Assessing sugarcane (Saccharum spp.) stalk growth helps to adequately manage the phenological stages of the crop. The aim of this study was to describe the height-growth curve of four sugarcane varieties (RB92579, RB93509, RB931530 and SP79-1011), in irrigated plant-cane and ratoon cane plantations, using the Logistic and Gompertz nonlinear models, while considering all deviations from assumptions. The model parameters were estimated based on the least squares method using the Gauss-Newton algorithm. To select the most suitable model, nonlinear measures, adjusted coefficient of determination (R2 adj), residual standard deviation (RSD), and corrected Akaike information criterion (AICc) were used. Based on the best models, stalk height growth rates and crop phenological stages were determined using critical points. All tests were performed in the free software environment for statistical computing and graphics, R. In general, the Logistic and Gompertz models without AR(1) better described the plant-cane and ratoon cane stalk height, respectively. All varieties showed early growth, and the RB92579 variety presented higher rates in both cycles.

An economic and environmentally feasible way to recycle sewage sludge is its use in agriculture.Information on carbon mineralization curves allows us to seek improvements in soil quality andcrop productivity. The objective of this work was to evaluate the nonlinear models that describecarbon mineralization in the soil. The experiment was conducted in laboratory and the design wascompletely randomized, with four replicates and three treatments. The following treatments wereevaluated: sewage sludge, black oat straw and sewage sludge + oat straw, incorporated into the soil.Pots with soil and the applied treatment were incubated for 110 days. The Stanford and Smith andCabrera models were used, considering structure of autoregressive errors AR (1) when necessary.The fittings were compared using the Akaike Information Criterion (AIC). The evaluated nonlinearmodels described the carbon decomposition dynamics of the treatments satisfactorily. The Stanfordand Smith model is suitable for describing the carbon decomposition in the soil + sludge and soil +oat straw treatments. The Cabrera model is suitable to describe the carbon decomposition of the soil+ sludge + straw treatment.Keywords: Mineralization. Stanford and Smith model. Cabrera model. Half-life.

Agricultural management is a viable way for recycling animal residues in feedlots. Thesubstances that make up organic residues change the dynamics of the organic matter decompositionin the soil. Information on carbon mineralization curves allows seeking improvements in soil qualityand, consequently, in crop productivity. The Stanford & Smith Nonlinear Model is the most usedto describe C mineralization of organic residues in the soil. This model considers organic residuesare composed of substances that are mineralized exponentially. The Cabrera Model considers twofractions, one composed of substances that are mineralized exponentially and other composed ofmore resistant substances with constant mineralization. The objective of this work was to comparenonlinear models that describe carbon mineralization, considering residues on surface or incorporatedinto the soil. The data evaluated were from an experiment with oat straw, liquid swine manure, andswine litter bedding. The Stanford & Smith and Cabrera Models were used considering structure offirst order autoregressive errors - AR(1), when necessary. The fittings were compared using the AkaikeInformation Criterion (AIC). The Cabrera Model was more adequate to describe C mineralization infour treatments (soil + incorporated liquid swine manure; soil + oat straw on surface + liquid swinemanure on surface; soil + incorporated straw; and soil + straw on surface). The Stanford & SmithModel was better in three treatments (soil + incorporated straw + incorporated liquid swine manure;swine litter bedding on surface; and incorporated swine litter bedding). None of the models describedthe treatment soil + liquid swine manure on surface.Keywords: Decomposition. Half-life. Stanford & Smith Model. Cabrera Model.

The aim of this study was to describe the growth curve of “Aurora 1” peaches using fruit height and diameter data over time through diphasic sigmoidal models constructed from eight combinations of the following models: Brody, Gompertz and Logistic. Data were obtained from an experiment carried out in 2005 in the municipality of Vista Alegre do Alto, São Paulo, Brazil. The parameters of models were adjusted by the least squares method using the Gauss-Newton algorithm implemented in the R software. Assumptions of normality, homogeneity and independence of residues were verified based on Shapiro-Wilk, Breush and Pagan and Durbin-Watson tests, respectively. The goodness of fit of models was verified according to the corrected Akaike information criterion (AICc), residual standard deviation (RSD), asymptote adjustment index (AI) and nonlinearity measures. All models adjusted for both fruit height and diameter variables met the assumptions of normality, independence and homoscedasticity of errors. In addition, all of them present good quality of fit to fruit height and diameter data, since they presented AI values close to one and low RSD values and non-linearity measures. However, the double Gompertz (GG) and the Logistic + Gompertz (LG) models presented, respectively, the best quality of fit to fruit height and diameter data in relation to the other models. It could be concluded that all diphasic sigmoidal models evaluated showed good fit to height and diameter data and can be used to describe the growth curve of “Aurora-1” peaches, according to goodness of fit criteria. However, it is important to highlight that GG and LG models presented the best quality of fit and can be selected to describe the height and diameter growth of “Aurora 1” peach fruits, respectively, with maximum expected growth close to 63 mm in height and 48 mm in diameter.

Zinc uptake is essential for crop development; thus, knowledge about soil zinc availability is fundamental for fertilization in periods of higher crop demand. A nonlinear first-order kinetic model has been employed to evaluate zinc availability. Studies usually employ few observations; however, inference in nonlinear models is only valid for sufficiently large samples. An alternative is the Bayesian method, where inferences are made in terms of probability, which is effective even with small samples. The aim of this study was to use Bayesian methodology to evaluate the fitness of a nonlinear first-order kinetic model to describe zinc extraction from soil with sewage sludge using seven different extraction solutions. The analysed data were obtained from an experiment using a completely randomized design and three replicates. Fifteen zinc extractions were evaluated for each extraction solution. Posterior distributions of a study that evaluated the nonlinear first-order kinetic model were used as prior distributions in the present study. Using the full conditionals, samples of posterior marginal distributions were generated using the Gibbs sampler and Metropolis-Hastings algorithms and implemented in R. The Bayesian method allowed the use of posterior distributions of another study that evaluated the model used as prior distributions for parameters  in the present study. The posterior full conditional distributions for the parameters  were normal distributions and gamma distributions, respectively. The Bayesian method was efficient for the study of the first-order kinetic model to describe zinc extraction from soil with sewage sludge using seven extraction solutions.