Sources of spatial complexity in two coastal plain soil landscapes

The spatial pattern of soils and soil properties in soil landscapes is considered here as a function of (1) systematic variation along catenas or associated with spatial patterns of soil-forming factors; and (2) local pseudo-random variations associated with local disturbances or small, unobserved variations in soil-forming factors. The problem is approached at two study sites in the U.S. Atlantic Coastal Plain using algebraic graph theory and the spectral radius of the soil adjacency matrix as a measure of complexity. The matrix is constructed based on the observed spatial contiguity of soil taxa, and soil factor sequences (SFS) are defined for each site based on systematic soil variation associated with variations in parent material, topography, sandy surface thicknesses, and secondary podzolization. The spectral radii of the networks described by the adjacency graphs are compared to those associated with the maximum for a graph of the same size, and the maximum associated with control entirely by variations in soil forming factors. At the Clayroot study site, which is entirely cropland, complexity of the adjacency matrix is less than Λ, the maximum that could be accounted for by the four identified SFS, due to redundant information in the SFS. The Littlefield site, by contrast, has a spectral radius greater than Λ. Here, where about half the site is forested, the contingent variation is likely associated with effects of individual trees on soil morphology. The utility of the adjacency analysis is in identifying whether soil heterogeneity is likely associated with SFS or with contingent factors not captured in SFS.