Multifractal analysis of soil fauna diversity indexes

Abstract

The objective of this study was to determine the multifractality of diversity indexes of edaphic fauna in areas with natural vegetation and in agricultural systems. Biological sampling was carried out in seven treatments (millet, maize, soybean, eucalyptus, preserved cerrado, disturbed cerrado and pasture), containing 130 pitfall traps, distributed in transects with 3 m of spacing between sampling points, totaling 390 m. The multifractal analysis was determined based on the moment method, where estimates such as the capacity dimensions, entropy and the correlation of the diversity indexes were calculated. The soybean area had greater Shannon diversity (2.69), however it had smaller abundance of individuals. The partition functions were adjusted with coefficient of determination > 0.90. The difference between D-10-D 10 , ranged from 0.080 to 1,707 for Pielou equitability in soybean cultivation, for richness in the area under the cultivation of eucalyptus. The singularity spectra expressed graphs with different degrees of heterogeneity for the soil fauna indexes, and the richness expressed the best structure. The area cultivated with soybean had a monofractal tendency, due to the homogeneous distribution of individuals of the edaphic fauna along the transect. The fractal analysis provided the description of patterns of variability that are not detected by classical methods.

Multiscale properties of weeds in no-till system

“…where μ(q,ε) corresponds to the partition function defined by Equation 3, and by replacing q with 0, 1, and 2 in Equation 2, we obtain the capacity dimension (D 0 , Equation 4), information dimension (D 1 , Equation 5), and correlation dimension (D 2 , Equation 6), respectively. 2015); however, for multifractal systems the dimensions must follow the relationship D 0 > D 1 > D 2 (Chhabra, Jensen, 1989;Banerjee et al, 2011;Vidal-Vázquez et al, 2013;Siqueira et al, 2018;Leiva et al, 2019;Silva, Siqueira, 2020); therefore, data on weed species (R. raphanistrum, Commelina ssp. and OW) follow the relationship D 0 > D 1 > D 2 (Table 2), indicating a multifractal behavior.…”

“…The D 1 dimension is related to the entropy information and quantifies the degree of disorder in the system. Thus, D 1 values close to 2 indicate systems with uniform distribution (Posadas et al, 2009), while D 1 values close to 1 represent subsets, with irregularities in the distribution of measurement values (Posadas et al, 2009;Leiva et al, 2019;Silva, Siqueira, 2020;Siqueira et al, 2022). Here, the values of D 1 varied between 1.866 and 1.666 (Table 2), indicating a tendency toward uniformity in the distribution of the scales in the study area.…”

“…on 01/26/2011 (2.131). The Hölder exponent (α 0 ) characterizes the multifractal scale of the system (Silva, Siqueira, 2020); therefore, there is an increasing trend over the period studied for R. raphanistrum and Commelina ssp. However, for the OW, the pattern was not repeated, with the lowest value described for OW on 08/19/2020 (α 0 = 1.650) and the highest for 10/22/2020 (α 0 = 2.131).…”

“…The structure of fractal objects or sets is characterized by an infinite number of dimensions (Hentschel, Procaccia, 1983), which allows for the description of the singularity spectrum (Chhabra, Jensen, 1989). Thus, multifractal analysis describes the structure of a system/object, since the methodology quantifies the spatial distribution of values on the scales (Leiva et al, 2019;Silva, Siqueira, 2020;Siqueira et al, 2022), thereby favoring the understanding of the heterogeneity of the data (Banerjee et al, 2011), which is not characterized by other methods.…”

“…of soil resistance to penetration in different relief units. Silva and Siqueira (2020) and Siqueira et al (2022) determined the multifractality of invertebrate soil fauna.…”