Nonlinear models to characterize cumulative gas production using the in vitro technique in Brachiaria grass silage harvested at three cutting ages
Abstract
The Brazilian ruminant production system, which relies on native or cultivated pastures, underscores the importance of silage for feed preservation in the tropical regions. This study aimed to evaluate different mathematical models for cumulative in vitro gas production in Brachiaria decumbens grass silages at three distinct cutting ages (56, 84, and 112 d). The in vitro gas production technique provided information on fermentation kinetics, were analyzed using mathematical models. The methodology included statistical tests to evaluate normality, independence, and heteroscedasticity of the residuals, as well as the application of various criteria for model selection. The results indicated that models such as Logistic, von Bertalanffy, Gompertz, Richards, Brody, and France were appropriate, but the France and Brody models provided the best overall fit. Based on the adopted criteria, the Brody model was found to be the most suitable for describing cumulative gas production across all cutting ages of Brachiaria grass. Cumulative gas production was highest at 56 days of growth, with the Brody model indicating superior production capacity during this period (191.14 mL/g dry matter). In conclusion, an appropriate choice of mathematical model is important for the accurate representation of gas production kinetics in Brachiaria grass silage.
Keywords: fermentation; tropical forage; model selection.
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1. Pereira-Flores ME, Justino F, Rodrigues JM, et al. Seasonal climate impact on Brazilian pasture (Brachiaria brizantha cv. Marandu): growth rate, CO efflux, and irrigation strategies. Theor. appl. climatol. 2023;151. Available from: https://doi.org/10.1007/s00704-022-04295-y
2. Magalhães, FA. Produção acumulada de gases pela técnica in vitro da silagem do capim Brachiaria decumbens em diferentes idades de corte. [Tese] Belo Horizonte (MG): Doutorado em Zootecnia, Escola de Veterinária, Universidade Federal de Minas Gerais; 2013 [citado em 23 de março de 2013]. Available from: https://hdl.handle.net/1843/BUOS-98LFGY
3. Assis JR, Fernandes GA, Mousquer CJ, et al. Modelos matemáticos aplicados à cinética de digestão ruminal e produção de gás in vitro. In: Galati RL, Queiroz MFS. Inovações na nutrição animal: desafios da produção de qualidade. 1st ed. Guarujá: Científica Digital; 2021. p. 164–179. Available from: https://doi.org/10.37885/210404121
4. Mello R, Magalhães ALR, Breda FC, Regazzi AJ. Modelos para ajuste da produção de gases em silagens de girassol e milho. Pesq. agropec. bras. 2008;2. Available from: https://doi.org/10.1590/S0100-204X2008000200016
5. Santos ALP, Moreira GR, Brito CCR, et al. Method to generate growth and degrowth models obtained from differential equations applied to agrarian sciences. Semina: Ciênc. agr. 2018;39. Available from: https://doi.org/10.5433/1679-0359.2018v39n6p2659
6. Emiliano PC, Vivanco MJ, Menezes FS. Information criteria: How do they behave in different models? Comput. stat. and dat. anal. 2014;69. Available from: https://doi.org/10.1016/j.csda.2013.07.032
7. Santos ALP, Brito CCR, Moreira GR, et al. New model of evaluation of sunflower and corn silages by the in vitro gas production technique. Semina: ciênc. agr. 2020;41. Available from: https://doi.org/10.5433/1679-0359.2020v41n4p1373
8. Figueiredo MPS, Moreira GR, Brito CCR, et at. Method to generate growth and degrowth models obtained from existing models compositions applied to animal sciences – the athens-canadian chicken growth case. Livest. sci. 2023;269. Available from: https://doi.org/10.1016/j.livsci.2023.105162
9. Laird AK. Dynamics of relative growth. Growth. 1965;29.
10. Schofield P, Pitt RE, Pell AN. Kinetics of fiber digestion from in vitro gas production. J. anim. sci. 1994;72. Available from: doi: https://doi.org/10.2527/1994.72112980x
11. Shapiro SS, Wilk MB. An analysis of variance test for normality (complete samples), Biometrika. 1965;52. Available from: https://doi.org/10.1093/biomet/52.3-4.591
12. Morettin PA, Toloi CMC. Análise de séries temporais. 2nd ed. São Paulo: Blucher; 2006. 564p. Português.
13. Breusch AR, Pagan TS. A simple test for heteroscedasticity and random coefficient variation. Econometrica. 1979;47.
14. Akaike H. A new look at the statistical model identification. IEEE Transact. Autom. Cont. 1974;19. Available from: https://doi.org/10.1109/TAC.1974.1100705
15. Schwarz G. Estimating the dimension of a model. Ann. Statist. 1978;6. Available from: https://doi.org/10.1214/aos/1176344136
16. França AFS, Silva ANR, Oliveira LG, et al. In vitro gas production from pearl millet cultivars under nitrogen levels, Rev. bras. saúde prod. anim. 2024;25. Available from: https://doi.org/10.1590/s1519-994020230034
17. Uçkardes F, Efe E. Investigation o the usability of some mathematical models in in vitro gas production techniques Slovak j. anim sci. 2014;47. Available from: https://office.sjas-journal.org/index.php/sjas/article/view/231
18. G. Castro. Características produtivas, agronômicas e nutricionais do capim-tanzânia em cinco diferentes idades ao corte. Arq. bras. med. vet. zootec. 2010;62. Available from: https://doi.org/10.1590/S0102-09352010000300022
19. Silva NV, Santos MVF, Silva VJ, et al. Morphological characteristics and kinetics of in vitro gas production of tall and dwarf elephant grass genotypes as affected by harvest frequencies. J. Agric. Sci. 2025;16. Available from: https://doi.org/10.1017/S0021859625000231
20. Cavalcanti AC, Saliba EOS, Couto Filho CC, et al. Avaliação de fenos produzidos com Andropogon gayanus em diferentes idades empregando-se a técnica de produção de gases. Rev. facult. agr. 2018;117. Available from: https://sedici.unlp.edu.ar/handle/10915/74058
21. Ribeiro GOJ, Velasco FO, Faria Junior WG, et al. Cinética de degradação in situ das silagens de capim Andropogon gayanus produzidas em três idades de corte. Arq bras. med. vet. zootec. 2014;66. Available from: https://doi.org/10.1590/1678-6780
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