Selecting statistical models to study the relationship between soybean yield and soil physical properties

Statistical models allow the representation of data sets and the estimation and/or prediction of the behavior of a given variable through its interaction with the other variables involved in a phenomenon. Among other different statistical models, are the autoregressive state-space models (ARSS) and the linear regression models (LR), which allow the quantification of the relationships among soil-plant-atmosphere system variables. To compare the quality of the ARSS and LR models for the modeling of the relationships between soybean yield and soil physical properties, Akaike's Information Criterion, which provides a coefficient for the selection of the best model, was used in this study. The data sets were sampled in a Rhodic Acrudox soil, along a spatial transect with 84 points spaced 3 m apart. At each sampling point, soybean samples were collected for yield quantification. At the same site, soil penetration resistance was also measured and soil samples were collected to measure soil bulk density in the 0-0.10 m and 0.10-0.20 m layers. Results showed autocorrelation and a cross correlation structure of soybean yield and soil penetration resistance data. Soil bulk density data, however, were only autocorrelated in the 0-0.10 m layer and not cross correlated with soybean yield. The results showed the higher efficiency of the autoregressive space-state models in relation to the equivalent simple and multiple linear regression models using Akaike's Information Criterion. The resulting values were comparatively lower than the values obtained by the regression models, for all combinations of explanatory variables.

Calibration of the century, apsim and ndicea models of decomposition and n mineralization of plant residues in the humid tropics

The aim of this study was to calibrate the CENTURY, APSIM and NDICEA simulation models for estimating decomposition and N mineralization rates of plant organic materials (Arachis pintoi, Calopogonium mucunoides, Stizolobium aterrimum, Stylosanthes guyanensis) for 360 days in the Atlantic rainforest bioma of Brazil. The models´ default settings overestimated the decomposition and N-mineralization of plant residues, underlining the fact that the models must be calibrated for use under tropical conditions. For example, the APSIM model simulated the decomposition of the Stizolobium aterrimum and Calopogonium mucunoides residues with an error rate of 37.62 and 48.23 %, respectively, by comparison with the observed data, and was the least accurate model in the absence of calibration. At the default settings, the NDICEA model produced an error rate of 10.46 and 14.46 % and the CENTURY model, 21.42 and 31.84 %, respectively, for Stizolobium aterrimum and Calopogonium mucunoides residue decomposition. After calibration, the models showed a high level of accuracy in estimating decomposition and N- mineralization, with an error rate of less than 20 %. The calibrated NDICEA model showed the highest level of accuracy, followed by the APSIM and CENTURY. All models performed poorly in the first few months of decomposition and N-mineralization, indicating the need of an additional parameter for initial microorganism growth on the residues that would take the effect of leaching due to rainfall into account.

Building predictive models of soil particle-size distribution

Is it possible to build predictive models (PMs) of soil particle-size distribution (psd) in a region with complex geology and a young and unstable land-surface? The main objective of this study was to answer this question. A set of 339 soil samples from a small slope catchment in Southern Brazil was used to build PMs of psd in the surface soil layer. Multiple linear regression models were constructed using terrain attributes (elevation, slope, catchment area, convergence index, and topographic wetness index). The PMs explained more than half of the data variance. This performance is similar to (or even better than) that of the conventional soil mapping approach. For some size fractions, the PM performance can reach 70 %. Largest uncertainties were observed in geologically more complex areas. Therefore, significant improvements in the predictions can only be achieved if accurate geological data is made available. Meanwhile, PMs built on terrain attributes are efficient in predicting the particle-size distribution (psd) of soils in regions of complex geology.

Evaluation of statistical and geostatistical models of digital soil properties mapping in tropical mountain regions

Soil properties have an enormous impact on economic and environmental aspects of agricultural production. Quantitative relationships between soil properties and the factors that influence their variability are the basis of digital soil mapping. The predictive models of soil properties evaluated in this work are statistical (multiple linear regression-MLR) and geostatistical (ordinary kriging and co-kriging). The study was conducted in the municipality of Bom Jardim, RJ, using a soil database with 208 sampling points. Predictive models were evaluated for sand, silt and clay fractions, pH in water and organic carbon at six depths according to the specifications of the consortium of digital soil mapping at the global level (GlobalSoilMap). Continuous covariates and categorical predictors were used and their contributions to the model assessed. Only the environmental covariates elevation, aspect, stream power index (SPI), soil wetness index (SWI), normalized difference vegetation index (NDVI), and b3/b2 band ratio were significantly correlated with soil properties. The predictive models had a mean coefficient of determination of 0.21. Best results were obtained with the geostatistical predictive models, where the highest coefficient of determination 0.43 was associated with sand properties between 60 to 100 cm deep. The use of a sparse data set of soil properties for digital mapping can explain only part of the spatial variation of these properties. The results may be related to the sampling density and the quantity and quality of the environmental covariates and predictive models used.

Liming in Agricultural Production Models with and Without the Adoption of Crop-Livestock Integration

ABSTRACT Perennial forage crops used in crop-livestock integration (CLI) are able to accumulate large amounts of straw on the soil surface in no-tillage system (NTS). In addition, they can potentially produce large amounts of soluble organic compounds that help improving the efficiency of liming in the subsurface, which favors root growth, thus reducing the risks of loss in yield during dry spells and the harmful effects of “overliming”. The aim of this study was to test the effects of liming on two models of agricultural production, with and without crop-livestock integration, for 2 years. Thus, an experiment was conducted in a Latossolo Vermelho (Oxisol) with a very clayey texture located in an agricultural area under the NTS in Bandeirantes, PR, Brazil. Liming was performed to increase base saturation (V) to 65, 75, and 90 % while one plot per block was maintained without the application of lime (control). A randomized block experimental design was adopted arranged in split-plots and four plots/block, with four replications. The soil properties evaluated were: pH in CaCl2, soil organic matter (SOM), Ca, Mg, K, Al, and P. The effects of liming were observed to a greater depth and for a long period through mobilization of ions in the soil, leading to a reduction in SOM and Al concentration and an increase in pH and the levels of Ca and Mg. In the first crop year, adoption of CLI led to an increase in the levels of K and Mg and a reduction in the levels of SOM; however, in the second crop year, the rate of decline of SOM decreased compared to the decline observed in the first crop year, and the level of K increased, whereas that of P decreased. The extent of the effects of liming in terms of depth and improvement in the root environment from the treatments were observed only partially from the changes observed in the chemical properties studied.

Interacción genotipo-ambiente en avena sativa l: utilizando los modelos AMMI y factorial de correspondencias

El objetivo fue (i) determinar la presencia de interacción genotipo-ambiente (IGA) en la producción forrajera de avena (Avena sativa L.) de genotipos tolerantes y no tolerantes a Schizaphis graminum empleando un número bajo de ambientes en la provincia de Buenos Aires (Argentina) mediante los modelos de efectos principales aditivos e interacción multiplicativa (AMMI) y análisis factorial de correspondencias (AFC) y (ii) comparar los resultados obtenidos por ambos métodos. Los ensayos se condujeron en La Dulce (Argentina) y La Plata (Argentina) (1993, 1994 y 1995). Se evaluaron 12 genotipos (comerciales y líneas avanzadas) en 12 ambientes (combinación de localidad, años y cortes). Los factores ambiente, genotipo e interacción explicaron un 41,15% (p<0,001), 7,88% (p<0,05) y 36,36% (p<0,001) de la suma de cuadrados del total respectivamente. El modelo AMMI mostró los tres primeros ejes del análisis de componentes principales (ACP) altamente significativos (p<0,001), explicando un 57,99%, 29,03% y 6,27% de la suma de cuadrados de la interacción respectivamente. Las tres primeros ejes del AFC explicaron un 58,98%, 29,58% y 5,60% de dicha suma de cuadrados, respectivamente. El uso conjunto de ambos métodos surge como una herramienta muy útil para reflejar y caracterizar la existencia de interacción genotipo-ambiente en avena.

Comparação de métodos de estimação da estabilidade fenotípica em animais da raça Holandesa

Este trabalho teve por objetivo comparar os métodos de regressão convencional, desvio do desempenho máximo, índice de risco e o modelo AMMI (Additive Multiplicative Models Interaction) na estimação de parâmetros de estabilidade de leite de vaca da raça Holandesa. Os resultados obtidos foram comparados com os do método de Toler. Foram utilizados registros de 22.560 lactações em até 305 dias, obtidos na Associação de Criadores de Gado Holandês de Minas Gerais (ACGHMG), entre os anos de 1989 e 1996. Os animais foram separados em seis grupos genéticos e submetidos a 14 ambientes. Os métodos de regressão convencionais apresentaram classificações, com relação às variações ambientais, muito diferentes da classificação do método de Toler; este último foi considerado mais adequado. O método AMMI não foi eficiente para estudar a estabilidade fenotípica dos grupamentos genéticos da raça Holandesa. Os métodos do desvio do desempenho máximo e do índice de risco apresentaram resultados semelhantes entre si e complementaram as informações fornecidas pelo método de Toler. Os grupamentos GC2 (segunda geração controlada) e PO (puro de origem) foram os que apresentaram as maiores produtividades médias, e se alternaram entre si como os mais estáveis nos diferentes métodos. Os grupamentos 31/32 e GC1 foram os de pior desempenho médio, e estão sempre entre os mais instáveis em todos os métodos.

Emprego da análise AMMI na avaliação da estabilidade produtiva em soja

O objetivo deste trabalho foi avaliar a influência da interação de genótipos com ambientes (GxA) na produtividade de grãos de um conjunto de linhagens de soja (Glycine max L.). Foram utilizados dados de 11 experimentos (ambientes) realizados no Estado de Goiás. Em cada experimento foram avaliados 18 genótipos, sendo quatro cultivares comerciais como testemunhas. O método de análise da interação foi o procedimento AMMI (modelo de efeitos principais aditivos e interação multiplicativa). O padrão significativo das interações GxA foi captado apenas pelo primeiro eixo principal AMMI, o qual explicou 36% da soma de quadrados GxA original, sugerindo contaminação da matriz de interações clássica por ruídos que prejudicam a qualidade das predições de respostas fenotípicas obtidas pelos métodos tradicionais. Quanto à estabilidade de comportamento, a maioria das linhagens experimentais destacou-se (com menores interações com ambientes) em relação às cultivares testemunhas. Estas, no entanto, foram relativamente mais produtivas, sobretudo a cultivar Conquista. Entre as novas linhagens, os genótipos L-16, L-13 e L-14 mostraram ser os mais promissores para fins de recomendação como cultivares.

Development and evaluation of neural network models to estimate daily solar radiation at Córdoba, Argentina

The objective of this work was to develop neural network models of backpropagation type to estimate solar radiation based on extraterrestrial radiation data, daily temperature range, precipitation, cloudiness and relative sunshine duration. Data from Córdoba, Argentina, were used for development and validation. The behaviour and adjustment between values observed and estimates obtained by neural networks for different combinations of input were assessed. These estimations showed root mean square error between 3.15 and 3.88 MJ m-2 d-1 . The latter corresponds to the model that calculates radiation using only precipitation and daily temperature range. In all models, results show good adjustment to seasonal solar radiation. These results allow inferring the adequate performance and pertinence of this methodology to estimate complex phenomena, such as solar radiation.

Análise AMMI com dados imputados em experimentos de interação genótipo x ambiente de algodão

O objetivo deste trabalho foi avaliar a conveniência de definir o número de componentes multiplicativos dos modelos de efeitos principais aditivos com interação multiplicativa (AMMI) em experimentos de interações genótipo x ambiente de algodão com dados imputados ou desbalanceados. Um estudo de simulação foi realizado com base em uma matriz de dados reais de produtividade de algodão em caroço, obtidos em ensaios de interação genótipo x ambiente, conduzidos com 15 cultivares em 27 locais no Brasil. A simulação foi feita com retiradas aleatórias de 10, 20 e 30% dos dados. O número ótimo de componentes multiplicativos para o modelo AMMI foi determinado usando o teste de Cornelius e o teste de razão de verossimilhança sobre as matrizes completadas por imputação. Para testar as hipóteses, quando a análise é feita a partir de médias e não são disponibilizadas as repetições, foi proposta uma correção com base nas observações ausentes no teste de Cornelius. Para a imputação de dados, foram considerados métodos usando submodelos robustos, mínimos quadrados alternados e imputação múltipla. Na análise de experimentos desbalanceados, é recomendável escolher o número de componentes multiplicativos do modelo AMMI somente a partir da informação observada e fazer a estimação clássica dos parâmetros com base nas matrizes completadas por imputação.

Genotype by environment interaction for seed yield per plant in rapeseed using AMMI model

The objective of this study was to assess genotype by environment interaction for seed yield per plant in rapeseed cultivars grown in Northern Serbia by the AMMI (additive main effects and multiplicative interaction) model. The study comprised 19 rapeseed genotypes, analyzed in seven years through field trials arranged in a randomized complete block design, with three replicates. Seed yield per plant of the tested cultivars varied from 1.82 to 19.47 g throughout the seven seasons, with an average of 7.41 g. In the variance analysis, 72.49% of the total yield variation was explained by environment, 7.71% by differences between genotypes, and 19.09% by genotype by environment interaction. On the biplot, cultivars with high yield genetic potential had positive correlation with the seasons with optimal growing conditions, while the cultivars with lower yield potential were correlated to the years with unfavorable conditions. Seed yield per plant is highly influenced by environmental factors, which indicates the adaptability of specific genotypes to specific seasons.

Stability and adaptability of runner peanut genotypes based on nonlinear regression and AMMI analysis

The objective of this work was to estimate the stability and adaptability of pod and seed yield in runner peanut genotypes based on the nonlinear regression and AMMI analysis. Yield data from 11 trials, distributed in six environments and three harvests, carried out in the Northeast region of Brazil during the rainy season were used. Significant effects of genotypes (G), environments (E), and GE interactions were detected in the analysis, indicating different behaviors among genotypes in favorable and unfavorable environmental conditions. The genotypes BRS Pérola Branca and LViPE‑06 are more stable and adapted to the semiarid environment, whereas LGoPE‑06 is a promising material for pod production, despite being highly dependent on favorable environments.

Degree of multicollinearity and variables involved in linear dependence in additive-dominant models

The objective of this work was to assess the degree of multicollinearity and to identify the variables involved in linear dependence relations in additive-dominant models. Data of birth weight (n=141,567), yearling weight (n=58,124), and scrotal circumference (n=20,371) of Montana Tropical composite cattle were used. Diagnosis of multicollinearity was based on the variance inflation factor (VIF) and on the evaluation of the condition indexes and eigenvalues from the correlation matrix among explanatory variables. The first model studied (RM) included the fixed effect of dam age class at calving and the covariates associated to the direct and maternal additive and non-additive effects. The second model (R) included all the effects of the RM model except the maternal additive effects. Multicollinearity was detected in both models for all traits considered, with VIF values of 1.03 - 70.20 for RM and 1.03 - 60.70 for R. Collinearity increased with the increase of variables in the model and the decrease in the number of observations, and it was classified as weak, with condition index values between 10.00 and 26.77. In general, the variables associated with additive and non-additive effects were involved in multicollinearity, partially due to the natural connection between these covariables as fractions of the biological types in breed composition.

Análise AMMI da produtividade de grãos em linhagens de soja selecionadas para resistência à ferrugem asiática

O objetivo deste trabalho foi quantificar os efeitos da interação genótipo x ambiente (GxE) sobre a produtividade de grãos em progênies de soja pré-selecionadas para resistência à ferrugem asiática (Phakopsora pachyrhizi). Doze ensaios de avaliação de progênies (linhagens F6 e F7) foram conduzidos em diferentes ambientes (combinação de locais, anos e tratamentos fungicidas para controle de doenças de final de ciclo, incluindo ou não a ferrugem). A análise "additive main effects and multiplicative interaction" (AMMI) capturou, como padrão da interação GxE, 57% da variação associada aos resíduos de não aditividade, dos quais 44% foram retidos no primeiro componente principal de interação e o restante, no segundo. O primeiro componente associou-se a diferenças entre os anos de avaliação, o que denota imprevisibilidade na predição. O segundo componente, no entanto, associou-se ao manejo diferenciado do cultivo, no que se refere ao controle ou não das doenças. Entre os genótipos de ampla adaptabilidade produtiva, as linhagens USP 02-16.045 e USP 10-10 apresentaram desempenho destacado.

Random regression models to estimate genetic parameters for milk production of Guzerat cows using orthogonal Legendre polynomials

The objective of this work was to compare random regression models for the estimation of genetic parameters for Guzerat milk production, using orthogonal Legendre polynomials. Records (20,524) of test-day milk yield (TDMY) from 2,816 first-lactation Guzerat cows were used. TDMY grouped into 10-monthly classes were analyzed for additive genetic effect and for environmental and residual permanent effects (random effects), whereas the contemporary group, calving age (linear and quadratic effects) and mean lactation curve were analized as fixed effects. Trajectories for the additive genetic and permanent environmental effects were modeled by means of a covariance function employing orthogonal Legendre polynomials ranging from the second to the fifth order. Residual variances were considered in one, four, six, or ten variance classes. The best model had six residual variance classes. The heritability estimates for the TDMY records varied from 0.19 to 0.32. The random regression model that used a second-order Legendre polynomial for the additive genetic effect, and a fifth-order polynomial for the permanent environmental effect is adequate for comparison by the main employed criteria. The model with a second-order Legendre polynomial for the additive genetic effect, and that with a fourth-order for the permanent environmental effect could also be employed in these analyses.