scholarly journals The use of the nonlinear models in the growth of pears of ‘Shinseiki’ cultivar

2017 ◽  
Vol 48 (1) ◽  
Author(s):  
Thais Destefani Ribeiro ◽  
Taciana Villela Savian ◽  
Tales Jesus Fernandes ◽  
Joel Augusto Muniz
Keyword(s):  
Logistic Model ◽  
Least Squares Method ◽  
Nonlinear Models ◽  
Logistic Models ◽  
Information Criterion ◽  
Fruit Weight ◽  
Coefficient Of Determination ◽  
Pear Fruit ◽  
Asian Pear ◽  
Residual Correlations

ABSTRACT: The goal of this study was to elucidate the growth and development of the Asian pear fruit, on the grounds of length, diameter and fresh weight determined over time, using the non-linear Gompertz and Logistic models. The specifications of the models were assessed utilizing the R statistical software, via the least squares method and iterative Gauss-Newton process (DRAPER & SMITH, 2014). The residual standard deviation, adjusted coefficient of determination and the Akaike information criterion were used to compare the models. The residual correlations, observed in the data for length and diameter, were modeled using the second-order regression process to render the residuals independent. The logistic model was highly suitable in demonstrating the data, revealing the Asian pear fruit growth to be sigmoid in shape, showing remarkable development for three variables. It showed an average of up to 125 days for length and diameter and 140 days for fresh fruit weight, with values of 72mm length, 80mm diameter and 224g heavy fat.

scholarly journals Proposals of non-linear models to adjust in vitro gas production at different incubation times in cassava genotypes

2021 ◽  
Vol 43 ◽  
pp. e22
Author(s):  
André Luiz Pinto dos Santos ◽  
Frank Sinatra Gomes da Silva ◽  
Guilherme Rocha Moreira ◽  
Cícero Carlos Ramos de Brito ◽  
Maria Lindomárcia Leonardo da Costa ◽  
...  
Keyword(s):  
Linear Models ◽  
Least Squares Method ◽  
Logistic Models ◽  
Information Criterion ◽  
Gas Production ◽  
Coefficient Of Determination ◽  
Absolute Deviation ◽  
In Vitro Gas Production ◽  
The One

The present study aimed to propose new two-compartment models from the combination of the Gompertz, Logistic and Von Bertalanffy models and to identify between Gompertz and Logistic models, in their uni and two-compartiment versions, the one that presents the highest quality of fit to cumulative gas production curves of five cassava genotypes: Brasília, Engana Ladrão, Dourada, Gema de Ovo e Amansa Burro. The gas production readings were 2, 4, 6, 8, 10, 12, 14, 17, 20, 24, 28, 32, 48, 72, and 96 hours after the start of the in vitro fermentation process. The estimation of the parameters for the models was made by the least squares method through the Gauss-Newton iterative process. The selection of the best model to describe the gas accumulation was based on the adjusted coefficient of determination, residual mean squares, mean absolute deviation, Akaike information criterion and Bayesian information criterion. Among the adjusted models, the proposed models were the best to describe the accumulation of gases over time according to the methodology and conditions under which this study was developed.

scholarly journals Nonlinear Models for Plant Height of Rye Cultivars at Sowing Times

2018 ◽  
Vol 10 (12) ◽  
pp. 157 ◽  
Author(s):  
Jéssica Andiara Kleinpaul ◽  
Alberto Cargnelutti Filho ◽  
Daniela Lixinski Silveira ◽  
Ismael Mario Marcio Neu ◽  
Cirineu Tolfo Bandeira ◽  
...  
Keyword(s):  
Plant Height ◽  
Nonlinear Models ◽  
Logistic Models ◽  
Information Criterion ◽  
Coefficient Of Determination ◽  
Maximum Acceleration ◽  
Inflection Points ◽  
Thermal Sum ◽  
Average Plant ◽  
The One

Adjusting nonlinear Gompertz and Logistic models will help in the understanding of the growth pattern of the rye crop and also in the height response of the plant, when planted in different environmental conditions. The the aims of this study were to adjust the nonlinear Gompertz and Logistic models for plant height and indicate the one that best describes growth of two rye cultivars in five sowing times. Ten uniformity trials were conducted with the rye crop in the 2016 harvest. In each trial, ten randomly selected plants were evaluated from the first expanded leaf weekly. In each plant height was measured. The adjustment of the Gompertz and Logistic models as a function of the accumulated thermal sum was performed with the average plant height at each evaluation. The parameters a, b, and c were estimated for each model. The confidence interval for each parameter and the inflection points, maximum acceleration, maximum deceleration and asymptotic deceleration were calculated. The quality of fit of the models was verified by the coefficient of determination, Akaike's information criterion and residual standard deviation. Intrinsic non-linearity and non-linearity of the parameter effect were quantified. Both models describe satisfactorily the plant height. The model that best describes the growth of rye cultivars is Logistic.

scholarly journals Productive traits of rye cultivars grown under different sowing seasons

2019 ◽  
Vol 23 (12) ◽  
pp. 937-944
Author(s):  
Jéssica A. Kleinpaul ◽  
Alberto Cargnelutti Filho ◽  
Fernanda Carini ◽  
Rafael V. Pezzini ◽  
Gabriela G. Chaves ◽  
...  
Keyword(s):  
Aerial Part ◽  
Dry Matter ◽  
Nonlinear Models ◽  
Logistic Models ◽  
Information Criterion ◽  
Thermal Time ◽  
Coefficient Of Determination ◽  
Maximum Acceleration ◽  
Intrinsic Nonlinearity ◽  
Productive Traits

ABSTRACT This study aimed to adjust the Gompertz and Logistic nonlinear models for the fresh and dry matter of aerial part and indicate the model that best describes the growth of two rye cultivars in five sowing seasons, as well as to characterize the growth of the cultivars regarding the fresh and dry matter of aerial part. Ten uniformity trials were conducted with the rye crop in 2016. A weekly sampling and evaluation of 10 plants per trial was performed from the time the plants presented one expanded leaf. For each plant, the fresh and dry matter of aerial part were weighed. The Gompertz and Logistic models were adjusted to the accumulated thermal time based on the measures of each trait in each assessment. Also the parameters a, b, and c for each model were estimated and calculated the interval of confidence for each parameter, as well as the inflection points, maximum acceleration, maximum deceleration and asymptotic deceleration. The quality of the model adjustments was verified using the coefficient of determination, Akaike information criterion, and residual standard deviation. The intrinsic nonlinearity and nonlinearity of the parameter effect was quantified. Both models satisfactorily describe the behavior of the fresh and dry matter of aerial part. The Logistic model best describes the growth of rye cultivars. The growth of the cultivars BRS Progresso and Temprano is distinct between sowing seasons. Cultivar BRS Progresso requires a lower thermal time until reaching 50% of its growth when compared to the Temprano cultivar.

scholarly journals Classical nonlinear models to describe the growth curve for Murrah buffalo breed

2012 ◽  
Vol 42 (3) ◽  
pp. 520-525 ◽  
Author(s):  
Ronyere Olegário de Araújo ◽  
Cintia Righetti Marcondes ◽  
Maria Cecília Florisbal Damé ◽  
Analía del Valle Garnero ◽  
Ricardo José Gunski ◽  
...  
Keyword(s):  
Logistic Model ◽  
Nonlinear Models ◽  
Logistic Models ◽  
Growth Curves ◽  
Coefficient Of Determination ◽  
Von Bertalanffy ◽  
Average Deviation ◽  
Absolute Deviation ◽  
Murrah Buffalo ◽  
Deviation Coefficient

With the objective of to adjust nonlinear models for the growth curves for a buffaloes herd raised in floodable lands in Rio Grande do Sul state, monthly records measured from birth to two years-old of 64 males and 63 females born between 1982 and 1989 were used. The models used were: Von Bertalanffy, Brody, Gompertz and Logistic. The parameters were estimated by NLIN procedure and the criteria used to evaluate the adjustment given by the models were: asymptotic standard deviation; coefficient of determination; average absolute deviation of residues and asymptotic index. Von Bertalanffy and Brody models overestimated the male asymptotic weight (A) in 15.9 and 171.3kg, respectively, and the Gompertz and Logistic models underestimated it in 4.5 and 13.4kg, respectively. For females, the Logistic model underestimated the asymptotic weight (-2.09kg), and Gompertz, Von Bertalanffy and Brody overestimated this parameter in 8.04, 17.7, and 280.33kg, respectively. The biggest average deviation was estimated by Brody model for both sexes, characterizing the biggest index. Considering the criteria, it is recommended the Gompertz and Logistic models for adjust females and males Murrah buffaloes breed growth curves.

scholarly journals Morphometric characteristics of the Mangalarga Marchador horse breed determined by nonlinear models

2019 ◽  
Vol 54 ◽  
Author(s):  
Felipe Amorim Caetano de Souza ◽  
Tales Jesus Fernandes ◽  
Fabiana Oliveira Cunha ◽  
Rafaela Aparecida Ribeiro ◽  
Fabiana Rezende Muniz ◽  
...  
Keyword(s):  
Logistic Model ◽  
Nonlinear Models ◽  
Information Criterion ◽  
Coefficient Of Determination ◽  
Morphometric Characteristics ◽  
R Software ◽  
Morphometric Measurements ◽  
Pregnant Females ◽  
Software Models ◽  
Males And Females

Abstract: The objective of this work was to evaluate the development of the morphometric characteristics of Mangalarga Marchador horses through nonlinear models. The transversal method was used to collect data on height at the withers (HW), body length (BL), and thoracic (TP) and cannon (CP) perimeters from 200 horses (75 males and 125 non-pregnant females), aged between 6 and 153 months. The parameters of the Brody, Gompertz, logistic, and von Bertalanffy nonlinear models were estimated using the R software. Models were compared and selected using the coefficient of determination, the residual standard deviation, and the corrected Akaike information criterion. For adult females, HW, BL, TP, and CP ranged between 146.45-148.34, 148.59-151.64, 179.07-182.88, and 18.25-18.76 cm, respectively. For males, HW, BL, and CP ranged between 148.55-151.80, 150.77-154.88, and 18.95-19.41 cm, respectively. The logistic model best expresses growth in HW for males and females, as well as in BL and CP for males, whereas the Brody model is the best predictor for HW, BL, TP, and CP for females. The increase in the values of the morphometric measurements is more rapid and homogeneous between the ages of 6 and 24 months, stabilizing at 60 months in both sexes.

scholarly journals Growth in weight and of some tissues in the bullfrog: fitting nonlinear models during the fattening phase

2014 ◽  
Vol 38 (6) ◽  
pp. 598-606 ◽  
Author(s):  
Marcelo Maia Pereira ◽  
Cleber Fernando Menegasso Mansano ◽  
Edney Pereira da Silva ◽  
Marta Verardino De Stéfani
Keyword(s):  
Food Intake ◽  
Logistic Model ◽  
Fat Body ◽  
Nonlinear Models ◽  
Logistic Models ◽  
Live Weight ◽  
Initial Weight ◽  
Expected Values ◽  
Growth Of Animals ◽  
Cumulative Food Intake

Knowledge of the growth of animals is important so that zootechnical activity can be more accurate and sustainable. The objective of this study was to describe the live weight, development of liver tissue and fat body, leg growth, and cumulative food intake of bullfrogs during the fattening phase using nonlinear models. A total of 2,375 bullfrog froglets with an initial weight of 7.03 ± 0.16 g were housed in five fattening pens (12 m²). Ten samplings were performed at intervals of 14 days to obtain the variables studied. These data were used to estimate the parameters of Gompertz and logistic models as a function of time. The estimated values of weight (Wm) and food intake (FIm) at maturity and time when the growth rate is maximum (t*) were closer to expected values when the logistic model was used. The Wm values for live weight and liver, adipose and leg weights and the FIm value for food intake were 343.7, 15.7, 19.6, 96.03 and 369.3 g, respectively, with t* at 109, 98, 105, 109 and 107 days. Therefore, the logistic model was the best model to estimate the growth and food intake of bullfrogs during the fattening phase.

scholarly journals Mathematical models to describe the growth curves of white-egg layers

2018 ◽  
Vol 39 (3) ◽  
pp. 1327
Author(s):  
Cleber Franklin Santos de Oliveira ◽  
João Marcos Novais Tavares ◽  
Gerusa Da Silva Salles Corrêa ◽  
Bruno Serpa Vieira ◽  
Silvana Alves Pedrozo Vitalino Barbosa ◽  
...  
Keyword(s):  
Mathematical Models ◽  
Mean Squared Error ◽  
Computer Software ◽  
Logistic Models ◽  
Growth Curves ◽  
Gompertz Model ◽  
Information Criterion ◽  
Coefficient Of Determination ◽  
Population Densities

The aim of this study was to compare mathematical models describing growth curves of white-egg layers at different population densities. To fit the models, 4,000 growing white-egg layers were utilized. The experimental design was completely randomized, with population densities of 71, 68, 65, 62, and 59 birds per cage in the starter phase and 19, 17, 15, 13, and 11 birds per cage in the grower phase, with 10 replicates each. Birds were weighed weekly to determine the average body weight and the weight gain. Gompertz and Logistic models were utilized to estimate their growth. The data analysis was carried out using the PROC NLMIXED procedure of the SAS® statistical computer software to estimate the parameters of the equation because mixed models were employed. The mean squared error, the coefficient of determination, and Akaike’s information criterion were used to evaluate the quality of fit of the models. The studied models converged for the description of the growth of the birds at the different densities studied, showing that they were appropriate for estimating the growth of white-egg layers housed at different population densities. The Gompertz model showed a better fit than the Logistic model.

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

2018 ◽  
Vol 39 (6) ◽  
pp. 2659 ◽  
Author(s):  
André Luiz Pinto dos Santos ◽  
Guilherme Rocha Moreira ◽  
Cicero Carlos Ramos de Brito ◽  
Frank Gomes-Silva ◽  
Maria Lindomárcia Leonardo da Costa ◽  
...  
Keyword(s):  
Differential Equations ◽  
Goodness Of Fit ◽  
Least Squares Method ◽  
Growth Curves ◽  
Information Criterion ◽  
Coefficient Of Determination ◽  
Absolute Deviation ◽  
Marquardt Algorithm ◽  
Maturation Rate ◽  
Biological Interpretation

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.

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

2019 ◽  
Author(s):  
André Luiz Pinto dos Santos ◽  
Guilherme Rocha Moreira ◽  
Frank Gomes-Silva ◽  
Cícero Carlos Ramos de Brito ◽  
Maria Lindomárcia Leonardo da Costa ◽  
...  
Keyword(s):  
Least Squares Method ◽  
Kinetic Curve ◽  
Information Criterion ◽  
Compartment Model ◽  
Gas Production ◽  
Coefficient Of Determination ◽  
Von Bertalanffy ◽  
Absolute Deviation ◽  
Two Compartment Model

AbstractMathematical 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-automatedin vitrotechnique 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 thein vitrofermentation 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.

scholarly journals Allometric models to estimate tree height in northern Amazonian ecotone forests

2019 ◽  
Vol 49 (2) ◽  
pp. 81-90 ◽  
Author(s):  
Reinaldo Imbrozio BARBOSA ◽  
Perla Natalia RAMÍREZ-NARVÁEZ ◽  
Philip Martin FEARNSIDE ◽  
Carlos Darwin Angulo VILLACORTA ◽  
Lidiany Camila da Silva CARVALHO
Keyword(s):  
Amazon Basin ◽  
Nonlinear Models ◽  
Tree Height ◽  
Information Criterion ◽  
Specific Model ◽  
Stem Diameter ◽  
Coefficient Of Determination ◽  
Allometric Models ◽  
Peripheral Areas ◽  
Total Tree

ABSTRACT Allometric models defining the relationship between stem diameter and total tree height in the Amazon basin are important because they refine the estimates of tree carbon stocks and flow in the region. This study tests different allometric models to estimate the total tree height from the stem diameter in an ecotone zone between ombrophilous and seasonal forests in the Brazilian state of Roraima, in northern Amazonia. Stem diameter and total height were measured directly in 65 recently fallen trees (live or dead). Linear and nonlinear regressions were tested to represent the D:H relation in this specific ecotone zone. Criteria for model selection were the standard error of the estimate (Syx) and the adjusted coefficient of determination (R²adj), complemented by the Akaike Information Criterion (AIC). Analysis of residuals of the most parsimonious nonlinear models showed a tendency to overestimate the total tree height for trees in the 20-40 cm diameter range. Application of our best fitted model (Michaelis-Menten) indicated that previously published general equations for the tropics that use diameter as the independent variable can either overestimate tree height in the study area by 10-29% (Weibull models) or underestimate it by 8% (climate-based models). We concluded that our site-specific model can be used in the ecotone forests studied in Roraima because it realistically reflects the local biometric relationships between stem diameter and total tree height. Studies need to be expanded in peripheral areas of northern Amazonia in order to reduce uncertainties in biomass and carbon estimates that use the tree height as a variable in general models.

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