Abstract Background Weeds have high spatial variability and show clustering behavior, with heterogeneity in scales that can be evaluated through multifractal analysis. Objective The objective of this study was to evaluate the spatial variability of weeds using multifractal analysis in a no-till area. Methods Sampling was conducted at 1,015 sampling points in an experimental plot with a regular grid of 5 × 5 m (2.38 ha) with no tillage. The area was cultivated with triticale (Triticum secale), and in the summer of 2011, the area was cultivated with soybean (Glycine max). Data were analyzed using descriptive statistics and multifractal analysis using the box-counting method to determine the scaling properties of the variables. Results The predominance of Raphanus raphanistrum was identified in the winter crop and Commelina ssp. during the summer. The singularity spectrum showed greater asymmetry for Raphanus raphanistrum and Commelina ssp. in relation to the category of other weeds (OW). The degree of multifractality varied throughout the study period, showing the ecological patterns of the studied species. Scale heterogeneity was revealed, with different degrees of multifractality that evidenced the processes of dispersion and colonization of the environment by the different weed species evaluated. Conclusions The species Raphanus raphanistrum and Commelina ssp. showed domains of low measurement values, and OW was the most heterogeneous.

RESUMO A resistência do solo à penetração (RP) é uma medida indireta do estado de compactação do solo. Assim, o objetivo deste trabalho foi caracterizar a RP em perfis verticais em uma área cultivada com cana-de-açúcar por meio de modelos multifractais para diferentes unidades de relevo. O experimento foi realizado em Latossolo Vermelho Amarelo textura argilosa, com 6.85 ha no município de Coelho Neto (Maranhão, Brasil), onde foram demarcados 60 pontos de amostragem. A área foi dividida em quatro unidades de relevo (Tipo A > 74 m; Tipo B de 71 a 74 m; Tipo C de 68 a 71 m e Tipo D de 65 a 68 m). A RP foi medida nos 60 pontos de amostragem utilizando um penetrômetro de impacto, e a RP determinada na camada de 0-0.60 m de profundidade a cada 0.01 m. A análise multifractal foi realizada considerando a propriedade de escala de cada perfil e tipificada o espectro de singularidade e de Rènyi estimados por meio do método do momento. A análise multifractal permitiu a identificação de padrões em diferentes escalas e com elevada heterogeneidade. O comportamento multifractal, foi representado pelo espectro de singularidade (α), versus f(α), e a dimensão generalizada (Dq). A análise multifractal permitiu a diferenciação entre os perfis das unidades de relevo (Tipos A, B, C e D), resultando em uma importante ferramenta para estudos da resistência do solo à penetração.

ABSTRACT Soil resistance to penetration (PR) is an indirect measure of the state of soil compaction. Thus, the objective of this study was to characterize PR in vertical profiles in an area cultivated with sugarcane using multifractal models for different relief units. The experiment was carried out in an Oxisol with a clay texture, with 6.85 ha in the municipality of Coelho Neto (Maranhão state, Brazil), where 60 sampling points were demarcated. The area was divided into four relief units (Type A > 74 m, Type B from 71 to 74 m, Type C from 68 to 71 m and Type D from 65 to 68 m). The PR was measured at the 60 sampling points using an impact penetrometer, and the PR determined in the 0-0.60 m depth layer every 0.01 m. The multifractal analysis was performed considering the scale property of each profile and typified the singularity and Rènyi spectra estimated using the current method. Multifractal analysis allowed the identification of patterns at different scales and with high heterogeneity. The multifractal behavior was represented by the singularity spectrum (α), versus f(α), and the generalized dimension (Dq). The multifractal analysis allowed the differentiation between the profiles of the relief units (Types A, B, C and D), resulting in an important tool for studies of soil resistance to penetration.

RESUMO O objetivo deste trabalho foi avaliar a variabilidade espacial da produtividade de soja, do estoque de carbono e de atributos físicos do solo por meio de técnicas multivariadas e de geoestatística. Os atributos foram determinados em um Latossolo Vermelho textura argilosa e coeso no município de Mata Roma (Maranhão, Brasil). Na área de estudo foram demarcados 70 pontos de amostragem, sendo avaliada a produtividade de soja e os atributos do solo nas camadas de 0-0,20 e 0,20-0,40 m de profundidade. Os dados foram analisados por meio de análise multivariada (ACP - Análise de Componentes Principais) e de ferramentas de geoestatística. A produtividade média de soja foi de 3370 kg ha-1. O semivariograma da produtividade, carbono orgânico (OC) e do estoque de carbono (Cst) na camada de 0-0,20 m se ajustaram ao modelo esférico. A ACP explicou 73.21% da estrutura da variância e covariância entre a produtividade e os atributos do solo na camada de 0-0.20 m [ACP 1 (26.89%), ACP 2 (24.10%) e ACP 3 (22.22%)] e 68.64% na camada de 0.20-0.40 m [ACP 1 (31.95%), ACP 2 (22.83%) e ACP 3 (13.85%)]. Os mapas de variabilidade espacial dos scores dos autovalores da ACP demonstraram que é possível a determinação de zonas de manejo utilizando a ACP 1 nas duas profundidades em estudo, todavia, com diferentes estratégias de manejo para cada uma das camadas.

ABSTRACT The objective of this study was to evaluate the spatial variability of soybean yield, carbon stock, and soil physical attributes using multivariate and geostatistical techniques. The attributes were determined in Oxisols samples with clayey and cohesive textures collected from the municipality of Mata Roma, Maranhão state, Brazil. In the study area, 70 sampling points were demarcated, and soybean yield and soil attributes were evaluated at soil depths of 0-0.20 and 0.20-0.40 m. Data were analysed using multivariate analyses (principal component analysis, PCA) and geostatistical tools. The mean soybean yield was 3,370 kg ha-1. The semivariogram of productivity, organic carbon (OC), and carbon stock (Cst) at the 0-0.20 m layer were adjusted to the spherical model. The PCA explained 73.21% of the variance and covariance structure between productivity and soil attributes at the 0-0.20 m layer [(PCA 1 (26.89%), PCA 2 (24.10%), and PCA 3 (22.22%)] and 68.64% at the 0.20-0.40 m layer [PCA 1 (31.95%), PCA 2 (22.83%), and PCA 3 (13.85%)]. The spatial variability maps of the PCA eigenvalue scores showed that it is possible to determine management zones using PCA 1 in the two studied depths; however, with different management strategies for each of the layers in this study.