Ajuste de modelos não lineares duplo sigmoides no crescimento do fruto de macaúba por inferência bayesiana

• Edilene Cristina Pedroso Azarias ^[1] ; Natiele de Almeida Gonzaga ^[1] ; Édipo Menezes da Silva ^[2] ; Edilson Marcelino Silva ^[1] ; Tales Jesus Fernandes ^[1] ; Joel Augusto Muniz ^[1]
  1. [1] Universidade Federal de Lavras

     Universidade Federal de Lavras

     Brasil

     
  2. [2] Universidade Federal Rural do Rio de Janeiro

     Universidade Federal Rural do Rio de Janeiro

     Brasil

     
• Localización: Ciencia rural, ISSN 0103-8478, Vol. 55, Nº. 9, 2025
• Idioma: portugués
• DOI: 10.1590/0103-8478cr20240448
• Títulos paralelos:
  • Fitting nonlinear double sigmoid models to macauba fruit growth data using Bayesian inference
• Enlaces
  • Texto completo
• Resumen
  • português

    A macaúba (Acrocomia aculeata) é uma palmeira nativa das regiões tropicais dos continentes americanos. É utilizada na alimentação, e aplicada na indústria cosmética e farmacêutica. Seus frutos são fontes de matéria-prima para a produção de petróleo e bioenergia. Determinar o momento ideal para a colheita dos frutos é fundamental para garantir a máxima qualidade, além de otimizar os processos de pós-colheita e armazenamento. Este estudo teve como objetivo caracterizar o acúmulo de massa seca total e do mesocarpo do fruto de macaúba ao longo do tempo utilizando inferência bayesiana na estimação dos parâmetros dos modelos de regressão não linear duplo Logístico e duplo Gompertz.

    Além de selecionar o modelo que melhor descreveu os dados. A coleta dos frutos foi realizada a partir de uma semana após a abertura da espata, continuando semanalmente até a queda natural dos frutos, às 62 semanas após a antese, sendo secos em estufa de ventilação forçada.

    As análises estatísticas foram conduzidas no software R. Foi utilizado o método numérico de reamostragem por importância ponderada. Na seleção dos modelos foram utilizados o critério da densidade preditiva ordenada (CPO) e o critério de informação da deviance (DIC). O modelo duplo Gompertz foi o que melhor se ajustou aos dados. O mesocarpo do fruto não apresentou diferença na velocidade de crescimento entre a primeira e segunda etapa de desenvolvimento. Na etapa final, apresentou valores próximos a 9g. A massa seca total mostrou crescimento mais acelerado na primeira etapa, com valores próximos a 34 g na etapa final.

  • English

    Macauba (Acrocomia aculeata) is a palm tree native to the tropical regions of the Americas. It is used as a food and applied in the cosmetic and pharmaceutical industries. Macauba fruit is a source of raw material for oil and bioenergy production. Determining the ideal time to harvest macauba fruit is essential to ensure maximum quality and optimize the post-harvest and storage processes. The present study characterized the accumulation of total dry mass and mesocarp dry mass of macauba fruit over time. We used Bayesian inference to estimate the parameters of the nonlinear double logistic and double Gompertz regression models to find the model that best describes the data. Fruit samples were collected from one week after spathe opening and continuing weekly until natural fruit drop, at 62 weeks after anthesis, and dried in a forced ventilation oven. Statistical analyses were conducted in the R software, and the weighted resampling method was used. The Criterion of density Predictive Ordered (CPO) and deviance information criterion (DIC) were used to select the models. The double Gompertz model best fitted the data. The fruit mesocarp showed no difference in growth rate between the first and second stages of development. In the final stage, it reached values close to 9 g. The total dry mass showed faster growth in the first stage, with values close to 34 g in the final stage.

• Referencias bibliográficas
  • ALVES, J. L. F. et al. Potential of macauba endocarp (Acrocomia aculeate) for bioenergy production: Multi-component kinetic study and estimation...
  • ANDRADE FILHO, M. G. de et al. Bayesian approach to growth curve with objective priori. Revista Brasileira de Biometria, v.28, n.2, p.161-181,...
  • AZARIAS, E. C. P. et al. Study of the growth of amaranthus weeds using non-linear models. Brazilian Journal of Biometrics, v.42, n.1, p.1-19,...
  • AZARIAS, E. C. P. et al. Use of von Bertalanffy and logistic models in the description of dry mass accumulation of weeds amaranthus retroflexus...
  • CICONINI, G. et al. Biometry and oil contents of Acrocomia aculeata fruits from the Cerrados and Pantanal biomes in Mato Grosso do Sul, Brazil....
  • COLOMBO, C. A. et al. Macauba: a promising tropical palm for the production of vegetable oil. Ocl, v.25, n.1, p.D108, 2018.
  • COOMBE, B. The development of fleshy fruits. Annual Review of Plant Physiology, v.27, n.1, p.507-528, 1976.
  • DIAS, E. F. et al. Macauba (Acrocomia aculeata) pulp meal as alternative raw material for growing-pigs. Livestock Science, v.252, p.104675,...
  • EVARISTO, A. B. et al. Harvest and post-harvest conditions influencing macauba (Acrocomia aculeata) oil quality attributes. Industrial Crops...
  • EVARISTO, A. B. et al. Physico-chemical characterization macaw palm fruit from three regions the state of Minas Gerais, Brazil. Revista Agrotecnologia,...
  • FERNANDES, J. G. et al. Description of the peach fruit growth curve by diphasic sigmoidal nonlinear models. Revista Brasileira de Fruticultura,...
  • FERNANDES, T. J. et al. Bayesian estimation of nonlinear models parameters in the description of growth coffee fruits. Brazilian Journal...
  • FERNANDES, T. J. et al. Double sigmoidal models describing the growth of coffee berries. Ciência Rural, v.47, n.8, p.e20160646, 2017.
  • FONSECA, J. V. S. et al. Low-fat and rich-fibers macauba (Acrocomia spp.) sauces: Physical and oxidative stability, nutritional quality and...
  • GELFAND, A.; DEY, K. D. Bayesian model choice: Asymptotics and Exacts Calculations. Journal of the Royal Statistical Society: Series B, v.56,...
  • GEWEKE, J. Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments. In: BERNARDO, J. M. et al. (Ed.)....
  • LYNCH, S. M. Applied Bayesian Statistics, SAGE Publications, 2021. 216 p. MACHADO, W. et al. Evaluation of two fruit ecotypes (totai and sclerocarpa)...
  • MARTINS FILHO, S. et al. Bayesian approach in the growth curves of two cultivars of common bean. Ciência Rural, v.38, p.1516-1521, 2008.
  • MONTOYA S. G. et al. Fruit development, growth, and stored reserves in macauba palm (Acrocomia aculeata), an alternative bioenergy crop. Planta,...
  • MOREIRA, S. L. S. et al. Above-and below-ground carbon accumulation in cultivated macauba palm and potential to generate carbon credits....
  • NUNES, A. A. et al. Good practices of harvest and processing provide high quality Macauba pulp oil. European Journal of Lipid Science and...
  • PEREIRA, J. M. et al. Comparison of the models for prediction of the mineralized nitrogen: a bayesian approach. Ciência e Agrotecnologia,...
  • PEREIRA, A. A. et al. Bayesian modeling of the coffee tree growth curve. Ciência Rural, v.52, n.9, p.e20210275, 2022.
  • RAFTERY A. L.; LEWIS, S. C. One long run with diagnostics: Implementation strategies for markov chain. Statistical Science, v.7, n.4, p.493-497,...
  • REIS, R. L. et al. Bayesian inference in genetic analysis of diploid populations: inbreeding coefficient and outcrossing rate estimation....
  • REIS, R. L. et al. Bayesian approach to sensitivity of models for inbreeding coefficient. Ciência Rural, v.39, p.1752- 1759, 2009.
  • REIS, R. L. et al. Bayesian comparison of models with an application to the Hardy-Weinberg equilibrium using the disequilibrium coefficient....
  • RUBIN, D. B. A noniterative sampling/importance resampling alternative to the data augmentation algorithm for creating a few imputations when...
  • SAVIAN, T. V. et al. Bayesian analisys for ruminal degradability models. Ciência Rural, v.39, p.2169-2177, 2009.
  • SILVA, E. M. et al. Adjustment of mixed nonlinear models on Blackberry fruit growth. Revista Brasileira de Fruticultura, v.45, p.e-665, 2023a....
  • SILVA, S. V. C. et al. Bayesian modeling of the maximum rainfall of Petrópolis (RJ) and Poços de Caldas (MG). Engenharia Sanitária e Ambiental,...
  • SILVA, E. M. et al. Bayesian approach to the zinc extraction curve of soil with sewage sludge. Acta Scientiarum-Technology, v.42, p.e46893,...
  • SILVA, E. M. et al. Description of blackberry fruit growth by nonlinear regression models. Revista Brasileira de Fruticultura, v.42, n.2,...
  • SILVA, E. M. et al. Evaluation of the critical points of the most adequate nonlinear model in adjusting growth data of ‘green dwarf’coconut...
  • SILVA, E. M. et al. Stanford & Smith nonlinear model in the description of co2 evolved from soil treated with swine manure: maximum entropy...
  • SMITH, A. F. M.; GELFAND, A. E. Bayesian statistics without tears: a sampling-resampling perspective. The American Statistician, v.46, n.2,...
  • STRAUB, D.; PAPAIOANNOU, I. Bayesian updating with structural reliability methods. Journal of Engineering Mechanics, v.141, n.3, p.04014134,...
  • R DEVELOPMENT CORE TEAM. R: A language and environment for statistical computing. R foundation for statistical computing, 4.0. 5, 2024.
  • TURKMAN, M. et al. Computational Bayesian statistics: an introduction. Cambridge University Press, 2019. ZARZAR, C. A. et al. Evidence of...