are real and not due to confounding effects. In the latter case, they would have shown
up in the common fraction of variation, not the pure spatial fraction. The question is
rather: why did the MSO not reveal these structures? This may be due to the fact that
no formal way of quantifying variance components in MSO has been devised as yet
(H. Wagner, pers. comm.). However, this does by no means invalidate the whole
approach which, combined with the powerful tools developed in this chapter,
increases our control over the complex process of extracting meaningful spatial
information from ecological data sets.
7.6 Space-Time Interaction Test in Multivariate ANOVA,
Without Replicates
7.6.1 Introduction
The title of this section may seem outrageous: everybody knows that one needs
replicates in an experimental design to be able to test an interaction term in ANOVA,
since it is the within-cell replicates that provide the degrees of freedom for the test.
1
2
3
4
5
6
7
0.000
0.001
0.002
0.003
0.004
0.005
Distance
Variance
Explained plus residual
Residual variance
Explained variance
C.I. for total variance
Sign. autocorrelation
63
393
546
406
329
245
433
Fig. 7.16 Plot of the MSO of an RDA of the Hellinger-transformed and detrended oribatid mite
data explained by the detrended environmental variables, controlling for spatial structure (6 MEM
variables). Further explanations: see text.
7.6 Space-Time Interaction Test in Multivariate ANOVA, Without Replicates
361