Compositional analysis for an unbiased measure of soil aggregation

Soil aggregation is an index of soil structure measured by mean weight diameter (MWD) or scaling factors often interpreted as fragmentation fractal dimensions (Df). However, the MWD provides a biased estimate of soil aggregation due to spurious correlations among aggregate-size fractions and scale-dependency. The scale-invariant Df is based on weak assumptions to allow particle counts and sensitive to the selection of the fractal domain, and may frequently exceed a value of 3, implying that Df is a biased estimate of aggregation. Aggregation indices based on mass may be computed without bias using compositional analysis techniques. Our objective was to elaborate compositional indices of soil aggregation and to compare them to MWD and Df using a published dataset describing the effect of 7 cropping systems on aggregation. Six aggregate-size fractions were arranged into a sequence of D-1 balances of building blocks that portray the process of soil aggregation. Isometric log-ratios (ilrs) are scale-invariant and orthogonal log contrasts or balances that possess the Euclidean geometry necessary to compute a distance between any two aggregation states, known as the Aitchison distance (A(x,y)). Close correlations (r > 0.98) were observed between MWD, Df, and the ilr when contrasting large and small aggregate sizes. Several unbiased embedded ilrs can characterize the heterogeneous nature of soil aggregates and be related to soil properties or functions. Soil bulk density and penetrater resistance were closely related to A(x,y) with reference to bare fallow. The A(x,y) is easy to implement as unbiased index of soil aggregation using standard sieving methods and may allow comparisons between studies.

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► Mean weight diameter and fractal dimension are biased measures of soil aggregation.
► Isometric log ratios (ilr) are unbiased balances between aggregate size proportions.
► Ilr coordinates explore several orthogonally arranged dimensions of soil architecture.
► Difference between two aggregation states is the Aitchison distance between ilrs.
► Aitchison distances could facilitate comparisons between studies on soil aggregation.