Blackberry is a small fruit with several properties beneficial to human health and its cultivation is an alternative for small producers due to its fast and high financial return. Studying the growth of fruits over time is extremely important to understand their development, helping in the most appropriate crop management, avoiding post-harvest losses, which is one of the aggravating factors of blackberry cultivation, being a short shelf life fruit. Thus, growth curves are highlighted in this type of study and modeling through statistical models helps understanding how such growth occurs. Data from this study were obtained from an experiment conducted at the Federal University of Lavras in 2015. The aim of this study was to adjust nonlinear, double Logistic and double Gompertz models to describe the diameter growth of four blackberry cultivars (‘Brazos’, ‘Choctaw’, ‘Guarani’ and ‘Tupy’). Estimations of parameters were obtained using the least squares method and the Gauss-Newton algorithm, with the “nls” and “glns” functions of the R statistical software. The comparison of adjustments was made by the Akaike information criterion (AICc), residual standard deviation (RSD) and adjusted determination coefficient (R2 aj). The models satisfactorily described data, choosing the Logistic double model for ‘Brazos’ and ‘Guarani’ cultivars and the double Gompertz model for ‘Tupy’ and ‘Choctaw’ cultivars.

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.

A method capable of reducing the environmental damage caused by swine manure and the soil enrichment with nutrients is based on the use of these residues together with the crops straw in soils for agricultural production. Through the use of carbon mineralization curves, it is possible to determine the best intervals for the use of organic matter from manure to better adapt the use of soil and crops. Dynamics of carbon present in manure can help in the selection of the best management. The objective of this study was to compare the fit of three nonlinear models that describe the carbonmineralization in soil over time, in addition to assessing the carbon stock of wheat straw alone and combined with swine manure. The experiment was carried out in a randomized block design, with four replications and eight treatments. The following treatments were tested: T1 – soil (S), T2 – soil + straw on the surface (SSUR), T3 – soil + incorporated straw (INCS), T4 – soil + manure on the surface (MSUR), T5 – soil + incorporated manure (INCM), T6 – soil + incorporated manure + straw on the surface (INCMSSUR), T7 - soil + incorporated manure + incorporated straw (INCMINCS), T8 – soil + straw on the surface + manure on the surface (SSURMSUR). Soil samples were incubated for 95 days, and ten observations were made throughout time. Carbon mineralization was described using nonlinear models Cabrera, Stanford and Smith and Juma, considering the autoregressive error structure AR (1), when necessary. The comparison of fit of models was made using the Akaike Information Criterion (AIC). The description of carbon mineralization of wheat straw and swine manure carried out by nonlinear models was satisfactory. The Cabrera model was the most appropriate to describe all treatments. The Stanford and Smith model, most used in the literature todescribe the mineralization of organic waste in soil, did not achieve better results in relation to the other nonlinear models for the treatments under study. In general, the treatments with straw on the surface resulted in a larger carbon stock in the soil, and with the addition of manure to the wheat straw, the carbon stock was lower, so it is interesting for producers to evaluate, according to their production targets, which is the best strategy to be adopted for the use of waste.

‘Green Dwarf’ coconut is a fruit of great economic interest, since all its components are used, in addition to water, its main component. It is a culture of humid tropics, widely produced in northeastern Brazil, being an important income source for the region. The phenology study of this type of fruit is extremely important, but there are few studies in literature. Regression models, especially nonlinear growth models, can be of great value to understand how fruit growth behaves. The scarcity of works of this nature may be linked to some difficulties in estimating parameters of nonlinear models, such as assigning initial values to the itterative process. Overcoming this difficulty, for regression analysis, linear or not, several steps need to be respected to ensure the validity of information. Much information can be extracted from nonlinear growth models, such as the asynotic value, growth rate and critical points (maximum acceleration point, inflection point, maximum deceleration point and asynotic deceleration point). The aim of this work was to describe the stages of nonlinear regression analysis and to estimate the critical points of ‘Green Dwarf ’ coconut growth curves. After initial adjustments, the only unmet assumption was independence, adding a first order autoregressive term. Again, models were adjusted and all parameters were significant, with both models, Gompertz and Logistic, adjusting well to data, with slight advantage for the Logistic model with better adjustment quality criteria values, with maximum expected LED and LEDKP values of 21.4037 cm and 21.5478 cm, respectively. The x and y axis of critical points were estimated, with values that can help producers to make more objective decisions about the appropriate time to harvest coconut fruits, considering the most diverse uses of this type of fruit.

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