This example shows the potential of combining multivariate geostatistical
methods with canonical ordination and MEM covariables when the aim of the
study is to test for and model species-environment relationships while discriminating
between the two major sources of concern related to spatial structures: spatial
dependence (Eq. 7.1) and spatial autocorrelation (Eq. 7.2). Some aspects of this
approach remain to be explored, however. Wagner (2004) notes “an important
discrepancy between the results presented here and those by Borcard et al. (1992)
[authors’ note: in this 1992 paper, a cubic polynomial of the spatial coordinates was
used for spatial modelling]. Borcard found that 12.2% of the total inertia was
spatially structured but could not be explained by the environmental variables. In
the spatial partitioning of CCA results by multi-scale ordination (MSO), however,
spatial autocorrelation appeared to be limited to distances smaller than 0.75 m, and
there was no evidence of any cyclic pattern that could account for such a large
portion of inertia. The large portion of nonenvironmental spatial structure identified
by Borcard et al. (1992) may partly be due to a confounding of the effects of space
and environment (Meot et al. 1998)”. Arguing from an opposite point of view, we
believe that the pure spatial structures revealed by canonical ordination (and especially in the MEM framework which would give an even larger pure spatial fraction)
1
2
3
4
5
6
7
0.000
0.001
0.002
0.003
0.004
0.005
0.006
Distance
Variance
Explained plus residual
Residual variance
C.I. for total variance
Sign. autocorrelation
63
393
546
406
329
433
245
Fig. 7.15 Plot of the MSO of an RDA of the Hellinger-transformed and detrended oribatid mite
data explained by the detrended environmental variables. Explanations: see text
360
7 Spatial Analysis of Ecological Data
methods with canonical ordination and MEM covariables when the aim of the
study is to test for and model species-environment relationships while discriminating
between the two major sources of concern related to spatial structures: spatial
dependence (Eq. 7.1) and spatial autocorrelation (Eq. 7.2). Some aspects of this
approach remain to be explored, however. Wagner (2004) notes “an important
discrepancy between the results presented here and those by Borcard et al. (1992)
[authors’ note: in this 1992 paper, a cubic polynomial of the spatial coordinates was
used for spatial modelling]. Borcard found that 12.2% of the total inertia was
spatially structured but could not be explained by the environmental variables. In
the spatial partitioning of CCA results by multi-scale ordination (MSO), however,
spatial autocorrelation appeared to be limited to distances smaller than 0.75 m, and
there was no evidence of any cyclic pattern that could account for such a large
portion of inertia. The large portion of nonenvironmental spatial structure identified
by Borcard et al. (1992) may partly be due to a confounding of the effects of space
and environment (Meot et al. 1998)”. Arguing from an opposite point of view, we
believe that the pure spatial structures revealed by canonical ordination (and especially in the MEM framework which would give an even larger pure spatial fraction)
1
2
3
4
5
6
7
0.000
0.001
0.002
0.003
0.004
0.005
0.006
Distance
Variance
Explained plus residual
Residual variance
C.I. for total variance
Sign. autocorrelation
63
393
546
406
329
433
245
Fig. 7.15 Plot of the MSO of an RDA of the Hellinger-transformed and detrended oribatid mite
data explained by the detrended environmental variables. Explanations: see text
360
7 Spatial Analysis of Ecological Data