Method to generate growth and degrowth models obtained from differential equations applied to agrarian sciences

Authors

  • André Luiz Pinto dos Santos Universidade Federal Rural de Pernambuco
  • Guilherme Rocha Moreira Universidade Federal Rural de Pernambuco
  • Cicero Carlos Ramos de Brito Instituto Federal de Pernambuco
  • Frank Gomes-Silva Universidade Federal Rural de Pernambuco
  • Maria Lindomárcia Leonardo da Costa Universidade Federal da Paraíba
  • Patrícia Guimarães Pimentel Universidade Federal do Ceará
  • Moacyr Cunha Filho Universidade Federal Rural de Pernambuco
  • Ivone Yurika Mizubuti Universidade Estadual de Londrina

DOI:

https://doi.org/10.5433/1679-0359.2018v39n6p2659

Keywords:

Growth curve, Non-linear model, New model, Model selection.

Abstract

This study aims to propose a method to generate growth and degrowth models using differential equations as well as to present a model based on the method proposed, compare it with the classic linear mathematical models Logistic, Von Bertalanffy, Brody, Gompertz, and Richards, and identify the one that best represents the mean growth curve. To that end, data on Undefined Breed (UB) goats and Santa Inês sheep from the works of Cavalcante et al. (2013) and Sarmento et al. (2006a), respectively, were used. Goodness-of-fit was measured using residual mean squares (RMS), Akaike information criterion (AIC), Bayesian information criterion (BIC), mean absolute deviation (MAD), and adjusted coefficient of determination . The models’ parameters (?, weight at adulthood; ?, an integration constant; ?, shape parameter with no biological interpretation; k, maturation rate; and m, inflection point) were estimated by the least squares method using Levenberg-Marquardt algorithm on the software IBM SPSS Statistics 1.0. It was observed that the proposed model was superior to the others to study the growth curves of goats and sheep according to the methodology and conditions under which the present study was carried out.

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Author Biographies

André Luiz Pinto dos Santos, Universidade Federal Rural de Pernambuco

Discente, Curso de Doutorado, Programa de Pós-Graduação em Biometria e Estatística Aplicada, Universidade Federal Rural de Pernambuco, UFRPE, Recife, PE, Brasil.

Guilherme Rocha Moreira, Universidade Federal Rural de Pernambuco

Prof., Programa de Pós-Graduação em Biometria e Estatística Aplicada, UFRPE, Recife, PE, Brasil.

Cicero Carlos Ramos de Brito, Instituto Federal de Pernambuco

Prof., Instituto Federal de Pernambuco, IFPE, Recife, Brasil.

Frank Gomes-Silva, Universidade Federal Rural de Pernambuco

Prof., Programa de Pós-Graduação em Biometria e Estatística Aplicada, UFRPE, Recife, PE, Brasil.

Maria Lindomárcia Leonardo da Costa, Universidade Federal da Paraíba

Profa, Departamento de Zootecnia, Universidade Federal da Paraíba, UFPB, Areia, PB, Brasil.

Patrícia Guimarães Pimentel, Universidade Federal do Ceará

Profa Dra, Departamento de Zootecnia, Universidade Federal do Ceará, UFCE, Ceará, CE, Brasil.

Moacyr Cunha Filho, Universidade Federal Rural de Pernambuco

Prof., Programa de Pós-Graduação em Biometria e Estatística Aplicada, UFRPE, Recife, PE, Brasil.

Ivone Yurika Mizubuti, Universidade Estadual de Londrina

Profa Dra, Departamento de Zootecnia, Universidade Estadual de Londrina, UEL, Londrina, PR, Brasil.

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Published

2018-11-30

How to Cite

Santos, A. L. P. dos, Moreira, G. R., Brito, C. C. R. de, Gomes-Silva, F., Costa, M. L. L. da, Pimentel, P. G., … Mizubuti, I. Y. (2018). Method to generate growth and degrowth models obtained from differential equations applied to agrarian sciences. Semina: Ciências Agrárias, 39(6), 2659–2672. https://doi.org/10.5433/1679-0359.2018v39n6p2659

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