Skip to main navigation menu Skip to main content Skip to site footer

Mathematical models for describing growth in peach (Prunus persica [L.] Batsch.) fruit cv. Dorado

Peach fruits cv. Dorado. Photo: E..H. Pinzón-Sandoval

Abstract

Among deciduous species, the peach tree (Prunus persica [L.] Batsch.) is of great importance in the high tropics. However, the growth behavior of this fruit for different cultivated varieties is unknown. So, adjustment to double sigmoid curves is assumed for all even though sigmoid type curves have been reported for many peach cultivar. This has led to the misinterpretation of information, impeding decision-making in terms of management. Non-linear regression models best describe the growth curves, where parameters are estimated by minimizing the sum of squares of the errors. In particular, the logistic model is one of the better options for correctly representing fruit growth. Therefore, the objective of this research was to determine the efficiency of mathematical models for describing growth in P. persica cv. Dorado fruits grown under conditions in the municipality of Tuta-Boyaca. The Logistic model was the most appropriate for describing the growth curves based on fresh or dry weight, while the Gompertz model was the most suitable for describing the polar and equatorial diameters of the Dorado variety fruits because they were used to generate these parameters with practical interpretations and they adequately represented the biological process.

Keywords

logistic model, non-linear model, sigmoid curve, Gompertz model, Weibull model

PDF

References

  • Almanza, P., H. Balaguera, and L. Africano. 2015. Fisiología y bioquímica de la maduración del fruto de durazno [Prunus persica ( L.) Batsch]. Una Revisión. Rev. Colomb. Cienc. Hortic. 9(1), 161-172. Doi: 10.17584/rcch.2015v9i1.3754
  • Archontoulis, S.V. and F.E. Miguez. 2015. Nonlinear regression models and applications in agricultural research. Agron. J. 107(2), 786-798. Doi: 10.2134/agronj2012.0506
  • Bertin, N. 2005. Analysis of the tomato fruit growth response to temperature and plant fruit load in relation to cell division, cell expansion and DNA endoreduplication. Ann. Bot. 95(3), 439-447. Doi: 10.1093/aob/mci042
  • Campos, T. 2013. Especies y variedades de hoja caduca en Colombia. pp. 47-67. In: Miranda, D., G. Fischer, and C. Carranza (eds.). Los frutales caducifolios en colombia Situación actual, sistemas de cultivo y plan de desarrollo. Sociedad Colombiana de Ciencias Hortícolas, Bogotá.
  • Carranza, C., O. Lanchero, D. Miranda, and B. Chaves. 2009. Growth analysis of ‘Batavia’ lettuce (Lactuca sativa L.) cultivated in a saline soil of the Bogota Plateau. Agron. Colomb. 27(1), 41-48.
  • Casierra-Posada, F., V.E. Barreto, and O.L. Fonseca. 2004. Crecimiento de frutos y ramas de duraznero (Prunus persica L. Batsch, cv. ’Conservero’) en los altiplanos colombianos. Agron. Colomb. 22(1), 40-45.
  • Chaar, J. and D. Astorga. 2012. Determinación del requerimiento de frío y de calor en duraznero [Prunus persica (L.) Batsch.] mediante un modelo de correlación. RIA Rev. Investig. Agropecu. 38(3), 289-298.
  • Cunha, L., M. Berlingieri, B. Mattiuz, R. Martins, and J. Durigan. 2007. Caracterização da curva de maturação de pêssegos ‘Aurora-1’, na região de Jaboticabal-SP. Rev. Bras. Frutic. 29(3), 661-665. Doi: 10.1590/S0100-29452007000300045
  • Dela Bruna, E. 2007. Curva de crescimento de frutos de pêssego em regiões subtropicais. Rev. Bras. Frutic. 29(3), 685-689. Doi: 10.1590/S0100-29452007000300050
  • Della Bruna, E. and A.L. Moreto. 2011. Desenvolvimento dos frutos de pêssego “Aurora” e nectarina “Sunraycer” no sul de Santa Catarina. Rev. Bras. Frutic. 33(Supl. 1), 485-492. Doi: 10.1590/s0100-29452011000500065
  • Ducuara-Cabrera, W. 2017. Los frutales caducifolios: un recorrido a través del contexto agroindustrial y social boyacense. Cult. Cient. 15, 78-90.
  • Fernandes, T.J., A.A. Pereira, J.A. Muniz, and T.V. Savian. 2014. Selection of nonlinear models for the description of the growth curves of coffee fruit. Coffee Sci. 9(2), 207-215.
  • Fischer, G., F. Casierra-Posada, and C. Villamizar. 2011. Producción forzada de duraznero (Prunus persica (L.) Batsch) en el altiplano tropical de Boyacá (Colombia). Rev. Colomb. Cienc. Hortic. 4(1), 19-32. Doi: 10.17584/rcch.2010v4i1.1223
  • Hanusz, Z., Z. Siarkowski, and K. Ostrowski. 2008. Zastosowanie modelu Gompertz’a w inżynierii rolniczej. Inżynieria Rolnicza 7(105), 71-77.
  • Hunt, R. 2016. Growth analysis, individual plants. pp. 421-429. In: Thomas, B., B.G. Murray, and D.J. Murphy (eds.). Encyclopedia of applied plant sciences. 2nd ed. Vol. 1. Elsevier, Oxford, UK. Doi: 10.1016/B978-0-12-394807-6.00226-4
  • Hurvich, C.M. and C.L. Tsai. 1993. A corrected akaike information criterion for vector autoregressive model selection. J. Time Ser. Anal. 14(3), 271-279. Doi: 10.1111/j.1467-9892.1993.tb00144.x
  • Leal do Prado, T.K., T. Villela Savian, and J.A. Muniz. 2013. Ajuste dos modelos gompertz e logístico aos dados de crescimento de frutos de coqueiro anão verde. Cienc. Rural 43(5), 803-809. Doi: 10.1590/S0103-84782013005000044
  • Marcelis, L.F.M. and E. Heuvelink. 2007. Concepts of modelling carbon allocation among plant argans. pp. 103-111. In: Proc. Frontis Workshop on Functional-Structural Plant Modelling in Crop Production. Springer, Dordrecht, The Netherlands.
  • Meier, U. 2001. Growth stages of mono- and dicotyledonous plants: BBCH Monograph. Open Agrar Repositorium, Berlin. Doi: 10.5073/20180906-074619
  • Menezes da Silva, É., M.H. Tadeu, V.F. da Silva, R. Pio, T.J. Fernandes, and J.A. Muniz. 2020. Description of blackberry fruit growth by nonlinear regression models. Rev. Bras. Frutic. 42(2), 1-11. Doi: 10.1590/0100-29452020177
  • Miguez, F., S. Archontoulis, and H. Dokoohaki. 2018. Nonlinear regression models and applications. pp. 401-447. In: Glaz, B. and K.M. Yeater (eds.). Applied statistics in agricultural, biological, and environmental sciences. American Society of Agronomy; Wiley, Madison, WI. Doi: 10.2134/appliedstatistics.2016.0003.c15
  • Muianga, C.A., J.A. Muniz, M.D.S. Nascimento, T.J. Fernandes, and T.V. Savian. 2016. Descrição da curva de crescimento de frutos do cajueiro por modelos não lineares. Rev. Bras. Frut. 38(1), 22-32. Doi: 10.1590/0100-2945-295/14
  • Paine, C.E.T., T.R. Marthews, D.R. Vogt, D. Purves, M. Rees, A. Hector, and L.A. Turnbull. 2012. How to fit nonlinear plant growth models and calculate growth rates: An update for ecologists. Methods Ecol. Evol. 3(2), 245-256. Doi: 10.1111/j.2041-210X.2011.00155.x
  • Peil, R.M. and J.L. Galvez. 2005. Reparto de materia seca como factor determinante de la producción de las hortalizas de fruto cultivadas en invernadero. Rev. Bras. Agrociênc. 11(1), 5-11.
  • Pinzón, E.H., A. Cruz Morillo, and G. Fischer. 2014. Physiological aspects of peach (Prunus persica [L.] BATSCH) in the high tropical zone: A review. Rev. U.D.C.A Actual. Divulg. Cient. 17(2), 401-411.
  • Pola, A.C., E. Della Bruna, Á.J. Back, and A.L. Moreto. 2016. Estimativa da duração da fase florescimento-colheita em variedades de pessegueiro em Urussanga, SC. Agrop. Catarinense 29(2), 68-73.
  • Quevedo García, E., G.O. Cancino Escalante, and A.R. Barragán Torres. 2017. Modelos de regresión para estimar el peso seco de órganos y área del limbo del duraznero, variedad jarillo. Rev. U.D.C.A Actual. Divulg. Cient. 20(2), 299-310. Doi: 10.31910/rudca.v20.n2.2017.388
  • Quevedo-García, E., A.E. Darghan, and G. Fischer. 2017. Clasificación de variables morfológicas del duraznero (Prunus persica L. Batsch) ‘Jarillo’ en la montaña santandereana colombiana mediante análisis discriminante lineal. Rev. Colomb. Cienc. Hortic. 11(1), 39-47. Doi: 10.17584/rcch.2017v11i1.6140
  • Raftery, A.E. 1986. Choosing models for cross-classifications. Am. Sociol. Rev. 51(1), 145. Doi: 10.2307/2095483
  • Ritz, C. and J.C. Streibig. 2005. Bioassay analysis using R. J. Stat. Softw. 12(5), 1-22. Doi: 10.18637/jss.v012.i05
  • Sari, B.G., A.D.C. Lúcio, C.S. Santana, and T.V. Savian. 2019. Describing tomato plant production using growth models. Sci. Hort. 246, 146-154. Doi: 10.1016/j.scienta.2018.10.044
  • Shabani, A., A.R. Sepaskhah, A.A. Kamgar-Haghighi, and T. Honar. 2018. Using double logistic equation to describe the growth of winter rapeseed. J. Agric. Sci. 156(1), 37-45. Doi: 10.1017/S0021859617000934
  • Silva, É.M., V.F. Silva, F.A. Fernandes, J.A. Muniz, and T.J. Fernandes. 2019. O crescimento de frutos de pêssegos caracterizados por modelos de regressão não lineares. Sigmae 8(2), 290-294.
  • Szabelska, A., M. Siatkowski, T. Goszczurna, and J. Zyprych. 2010. Comparison of growth models in package R. Nauka Przyr. Tech. 4(4), 1-9.
  • Thompson, D.S. 2001. Extensiometric determination of the rheological properties of the epidermis of growing tomato fruit. J. Exp. Bot. 52(359), 1291-1301. Doi: 10.1093/jxb/52.359.1291
  • Torres, E. 2006. Agrometeorologia. 2nd ed. Editorial Trillas, Mexico, DF
  • Trudgill, D.L., A. Honek, D. Li, and N.M. Van Straalen. 2005. Thermal time: Concepts and utility. Ann. Appl. Biol. 146(1), 1-14. Doi: 10.1111/j.1744-7348.2005.04088.x
  • Yin, X., J. Goudriaan, E.A. Lantinga, J. Vos, and H.J. Spiertz. 2003. A flexible sigmoid function of determinate growth. Ann. Bot. 91(3), 361-371. Doi: 10.1093/aob/mcg029

Downloads

Download data is not yet available.

Most read articles by the same author(s)