Chemovariations in essential oils were used for studying the spatial chemical structure of eight E. dysenterica populations in Central Brazilian Cerrado. Previously, multivariate Mantel autocorrelogram and chemical matrix variation partitioning, using the spatial and environmental data sets as predictors, have suggested a highly significant spatial variation in essential oils. In the present study, spatial chemometric methods using variograms and probability maps detected and characterized the spatial chemical structure among populations, as well as the environmental factors responsible for them. All these strategies indicated that the populations differ chemically whenever the geographical distance exceeds 120 km, an indicator of the minimal distance between samples required for conserving the genetic diversity of populations. Although being scarcely used with secondary metabolites, these methodologies may be used in a wide range of applications in species management and may lead to an effective integration of genetic, chemical and ecological perspectives.

Abstract Roughness is a fundamental feature to define rock deformability and resistance. A detailed characterization of discontinuity surface geometry is essential for understanding some of the rock’s mechanical behaviors. Fractal geometry has been used by several authors to correlate parameters such as the Hurst coefficient for JRC (Joint Roughness coefficient) to better describe a surface geometry. Surface profiles might be characterized by a fractal dimension that represents the small scale of the geometric recurrence. In this paper, we propose to modify the methodology used to identify the Hurst coefficient incorporating the rodogram function in the JRC analysis. The proposed function is less influenced by drifting effects, and seems to be more precise than the commonly used variogram function. Robust mathematical models of spatial continuity can be a better alternative to characterize the roughness of rock discontinuities.

Abstract Precipitation is an important object of study and plays an important role in the dynamics of rainfall distribution in a region. This study investigated the spatial and temporal variation of precipitation in the São Francisco River Basin (SFRB). A historical series of data from 1989 to 2018 was analyzed, and a random function was decomposed into trend and residual components for analysis of precipitation. Interpolation techniques were used to analyze precipitation spatial behavior over time, using high-resolution precipitation maps. Our results showed that the exponential model prevailed in four periods. The findings also showed a high precipitation variability in the SFRB and enabled us to monitor precipitation behavior over the years, as well as in the different sub-regions in SFRB. Finally, important information was obtained, enabling, for instance, the identification of vulnerable areas suffering from lack of rainfall.

Abstract: The objective of this work was to analyze the spatial distribution and the behavior of species richness and diversity in a shrub savanna fragment, in 2003 and 2014, using ordinary kriging, in the state of Minas Gerais, Brazil. In both evaluation years, the measurements were performed in a fragment with 236.85 hectares, in which individual trees were measured and identified across 40 plots (1,000 m2). Species richness was determined by the total number of species in each plot, and diversity by the Shannon diversity index. For the variogram study, spatial models were fitted and selected. Then, ordinary kriging was applied and the spatial distribution of the assessed variables was described. A strong spatial dependence was observed between species richness and diversity by the Shannon diversity index (<25% spatial dependence degree). Areas of low and high species diversity and richness were found in the shrub savanna fragment. Spatial distribution behavior shows relative stability regarding the number of species and the Shannon diversity index in the evaluated years.

The injury imposed by Tibraca limbativentris Stål in plants of rice can negatively affect the production and reduce grain yield. Knowing the spatial arrangement of this species allows fast and accurate sampling and identifies focuses of infestation determining the ideal moment of decision-making for the control. The aim of this study was to investigate the spatial and probabilistic distribution of adults and nymphs of T. limbativentris in irrigated rice. Fifteen fields with plants of 50-80 days after emergency were sampled on approximately regular grids in 2008, 2010, and 2011. Poisson and Negative binomial distributions were tested and Pearson chi-squared test was used to determine a probability distribution with the best fit. Polynomial regressions of the number of individuals versus geographical coordinates were used to try detecting trends related with macroscale. Later, semivariograms were used to interpret the spatial dependence and distribution of insects. The semivariance of the samples obtained with nymphs showed patterns grouped in 13% of fields sampled. Similar pattern was also obtained by semivariograms of adults in 26% of fields sampled. However, there were no spatial dependence in the most of the sampled fields with adults (74%) and nymphs (87%). In conclusion, adults and nymphs of T. limbativentris are randomly distributed in irrigated rice fields, though rarely clustered pattern can occur. The probability distribution that best fits the data sampling is the Negative binomial. Adults and nymphs do not inhabit the same local in the rice field. Population levels above the value of economic damage may occur, but individuals are not present in about 2/3 of the units sampled. Polynomial regression models tested are not appropriate to fit the trends related to macro-scale in irrigated rice fields.