Rényi dimensions and pedodiversity indices of the earth pedotaxa distribution

Pedodiversity, the study and measurement of soil diversity, may be considered as a framework to analyze spatial patterns. Recently, selfsimilar multifractal patterns have been recently reported in the pedotaxa-abundance distributions at the planetary scale. This is the result to be expected from the complexity of earth soil systems. When the state of soil is understood as the outcome of nonlinear chaotic dynamic, highly irregular patterns with so-called multifractal behavior should be common. This opens the opportunity to use parameters of fractal theory to characterize pedodiversity. We compute Rényi generalized dimensions for the abundance distribution of pedotaxa for the five landmasses and the whole World drawn from the most detailed available global dataset based on the second level of the FAO 1974 classification units. We explore the effective relationship between diversity indices and Rényi dimensions. We show how multifractal analysis unifies diversity indices and how they should be interpreted offering a coherent perspective with a single mathematical procedure to analyze spatial patterns of the pedosphere.