Garten et al. 2007

Garten CT Jr., Kang S, Brice DJ, Schadt CW, Zhou J. 2007. Variability in soil properties at different spatial scales (1m-1km) in a deciduous forest ecosystem. Soil Biology & Biochemistry 39: 2621-2627.

These authors examined some of the fundamental assumptions of geospatial analysis as applied to soil properties, in a pair of transects that I strongly suspect have been used repeatedly for many studies in Tennessee (see, e.g. Zhou et al. 2008). One of the fundamental assumptions is of spatial autocorrelation, that is, samples in close proximity will be more similar to each other than samples separated by greater distances. In this study, this assumption was stated as the null hypothesis “there are no differences in variance at different spatial scales”; a rejection of this null hypothesis can be interpreted as support for the “common sense” (their wording) principle of spatial autocorrelation, at least among the spatial scales discussed here (i.e. metres to kilometres). This and other important assumptions of geospatial analysis come from a series of papers applying these principles to soils, which I should probably read soon.

The 11 soil variables examined in this paper were distinctly non-orthogonal in their relationships. Many of the variables were calculated directly from other variables, and the majority takes the form of either ratios (such as C-to-N) or fractions (such as silt content). The Principle Components Analysis (PCA) these authors conducted on their final, grand-total dataset indicated that the usual suspects of soil properties were important – soil Carbon, soil Nitrogen, and soil Texture are one way to summarize the first three PC variables.

I looked up and read this paper mainly because of the statistical tests used here and the discussion of them. They conducted 5 main statistical tests.
1. Bartlett’s test for equal variances at different distances.
2. Bartlett’s test is sensitive to non-normal data, so they also used the non-parametric Spearman’s Rank Correlation between coefficients of variation (100 x S.D./mean). The other reason a non-parametric test was used was that the functional relationship (linear vs. non-linear) between variance and sampling distance was unknown.
3. Mantel and Partial Mantel tests. These were the central analysis, I think, and provided most of the key results regarding the tests of the main hypotheses. Apparently, Burrough (1993) recommends semivariogram analysis, but the present data set was not amenable to such.
4. PCA, as mentioned above.
5. Power analysis. How many samples would they need to collect to be more certain of being close to the true mean value in their estimates?
Besides the PCA, which produced utterly unsurprising results, I think the statistical tests deployed here will serve as models for my own analysis of 2009 and putative 2010 datasets from the High Arctic. In particular, the Mantel tests and the Power analysis should be very useful in my own examinations.

Overall, the geospatial assumption of spatial autocorrelation was not very well supported by this study. Many soil properties appear to be highly variable at small spatial scales, such that samples collected within a few metres of each other are as variable as samples collected from up to a kilometre away, at least in a temperate forest ecosystem as studied here. This is particularly surprising in light of the consideration of the structure of such a forest, where individual trees presumably have strong impacts on soil properties within perhaps 5 to 10 metres of their trunks.