Proposal for a new non-linear model to describe growth curves

This study was developed with longitudinal data measurements of Norfolk rabbits from birth to 119 days of age to estimate the average growth curve, with the primary objective of proposing a non-linear model. It also selected the most appropriate sigmoidal model to describe the growth of Norfolk rabbits. The adjustments provided by the logistic, von Bertalanffy, Gompertz, Brody, Richards, and proposed models were compared. The parameters were estimated using the "nls" function of the "stats" package in R software, the least-squares method, and the Gauss-Newton convergence algorithm. The goodness-of-fit comparison was based on the following criteria: adjusted coefficient of determination (), mean square error (MSE), mean absolute deviation (MAD), Akaike information criterion (AIC), and Bayesian information criterion (BIC). Cluster analysis helped select and classify the non-linear growth models, considering the other goodness-of-fit criteria results. The proposed non-linear, von Bertalanffy, Gompertz, and Richards models described the growth curve of Norfolk rabbits satisfactorily, providing parameters with practical interpretations. The goodness-of-fit criteria showed that the proposed and von Bertalanffy models best represented the growth of rabbits.

New bicompartmental model: an application for the production of gases using the in vitro technique / Novo modelo bicompartimental: uma aplicação para a produção de gases pela técnica in vitro

The purpose of this study was to propose a bicompartmental nonlinear model and to identify the best-performing model between the proposed model and the bicompartmental logistic (BL) mode regarding the quality of fit to the curve of cumulative gas production (CGP) using corn silage, sunflower, and their mixtures. Gas production was measured 2, 3, 4, 6, 8, 9, 10, 12, 15, 19, 24, 30, 36, 48, 72, and 96 h after beginning the in vitro fermentation process. The generated data were used to generate the parameters of each model tested using the stats package of the R computational tool version 4.0.4. The mathematical models were subjected to the following selection criteria: the adjusted coefficient of determination (Raj.), residual mean square (RMS), mean absolute deviation (MAD), and Akaike information criterion (AIC). It was demonstrated that the proposed model had better performance with a high Raj., and lower values of RMS, AIC, and MAD than the bicompartmental logistic model for the prediction of the parameters of cumulative gas production (CGP), per to present a superior fit in the set of criteria according to the methodology and conditions in which the present study was developed.(AU)

No presente trabalho, com silagem de milho, girassol e suas misturas, objetivou-se propor um modelo não linear bicompartimental e identificar entre o modelo proposto e Logístico Bicompartimental (LB), aquele que apresenta maior qualidade de ajuste à curva de cinética de produção cumulativa de gases (PCG). A leitura da produção de gás foi realizada nos tempos 2, 3, 4, 6, 8, 9, 10, 12, 15, 19, 24, 30, 36, 48, 72 e 96 horas, após o início do processo de fermentação in vitro. Os dados gerados foram utilizados para geração dos parâmetros de cada modelo testado com auxílio do pacote stats da ferramenta computacional R versão 4.0.4. Os modelos matemáticos foram submetidos aos seguintes critérios de seleção o coeficiente de determinação ajustado (Raj.), quadrado médio do resíduo (QMR), desvio médio absoluto (DMA) e o critério de informação de Akaike (AIC). Foi demonstrado que o modelo proposto teve melhor desempenho com altos Raj., e menores valores de QMR, AIC e DMA, por apresentar um ajustamento superior no conjunto dos critérios em comparação com o modelo logístico bicompartimental para a predição dos parâmetros de produção cumulativa de gases (PCG) de acordo com a metodologia e condições em que foi desenvolvido o presente estudo.(AU)

Proposal of a non-linear model to adjust in vitro gas production at different incubation times

This work aims to propose a new model named Gompertz-Von Bertalanffy bicompartmental (GVB), a combination of the models Gompertz and Von Bertalanffy. The GVB models is applied to fit the kinetic curve of cumulative gas production (CGP) of four foods (SS ­ sunflower silage; CS ­ corn silage; and the mixtures 340SS ­ 660 gkg-1 of corn silage and 340 gkg-1 of sunflower silage; and 660SS ­ 340 gkg-1 of corn silage and 660 gkg-1 of sunflower silage). The GVB fit is compared to models Logistic-Von Bertalanffy bicompartmental (LVB) and bicompartmental logistic (BL). All the process studied employed the semi-automatic "in vitro" technique of producing gases used in ruminant nutrition. The gas production readout was performed at times 2, 4, 6, 8, 10, 12, 15, 19, 24, 30, 48, 72, and 96 h. The data generated were used to estimate the models' parameters by the least squared method with the iterative Gauss-Newton process. The data fit quality of the models was verified using the adjusted coefficient of determination criterion (), mean residual square (MRS), Akaike information criterion (AIC), and mean absolute deviation (MAD). Among the analyzed models, the LVB model presented the best quality of fit evaluators for CS. In contrast, the GVB model showed better quality of fit to describe CGP over time for 340SS, 660SS, and SS, presenting the highest values of () and the lowest values of MSR, AIC, and MAD.

New model of evaluation of sunflower and corn silages by the in vitro gas production technique / Novo modelo para avaliação das silagens de girassol e milho pela técnica in vitro de produção de gás

This study aimed to propose a model called Two-compartment Logistic-von Bertalanffy (LVB) and to identify among the proposed and Two-compartment Logistic (TL) models the one that has the best goodness of fit to the kinetic curve of cumulative gas production (CGP) of sunflower and corn silages alone and combined using the in vitro semi-automated gas production technique. A random block splitplot experimental design was employed in which the inoculums were the blocks, the incubation times were the split-plots, and the experimental diets were: CS - corn silage, SS - sunflower silage (as single roughage), and their mixtures, i.e., 340SS (660 g kg-1 corn silage and 340 g kg-1 sunflower silage) and 660SS (340 g kg-1 corn silage and 660 g kg-1 sunflower silage). The parameters were estimated by the least squares method using the iterative Gauss-Newton process in the software R version 3.4.1. The criteria adopted were: adjusted coefficient of determination (R2 adj.), residual mean squares (RMS), mean absolute deviation (MAD), Akaike information criterion (AIC), Bayesian information criterion (BIC), and relative efficiency (RE). The TL model had higher R2 adj. values compared to LVB, however, such difference may be considered negligible. The LVB model had RE above one, which indicates it is superior to the TL model, in addition to the lowest RMS, MAD, AIC, and BIC values, The Two compartment Logistic-von Bertalanffy model had the best fit to describe the CGP over time according to the methodology and conditions of the present study.(AU)

O objetivo deste trabalho é propor um modelo denominado Logístico-Von Bertalanffy bicompartimental (LVB) e identificar entre os modelos proposto e Logístico bicompartimental (LB), aquele apresenta maior qualidade de ajuste à curva de cinética de produção cumulativa de gases (PCG) das silagens de girassol, de milho e de suas misturas, através da técnica "in vitro" semiautomática de produção de gases. O delineamento experimental foi em blocos ao acaso, onde os inóculos equivalem aos blocos, os tempos de incubação às subparcelas, e as dietas experimentais foram: SM - silagem de milho; 340SG - 660 g kg-1 de silagem de milho e 340 g kg-1 de silagem de girassol; 660SG - 340 g kg-1 de silagem de milho e 660 g kg-1 de silagem de girassol e SG - silagem de girassol. Os parâmetros foram estimados pelo método de mínimos quadrados utilizando o processo iterativo de Gauss-Newton, a partir do programa R versão 3.4.1. Os critérios adotados foram: o coeficiente de determinação ajustado (R2 adj.), quadrado médio do resíduo (QMR), desvio médio absoluto (DMA), critério de informação de Akaike (AIC), critério Bayesiano de Schwarz (BIC) e a eficiência relativa (ER). O modelo LB apresentou os maiores valores de R2 adj. comparado ao LVB, porém, essa diferença entre eles pode ser considerada desprezível. O modelo LVB apresentou RE maior que um, indicando superioridade em relação ao LB, além disso, obteve os menores valores de QMR, DMA, AIC e BIC. Dentre os modelos ajustados, o modelo Logístico-Von Bertalanffy bicompartimental apresentou melhor qualidade de ajuste para descrever a PCG ao longo do tempo, de acordo com a metodologia e condições em que foi desenvolvido o presente estudo.(AU)

Generation of models from existing models composition: An application to agrarian sciences.

Mathematical models that describe gas production are widely used to estimate the rumen degradation digestibility and kinetics. The present study presents a method to generate models by combining existing models and to propose the von Bertalanffy-Gompertz two-compartment model based on this method. The proposed model was compared with the logistic two-compartment one to indicate which best describes the kinetic curve of gas production through the semi-automated in vitro technique from different pinto peanut cultivars. The data came from an experiment grown and harvested at the Far South Animal Sciences station (Essul) in Itabela, BA, Brazil and 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. The parameters were estimated by the least squares method using the iterative Gauss-Newton process in the software R version 3.4.1. The best model to describe gas accumulation was based on the adjusted coefficient of determination, residual mean squares, mean absolute deviation, Akaike information criterion, and Bayesian information criterion. The von Bertalanffy-Gompertz two-compartment model had the best fit to describe the cumulative gas production over time according to the methodology and conditions of the present study.

Method to generate growth and degrowth models obtained from differential equations applied to agrarian sciences / Método gerador de modelos de crescimento e decrescimento obtidos a partir de equações diferenciais aplicado as ciências agrárias

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.(AU)

O objetivo deste trabalho é propor um método gerador de modelos de crescimento e decrescimento por meio de equações diferenciais, bem como apresentar um modelo a partir do método proposto, compará-lo entre os modelos matemáticos não lineares clássicos seguintes, Logístico, Von Bertalanffy, Brody, Gompertz, e Richards e identificar aquele que representa melhor a curva média de crescimento. Para isso, foram utilizados dados de caprino (SRD - Sem Raça Definida) e de ovinos da raça Santa Inês oriundos, respectivamente, dos trabalhos de Cavalcante et al. (2013) e Sarmento et al. (2006a). A qualidade de ajuste foi medida por meio do quadrado médio do resíduo (QMR), critério de informação de Akaike (AIC), critério de informação Bayesiano (BIC), desvio médio absoluto (DMA) e coeficiente de determinação ajustado . Os parâmetros dos modelos (?, peso à idade adulta; ?, uma constante de integração; ?, parâmetro de forma sem interpretação biológica; k, taxa de maturação; e m, ponto de inflexão) foram estimados pelo método de mínimos quadrados utilizando o algoritmo de Levenberg-Marquardt por meio do Software IBM SPSS Statistics 1.0. Observou-se que o modelo Proposto foi superior aos outros modelos para o estudo das curvas de crescimento de caprinos e ovinos de acordo com a metodologia e condições em que foi desenvolvido o presente estudo.(AU)

Method to generate growth and degrowth models obtained from differential equations applied to agrarian sciences / Método gerador de modelos de crescimento e decrescimento obtidos a partir de equações diferenciais aplicado as ciências agrárias

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.

O objetivo deste trabalho é propor um método gerador de modelos de crescimento e decrescimento por meio de equações diferenciais, bem como apresentar um modelo a partir do método proposto, compará-lo entre os modelos matemáticos não lineares clássicos seguintes, Logístico, Von Bertalanffy, Brody, Gompertz, e Richards e identificar aquele que representa melhor a curva média de crescimento. Para isso, foram utilizados dados de caprino (SRD - Sem Raça Definida) e de ovinos da raça Santa Inês oriundos, respectivamente, dos trabalhos de Cavalcante et al. (2013) e Sarmento et al. (2006a). A qualidade de ajuste foi medida por meio do quadrado médio do resíduo (QMR), critério de informação de Akaike (AIC), critério de informação Bayesiano (BIC), desvio médio absoluto (DMA) e coeficiente de determinação ajustado . Os parâmetros dos modelos (?, peso à idade adulta; ?, uma constante de integração; ?, parâmetro de forma sem interpretação biológica; k, taxa de maturação; e m, ponto de inflexão) foram estimados pelo método de mínimos quadrados utilizando o algoritmo de Levenberg-Marquardt por meio do Software IBM SPSS Statistics 1.0. Observou-se que o modelo Proposto foi superior aos outros modelos para o estudo das curvas de crescimento de caprinos e ovinos de acordo com a metodologia e condições em que foi desenvolvido o presente estudo.