Selection of non-linear models and the study of conilon coffee fruit growth

Authors

DOI:

https://doi.org/10.33448/rsd-v11i4.27093

Keywords:

Modeling; Biometrics; Coffea canephora; Clones.

Abstract

The objective was to develop growth curves for fruit dry mass in Coffea canephora clones, select the best non-linear regression model, estimate the rate of mass gain, analyze differences in fruit development located in the lower, middle and upper thirds of the coffee canopy and generate an equation that describes the process. Eleven data collections were carried out, starting in the pellet phase of nine clones with 30 plants, with 50 fruits being collected in each position of the coffee tree canopies. To obtain the dry matter mass, the fruits were dried in an oven with forced air circulation at 65 °C until constant weight. The mathematical models Brody, Gompertz, Logístico, Mitscherlich and von Bertalanffy were applied. The quality of the equations was evaluated using eight statistical parameters and the confidence intervals of β1, β2 and β3 of the regressions estimated based on the likelihood profile. After selecting the best model, the fruit growth curves were estimated considering the three positions in the coffee canopy. All statistical analyzes were performed in the R software. The Logistic model presents greater reliability to describe the accumulation of dry matter mass in fruits. There were no differences between positions in the coffee canopy. The β3 parameter can be used as an early indicator for Coffea canephora and guide breeding programs. Clones 204, 407 and P1 provided curves with higher quality in relation to the parameters evaluated.

References

Akaike, H. A. (1974). New Look at the Statistical Model Identification. IEEE Transactions on automatic control, 19(6), 716-723.

Bates, D., Watts, D. (1980). Relative curvature measures of nonlinearity. Journal of the Royal Statistical Society, Series B (Methodological), 42(1), 1-25.

Brody, S. (1945). Bioenergetics and growth. New York: Reinhold, 1023 p.

Companhia Nacional de Abastecimento. (2021). Acompanhamento da safra brasileira de café, safra 2021, quarto levantamento. 8(4), 1-55.

Covre, A. M., Partelli, F.L., Bonomo R. & Gontijo, I. (2018). Micronutrients in the fruits and leaves of irrigated and non-irrigated coffee plants. Journal of Plant Nutrition. DOI: 10.1080/01904167.2018.1431665.

Croissant, Y. & Millo, G. (2008). Panel Data Econometrics in R: The plm Package. Journal of Statistical Software, 27(2), 1-43. doi: 10.18637/jss.v027.i02. URL: https://doi.org/10.18637/jss.v027.i02.

Cruz, R.M. (2020). Critérios de informação e seleção de modelos lineares mistos [Dissertação de Mestrado, Instituto de Matemática e Estatística, Universidade de São Paulo].

Dubberstein, D., Partelli, F. L., Dias, J. R. M., & Espindola, M. C. (2016). Concentration and accumulation of macronutrients in leaf of coffee berries in the Amazon, Brazil. Australian Journal of Crop Science, 10(5), 701-710. doi: 10.21475/ajcs.2016.10.05.p7424.

Dubberstein, D., Partelli, F. L., Espindola, M. C. & Dias, J. R. M. (2019). Concentration and accumulation of micronutrients in robust coffee. Acta Scientiarum. Agronomy, 41. doi: 10.4025/actasciagron.v41i1.42685.

Elzhov, T.V., Mullen, K. M., Spiess, A. N. & Bolker, B. (2016). Minpack.lm: R Interface to the Levenberg-Marquardt Nonlinear Least-Squares Algorithm Found in MINPACK, Plus Support for Bounds. 2(1). https://CRAN.R-project.org/package=minpack.lm.

Fernandes, F. A., Fernandes, T. J., Pereira, A. A., Meirelles, S. L. C. & Costa, A. C. (2019). Growth curves of meat-producing mammals by von Bertalanffy's model. Pesquisa Agropecuária Brasileira, 54, 1-8. doi: 10.1590/S1678-3921.pab2019.v54.01162.

Fernandes, T. J., Pereira, A. A., Muniz, J.A. & Savian, T. V. (2014). Seleção de modelos não lineares para a descrição das curvas de crescimento do fruto do cafeeiro. Coffee Science, 9(2), 207-215.

Fox, J. & Weisberg, S. (2019). An R Companion to Applied Regression, Third Edition. URL: https://socialsciences.mcmaster.ca/jfox/Books/Companion/.

Gompertz, B. 1825. On the nature of the function expressive of the law of human mortality and on a new model of determining life contingencies. Philosophical Transactions of the Royal Society of London. 115, 513–585. (10.1098/rstl.1825.0026)

Jane, S. A., Fernandes, F. A., Silva, E. M., Muniz, J. A. & Fernandes, T. J. (2019). Comparação dos modelos polinomial e não lineares na descrição do crescimento de pimenta. Revista Brasileira de Ciências Agrárias, 14(4), 1-7. doi:10.5039/agraria.v14i4a7180.

Jane, S.A., Fernandes, F.A., Muniz, J.A. & Fernandes, T.J. (2020a). Nonlinear models on description of sugarcane height and diameter variety RB92579. Revista Ciência Agronômica, 51(4), e.20196660.

Jane, S. A., Fernandes, F. A., Silva, E. M., Muniz, J. A., Fernandes, T. J., & Pimentel, G. V. (2020b). Adjusting the growth curve of sugarcane varieties using nonlinear models. Ciência Rural, 50(3).

Laviola, B. G., Martinez, H. E. P., Salomão, L. C. C., Cruz, C. D. & Mendonça, S. M. (2007). Acúmulo de nutrientes em frutos de cafeeiro em quatro altitudes de cultivo: cálcio, magnésio e enxofre. Revista Brasileira de Ciência do Solo, 31, 1451-1462.

Leon, J. & Fournier, L. (1962). Crecimiento y desarrollo del fruto de Coffea arabica. Turrialba, 12, 65-74.

Mitscherlich, E. A. (1919). Das Gesetz des Pflanzenwachstums. Landwirtsch Jahrb, 53, 167-182.

Morais, E.O., Ribeiro, K.L., Veloso, R.B. & Veloso, M.D.M. (2020). Application of linear and nonlinear regression models for biomass and carbon stock volume estimates. Braz. J. of Develop., 6(7), 45621-45632. doi: 10.34117/bjdv6n7-259.

Muianga, C.A., Muniz, J.A., Nascimento, M.S., Fernandes, T.J. & Savian, T.V. (2016). Por descrição da curva de crescimento de frutos do cajueiro modelos não lineares. Revista Brasileira de Fruticultura, 38(1), 22-32.

Partelli, F. L., Espindula, M. C., Marré, W. B. & Vieira, H. D. (2014). Dry matter and macronutriente accumulation in fruits of conilon coffee with different ripening cicles. Revista Brasileira de Ciência do Solo, 38, 214-222.

Pinheiro, J., Bates, D., DebRoy, S. & Sarkar, D. (2019). nlme: Linear and Nonlinear Mixed Effects Models. R package version 3.1-139. URL: https://CRAN.R-project.org/package=nlme.

Prado, T. K. L. do., Savian, T. V., & Muniz, J. A. (2013). Ajuste dos modelos Gompertz e Logístico aos dados de crescimento de frutos de coqueiro anão verde. Ciência Rural, 43(5), 803-809. doi:10.1590/S0103-84782013005000044.

Prado, T.K.L., Savian, T.V., Fernandes, T.J. & Muniz, J.A. (2020). Study on the growth curve of the internal cavity of ‘Dwarf green’coconut fruits. Revista Ciência Agronômica, 51(3).

Prado, T.K.L., Savian, T.V. & Muniz, J.A. (2013). Ajuste dos modelos Gompertz e Logístico aos dados de crescimento de frutos de coqueiro anão verde. Ciência Rural, 43(5), 803-809.

R Core Team (2019). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL: https://www.R-project.org/.

Ratkowsky, D. A. (1983). Nonlinear Regression Modeling: a Unified Practical Approach. Marcel Dekker, New York.

Rena, A. B., Barros, R. S. & Maestri, M. (2001) Desenvolvimento reprodutivo do cafeeiro. In L., Zambolim (Ed.). Tecnologias de produção de café com qualidade. p. 101-128. Viçosa: UFV.

Ronchi, C.P. & DaMatta, F.M. (2019). Aspectos Fisiológicos do Café Conilon. In: R. G., Ferrão, A. F. A., Fonseca, M. A. G., Ferrão, L. H., De Muner. (Eds.), Conilon Coffee english translation Marcelle Gualda Pasolini, edition updated and expanded, 974.

Salazar-Gutiérrez, M. R., Chaves, C. B., Riaño, N. M., Arcila, P. J. & Jaramillo, R. A. (1994). Crecimiento del fruto de café Coffea arabica L. var Colombia. Cenicafé, 45, 1-50.

Sari, B.G., Lúcio, A.D.C., Samanta, C.S. Olivoto, T., Diel, M.I. & Krysczun, D.K. (2019). Nonlinear growth models: An alternative to ANOVA in tomato trials evaluation. European Journal of Agronomy, 104, 21-36.

Sarkar, D. (2008). Lattice: Multivariate Data Visualization with R. Springer. R. Springer Science & Business Media.

Schwarz, G. (1978). Estimating the dimension of a model. Annals of Statistics, 6, 461- 464.

Silva, É. M. da, Tadeu, M. H., Silva, V. P. da, Pio, R., Fernandes, T. J. & Muniz, J. A. (2020). Description of blackberry fruit growth by nonlinear regression models. Revista Brasileira de Fruticultura, 42(2).

Silva, E.M., Fruhauf, A.C., Silva, E.M., Muniz, J.A., Fernandes, J.F. & Silva, V.F. (2021). Evaluation of the critical points of the most adequate nonlinear model in adjusting growth data of ‘green dwarf’ coconut fruits. Revista Brasileira de Fruticultura, 43(1). doi: http://dx.doi.org /10.1590/0100-29452021726.

Silva, W. S., Fernandes, F. A., Muniz, F. R., Muniz, J. A., & Fernandes, T. J. (2021). Eucalyptus grandis x eucalyptus urophylla growth curve in different site classifications, considering residual autocorrelation. Revista Brasileira de Biometria, 39(1), 122-138.

Spiess, A.N. (2018). qpcR: Modelling and Analysis of Real-Time PCR Data. R package version 1.4-1. https://CRAN.R-project.org/package=qpcR.

Venables, W. N. & Ripley, B. D. (2002). Modern Applied Statistics with S. Fourth Edition.

Von Bertalanffy, L. (1957). Quantitative laws for metabolism and growth. The quarterly review of biology, 32(3), 217-231.

Wormer, T. M. (1964). The growth of the coffee berry. Annals of Botany, 28, 47-55.

Zeileis, A.; Hothorn, T. (2002). Diagnostic Checking in Regression Relationships. R News, 2(3) 7-10. URL https://CRAN.R-project.org/doc/Rnews/.

Published

16/03/2022

How to Cite

SENRA, J. F. de B. .; SILVA, J. A. da .; FERREIRA, A.; ESPOSTI, M. D. D. .; SILVA, U. R. .; MILHEIROS, I. S. .; ZACARIAS, A. J. . Selection of non-linear models and the study of conilon coffee fruit growth. Research, Society and Development, [S. l.], v. 11, n. 4, p. e21511427093, 2022. DOI: 10.33448/rsd-v11i4.27093. Disponível em: https://rsdjournal.org/index.php/rsd/article/view/27093. Acesso em: 16 apr. 2024.

Issue

Section

Agrarian and Biological Sciences