes 1, 2 and
5, which correspond to distances 0, 1 and 4 along the abscissa), suggesting that it is
not appropriate to run a non-spatial, global species-environment analysis with the
implicit assumption that the relationships are scale-invariant. On the contrary, we
can expect the regression parameters to vary with scale, so that a global estimation is
meaningless unless one controls for the regional-scale spatial structure causing the
problem.
356
7 Spatial Analysis of Ecological Data