Multifractal and joint multifractal analysis of soil invertebrate fauna, altitude, and organic carbon1

Abstract

The objectives of this study were to evaluate the degree of multifractality of the spatial distribution of altitude, organic carbon concentration, and invertebrate fauna diversity, and to characterize the degree of joint multifractal association among these variables. Soil sampling was performed every 20 m across a 2,540 m transect, with a total of 128 sampling points in a sugarcane area in Goiana municipality, Pernambuco State. For each sampling point, the altitude, organic carbon concentration, and macrofauna diversity (diversity indices and functional groups) were evaluated. Spatial distributions of altitude, organic carbon concentration, and macrofauna diversity were characterized by the generalized dimension spectrum (Dq) and singularity spectrums [f(α) versus α], which presented multifractal behavior with different degrees of heterogeneity in scales. Joint multifractal analysis was useful for revealing the relationships at multiple scales between the studied variables, as demonstrated by the non-detected associations using traditional statistical methods. To quantify the spatial variability of edaphic fauna based on the multiple scales and association sets in the joint dimension, the impact of agricultural production systems on biological diversity can be described. All of the studied variables displayed a multifractal behavior with greater or lower heterogeneity degree depending on the variable, with altitude and organic carbon being the most homogeneous attributes.