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

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.

The growth of domestic goats and sheep: A meta study with Bertalanffy-Pütter models

“…As to the sources and the breeds of goats, G01-G02 were Anglo Nubian (and crossbreds) from Brazil (Arre et al., 2019 ; Cavalcante et al., 2013 ; Santos et al., 2018 ), G03-G08 colored and white Angora from Turkey (Cak et al., 2017 ; Ödzdemir et al., 2009 ), G09-G10 Beetal from Pakistan ( Teleken, Galvão & Weber, 2017 ; Waheed, Khan & Sarwar, 2010 ), G11-G22 Boer from Mexico ( Garcia-Muñiz, Ramirez-Valverde, Núñez-Domínguez & Hidalgo, 2019 ), G23 Repartida from Brazil ( Pires et al., 2017 ), G24 Saanen from Turkey ( Kor, Baspinar, Karaca & Keskin, 2006 ), and G25-G29 unspecified breeds from Tunisia and Turkey ( Mabrouk et al., 2010 ; Tatar, Tekel, Özkan, Baritci & Dellal, 2009 ).…”

Urochloa Grass Growth as a Function of Nitrogen and Phosphorus Fertilization

“…The adjusted coefficient of model determination as presented by Santos et al (2018) is expressed by: , where, and…”

Method to generate growth and degrowth models obtained from combinations of existing models applied to agrarian sciences

“…The DM content at 105 °C was determined by drying until constant weight, crude protein (CP) and acid detergent insoluble protein (ADIP) were defined using the Kjeldahl method according to the AOAC [1], and neutral detergent fiber (NDF) and acid detergent fiber (ADF) were determined according to [31]. Gas production was read at 2,4,6,8,10,12,14,17,20,24,28,32,48,72, and 96 h after the start of the in vitro fermentation process at the Federal University of Minas Gerais (UFMG) according to the equation proposed by [15].…”

“…These models were used in studies such as those by [16,30] for cumulative gas production kinetics. More recently, [24] presented the von Bertalanffy and Gompertz models, among others, (see Table 1, p. 2664) as sub-cases of what they called the method to generate growth models obtained from differential equations. Thus, the development of the mathematical model proposed resulted from the combination of the two models:  von Bertalanffy: (9)…”

“…[9,32] concluded that new models are still needed that can yield more biologically significant results with good mathematical fit of broad ranges of curve shapes with variable inflection points. In addition, creating new models for overall and specific situations is highly justifiable in face of the dynamics with which non-linear models have been applied in biological researches [2,23,24].…”