Resumo Análise espacial e temporal da interiorização da Covid-19 em Pernambuco, considerando-se os fatores socioeconômicos correlacionados. Estudo ecológico, março a junho de 2020. Geraram-se mapas a partir do coeficiente de incidência por município de residência para determinar a dinâmica espacial da Covid-19. Estudou-se a correlação entre indicadores socioeconômicos e o coeficiente nas regiões metropolitana do Recife (RMR) e interior. Suavizou-se este coeficiente e calculou-se o teste de Moran global. Os primeiros casos foram registrados em Recife e arredores. O caminho para a autoctonia se deu em municípios vizinhos e naqueles supridos por grandes rodovias. A maior incidência na RMR (640,22/100.000 hab) correlacionou-se à maior população e densidade demográfica e menor taxa de urbanização e IDH-M. No interior a incidência (361,29/100.000 hab) esteve correlacionada à maior população, densidade demográfica e taxa de urbanização, e menor área (p<0,05). As áreas de maior risco concentraram-se na RMR, mas o interior apresentou áreas de transição, indicando tendência à interiorização (p<0,05). Ter ciência do padrão de distribuição espacial da Covid-19, aliada aos fatores associados poderão contribuir para maior efetividade das ações de controle.

Abstract This study involved an ecological study between March and June 2020 consisting of a spatial and temporal analysis of the spread of Covid-19 to the interior of Pernambuco and related socioeconomic factors. Maps were generated from the incidence coefficient by municipality of residence to determine the spatial dynamics of Covid-19. The correlation between socioeconomic indicators and the coefficient in the metropolitan regions of Recife (MRR) and inland regions was studied. This coefficient was levelled, and the global Moran test was applied. The first cases were recorded in and around Recife. The spread of the virus took place in neighboring municipalities and in those served by major highways. The highest incidence in MRR (640.22/100,000 inhabitants) was correlated to larger population and demographic density and lower rate of urbanization and IDH-M. Inland, the incidence (361.29/100,000 inhabitants) was correlated with a larger population, demographic density and urbanization rate, and a smaller area (p<0.05). The areas of greatest risk were concentrated in MRR, but the interior showed areas of transition, indicating a tendency to spread (p<0.05). Being aware of the spatial distribution pattern of Covid-19, combined with the associated factors, may contribute to greater effectiveness of control actions.

Resumo Análise espacial e temporal da interiorização da Covid-19 em Pernambuco, considerando-se os fatores socioeconômicos correlacionados. Estudo ecológico, março a junho de 2020. Geraram-se mapas a partir do coeficiente de incidência por município de residência para determinar a dinâmica espacial da Covid-19. Estudou-se a correlação entre indicadores socioeconômicos e o coeficiente nas regiões metropolitana do Recife (RMR) e interior. Suavizou-se este coeficiente e calculou-se o teste de Moran global. Os primeiros casos foram registrados em Recife e arredores. O caminho para a autoctonia se deu em municípios vizinhos e naqueles supridos por grandes rodovias. A maior incidência na RMR (640,22/100.000 hab) correlacionou-se à maior população e densidade demográfica e menor taxa de urbanização e IDH-M. No interior a incidência (361,29/100.000 hab) esteve correlacionada à maior população, densidade demográfica e taxa de urbanização, e menor área (p<0,05). As áreas de maior risco concentraram-se na RMR, mas o interior apresentou áreas de transição, indicando tendência à interiorização (p<0,05). Ter ciência do padrão de distribuição espacial da Covid-19, aliada aos fatores associados poderão contribuir para maior efetividade das ações de controle.

Abstract This study involved an ecological study between March and June 2020 consisting of a spatial and temporal analysis of the spread of Covid-19 to the interior of Pernambuco and related socioeconomic factors. Maps were generated from the incidence coefficient by municipality of residence to determine the spatial dynamics of Covid-19. The correlation between socioeconomic indicators and the coefficient in the metropolitan regions of Recife (MRR) and inland regions was studied. This coefficient was levelled, and the global Moran test was applied. The first cases were recorded in and around Recife. The spread of the virus took place in neighboring municipalities and in those served by major highways. The highest incidence in MRR (640.22/100,000 inhabitants) was correlated to larger population and demographic density and lower rate of urbanization and IDH-M. Inland, the incidence (361.29/100,000 inhabitants) was correlated with a larger population, demographic density and urbanization rate, and a smaller area (p<0.05). The areas of greatest risk were concentrated in MRR, but the interior showed areas of transition, indicating a tendency to spread (p<0.05). Being aware of the spatial distribution pattern of Covid-19, combined with the associated factors, may contribute to greater effectiveness of control actions.

ABSTRACT The aim of the present study was to assess the relative competition between white clover (cv. BRS URS Entrevero) and weed species Silene gallica L. through replacement series. The experiments followed a completely randomized design with four replications. The first study showed that the shoot dry mass of both species (white clover and S. gallica) became constant with 16 plants.pot-1 or 400 plants.m-2. In 2017, a study was conducted and it was repeated in 2018 in order to assess white clover competition with S. gallica under different crop: weed proportions pot-1 (100:00; 75:25; 50:50; 25:75 and 00:100). Competitiveness analysis was carried out through diagrams applied to replace experiments and through the relative competition indices. Morphological parameters such as plant height, leaf area and shoot dry mass of the crop and the weed were measured when S. gallica plants bloomed (105 days after species emergence). Results have proven the phenotypic plasticity of temperate-climate foragers such as white clover. This outcome shows that the competitive relationship with Silene gallica changes due to plant proportions composing the association. Therefore, it was possible to conclude that the species show similar competitive ability.

ABSTRACT The goal of this study was to use the spatial bootstrap method to model the spatial dependence structure of soybean yield and soil chemical attributes in an agricultural area. The study involved developing confidence intervals in probability plots to determine the probability distributions assumed by the data; determine the empirical distributions of the semivariances and model parameters, allowing to obtain statistics and confidence intervals; and to construct maps for the variables. The quantile-quantile plots indicated that the data follows a normal distribution. The confidence intervals for the semivariances helped to model the spatial dependence structure, and the descriptive statistics of the bootstrap replicates of the model parameters allowed to test the consistency of the estimates. The soil chemical attributes (calcium, potassium, and organic matter) were at levels suitable for soybean cultivation. However, the pH was below the ideal range in most of the study area, and water stress during cultivation decreased the mean yield. Therefore, according to the results, a recommendation to the farmer is to correct the soil pH to increase the yield.

ABSTRACT This study aims to quantify the uncertainties associated to the parameters of a Gaussian spatial linear model (GSLM) and the assumption of normality residuals in the modeling of the spatial dependence of the soybean yield as a function of soil chemical attributes. The spatial bootstrap methods were used to determine the point and interval estimators associated with the model parameters. Hypothesis tests were carried out on the significance of the model parameters and the quantile-quantile probability plot was elaborated to verify the data normality. The uncertainties associated to the parameters of the spatial dependence structure were quantified and the potassium content, phosphorus content and soil pH covariates were significant to explain the soybean yield mean. These covariates were used in the elaboration of a new model, which provided the elaboration of a contour map of soybean yield. Analysis of the quantile-quantile plot indicated that soybean yield data follow a normal probability distribution.

RESUMO Na análise de dados espaciais em agricultura, a presença de pontos influentes pode alterar consideravelmente os resultados das análises de dependência espacial e, consequentemente, a construção dos mapas. Quando se referem a atributos físico-químicos do solo e da produtividade, os mapas devem representar uma estimativa eficiente das condições reais do campo, já que são importantes informações utilizadas para a manutenção de um sistema agrícola de manejo localizado, com a otimização da aplicação de insumos agrícolas, visando à maior produtividade. Este trabalho teve por objetivo apresentar as técnicas gráficas hair-plot, de influência local (Ci e |Lmax|) de identificação de observações influentes em dados contínuos espaciais georreferenciados, coletados em uma área experimental de cultivo comercial, com 167,35 hectares, onde o sistema agrícola de manejo localizado é adotado. Como resultados apresentam-se os pontos potencialmente influentes e os mapas construídos com e sem eles. Na comparação entre os mapas com e sem estes pontos, as métricas de comparação dos mapas mostraram a importância da identificação dos pontos influentes em uma base de dados espaciais. Sendo assim, a existência de pontos influentes deve ser investigada para entender o motivo de seu comportamento atípico, já que eles modificam, consideravelmente, os mapas gerados.

ABSTRACT Influencing points in agricultural spatial analysis may change considerably results on spatial dependence and hence map building. With regards to physico-chemical soil properties and crop yield, such maps should efficiently estimate current field conditions, being important for an agricultural site-specific management, optimizing thus input applications in order to increase yields. This study aimed to analyze hair-plot graphic techniques, with local influence (Ci and |Lmax|) to identify influencing points within a set of georeferenced spatial continuous data. These information were gathered from an experimental area with 167.35 hectares, wherein an agricultural site-specific management has been adopted. As a result, we obtained potentially influencing points and then outlined maps with and without the use of them. By comparing both maps, we could note by metric comparison that it is of major importance to identify those points on a spatial database. Thus, such investigations must be carried out to understand cases of unusual performance, since they considerably modify the generated maps.

RESUMO Neste trabalho, teve-se o objetivo de estudar e comparar mapas temáticos da produtividade da soja para diferentes grades amostrais, utilizando métodos geoestatísticos (função semivariância e krigagem). A análise foi realizada com dados da produtividade de soja em t ha-1 numa área comercial com grades regulares e distâncias entre pontos de 25x25 m, 50x50 m, 75x75 m e 100x100 m, com 549; 188; 66 e 44 pontos amostrais, respectivamente, e dados obtidos pelo monitor de colheita. Também foram gerados esquemas amostrais otimizados, com o algoritmo chamado Têmpera Simulada, usando a maximização da medida de acurácia exatidão global, como critério de otimização. Foi verificado que fatores como o tamanho da amostra e a densidade amostral influenciaram na descrição da distribuição espacial da produtividade da soja feita por meio dos mapas temáticos. Quando se aumentou o tamanho amostral, houve aumento da eficiência dos mapas temáticos quanto à descrição da variabilidade espacial da produtividade da soja (maiores valores dos índices de acurácia e os menores valores para a soma quadrada do erro de estimação). Além disso, os mapas mais acurados foram obtidos considerando as configurações amostrais otimizadas com 188 e 549 pontos amostrais.

ABSTRACT This study aimed to compare thematic maps of soybean yield for different sampling grids, using geostatistical methods (semivariance function and kriging). The analysis was performed with soybean yield data in t ha-1 in a commercial area with regular grids with distances between points of 25x25 m, 50x50 m, 75x75 m, 100x100 m, with 549, 188, 66 and 44 sampling points respectively; and data obtained by yield monitors. Optimized sampling schemes were also generated with the algorithm called Simulated Annealing, using maximization of the overall accuracy measure as a criterion for optimization. The results showed that sample size and sample density influenced the description of the spatial distribution of soybean yield. When the sample size was increased, there was an increased efficiency of thematic maps used to describe the spatial variability of soybean yield (higher values of accuracy indices and lower values for the sum of squared estimation error). In addition, more accurate maps were obtained, especially considering the optimized sample configurations with 188 and 549 sample points.

RESUMO Este trabalho teve como objetivo comparar mapas temáticos construídos a partir de conjuntos de dados referentes à produtividade da soja, com diferentes grades amostrais regulares de 25x25 m; 50x50 m; 75x75 m e 100x100 m, utilizando técnicas de krigagem. No ajuste dos modelos teóricos a semivariâncias experimentais, utilizou-se para a estimação dos parâmetros o método de máxima verossimilhança. A comparação dos mapas temáticos foi realizada por meio dos índices de acurácia, obtidos a partir da matriz de erros. Foi verificado que fatores tais, como o tamanho amostral e a densidade amostral entre pontos, interferem na escolha do modelo teórico espacial, nas estimativas dos parâmetros e na construção dos mapas temáticos.

ABSTRACT The purpose of this paper was to compare thematic maps constructed from data sets related to soybean productivity with different regular sampling grids of 25x25 m, 50 x50 m, 75 x 75 m and 100x100 m, using kriging techniques. In the theoretical models fitted to the experimental semivariances, it was used the maximum likelihood method for parameter estimation. The comparison of thematic maps were made by accuracy indices, obtained from the error matrix. The results showed that factors such as sample size and sample density between points interfere in the choice of the theoretical spatial model, the parameter estimates and the construction of thematic maps.

D.M. Grzegozewski, M.A. Uribe-Opazo, F. De Bastiani, and M. Galea. 2013. Local influence when fitting Gaussian spatial linear models: an agriculture application. Cien. Inv. Agr. 40(3): 523-535. Outliers can adversely affect how data fit into a model. Obviously, an analysis of dependent data is different from that of independent data. In the latter, i.e., in cases involving spatial data, local outliers can differ from the data in the neighborhood. In this article, we used the local influence technique to identify influential points in the response variables using two different schemes of perturbations. We applied this technique to soil chemical properties and soybean yield. We evaluated the effects of the influential points on the spatial model selection, the parameter estimation by maximum likelihood and the construction of thematic maps by kriging. In the construction of the thematic maps in studies with and without the influential points, there were changes in the levels of nutrients, allowing for the appropriate application of input, generating greater savings for the producer and contributing to the protection of the environment.

D.M. Grzegozewski, M.A. Uribe-Opazo, F. De Bastiani y M. Galea. 2013. Influencia local a modelos espaciales lineales Gaussianos: Aplicación a la agricultura. Cien. Inv. Agr. 40(3): 523-535. Los valores discrepantes pueden afectar negativamente el ajuste de un modelo. El análisis de datos dependientes es diferente al de datos independientes. En el primer caso, envuelven datos espaciales que pueden tener valores discrepantes localmente y que tienen algunas características diferentes de los datos vecinos. En este artículo, el objetivo fue detectar los puntos influyentes por medio de la técnica de influencia local en la variable de respuesta, mediante el uso de dos esquemas diferentes de perturbaciones denominados: perturbación aditiva y perturbación de Zhu. Se aplicó esta técnica a las propiedades químicas del suelo y a la productividad de la soja. Se evaluaron los efectos de los puntos influyentes en la elección del modelo, en la estimación de parámetros de máxima verosimilitud y la construcción de mapas temáticos mediante "kriging". En la construcción de mapas temáticos, se pudo observar alteraciones en los niveles de nutrientes al realizar el estudio con y sin los puntos de influencia, de tal forma que permite una aplicación apropiada de los insumos, lo que genera un mayor ahorro para el productor y en la contribución a la protección del medio ambiente.

Realizou-se um estudo sobre a variabilidade espacial de dados de resistência do solo à penetração (RSP), nas camadas de 0,0-0,1 m, 0,1-0,2 m e 0,2-0,3 m de profundidade, utilizando métodos estatísticos em forma univariada, isto é, utilizando a geoestatística tradicional, construindo os mapas temáticos por krigagem ordinária para cada camada em estudo. Foi analisada a RSP na camada de 0,2-0,3 m de profundidade por meio de um modelo espacial linear (SLM), em que se consideraram as camadas de 0,0-0,1 m e 0,1-0,2 m como covariáveis, obtendo um modelo de estimação e um mapa temático por krigagem universal. Os mapas temáticos da RSP da camada de 0,2-0,3 m de profundidade, construídos por ambos os métodos, foram comparados por meio de medidas de acurácia obtidas a partir da construção da matriz de erros e da matriz de confusão. Verificou-se semelhança entre os mapas temáticos. Todos os mapas mostraram que a RSP é mais alta na região norte.

A study about the spatial variability of data of soil resistance to penetration (RSP) was conducted at layers 0.0-0.1 m, 0.1-0.2 m and 0.2-0.3 m depth, using the statistical methods in univariate forms, i.e., using traditional geostatistics, forming thematic maps by ordinary kriging for each layer of the study. It was analyzed the RSP in layer 0.2-0.3 m depth through a spatial linear model (SLM), which considered the layers 0.0-0.1 m and 0.1-0.2 m in depth as covariable, obtaining an estimation model and a thematic map by universal kriging. The thematic maps of the RSP at layer 0.2-0.3 m depth, constructed by both methods, were compared using measures of accuracy obtained from the construction of the matrix of errors and confusion matrix. There are similarities between the thematic maps. All maps showed that the RSP is higher in the north region.