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 Mathematical Models for Tumor Growth and the Reduction of Overtreatment

2018 ◽  
Vol 80 (01) ◽  
pp. 072-078 ◽  
Author(s):  
Berdine Heesterman ◽  
John-Melle Bokhorst ◽  
Lisa de Pont ◽  
Berit Verbist ◽  
Jean-Pierre Bayley ◽  
...  
Keyword(s):  
Tumor Growth ◽  
Mathematical Models ◽  
Goodness Of Fit ◽  
Mean Squared Error ◽  
Age At Onset ◽  
Growth Curves ◽  
Magnetic Resonance Images ◽  
Coefficient Of Determination ◽  
Growth Data ◽  
Significant Difference

Background To improve our understanding of the natural course of head and neck paragangliomas (HNPGL) and ultimately differentiate between cases that benefit from early treatment and those that are best left untreated, we studied the growth dynamics of 77 HNPGL managed with primary observation. Methods Using digitally available magnetic resonance images, tumor volume was estimated at three time points. Subsequently, nonlinear least squares regression was used to fit seven mathematical models to the observed growth data. Goodness of fit was assessed with the coefficient of determination (R 2) and root-mean-squared error. The models were compared with Kruskal–Wallis one-way analysis of variance and subsequent post-hoc tests. In addition, the credibility of predictions (age at onset of neoplastic growth and estimated volume at age 90) was evaluated. Results Equations generating sigmoidal-shaped growth curves (Gompertz, logistic, Spratt and Bertalanffy) provided a good fit (median R 2: 0.996–1.00) and better described the observed data compared with the linear, exponential, and Mendelsohn equations (p < 0.001). Although there was no statistically significant difference between the sigmoidal-shaped growth curves regarding the goodness of fit, a realistic age at onset and estimated volume at age 90 were most often predicted by the Bertalanffy model. Conclusions Growth of HNPGL is best described by decelerating tumor growth laws, with a preference for the Bertalanffy model. To the best of our knowledge, this is the first time that this often-neglected model has been successfully fitted to clinically obtained growth data.

scholarly journals Nonlinear mixed effects models for comparing growth curves for Guzerá cattle

2020 ◽  
Vol 21 ◽  
Author(s):  
Raphael Fernandes Soares ALVES ◽  
Kaléo Dias PEREIRA ◽  
Antônio Policarpo Souza CARNEIRO ◽  
Paulo Cesar EMILIANO ◽  
Paulo Luiz Souza CARNEIRO ◽  
...  
Keyword(s):  
Mean Squared Error ◽  
Growth Models ◽  
Random Effect ◽  
Growth Curves ◽  
Information Criterion ◽  
Fixed Effect ◽  
Coefficient Of Determination ◽  
Nonlinear Mixed Effects Models ◽  
Absolute Deviation ◽  
Production Region

ABSTRACT The objective of the present work was to evaluate the accuracy of the fitted Gompertz and von Bertalanffy models for male and female Guzerá cattle, respectively. Four production regions in Northeast Brazil were included in the models as a fixed effect, and the animals were included as a random effect. In addition, the coefficients of the growth models in the production regions were compared. The accuracy of the fit equations was assessed with the Akaike information criterion, Bayesian information criterion, mean absolute deviation, mean squared error, and coefficient of determination. Confidence intervals were used for comparing the production regions. The Guzerá males in the Gado-Algodão and Serra Geral da Bahia production regions were statistically equal in asymptotic weight, and the animals in the Itapetinga-Valadares and Mata-Agreste regions had equivalent maturity rates. The Guzerá females in the Itapetinga-Valadares and Serra Geral da Bahia regions had the same asymptotic weight. The maturity rates in Itapetinga-Valadares were equal to those estimated for Mata-Agreste and Serra Geral da Bahia. The inclusion of the fixed effect of the production region and the random effect of the animals in the models improved the fit quality and increased the possibility of generating growth curves for each region.

scholarly journals Chanter model: nonlinear modeling of the fruit growth of cocoa

2019 ◽  
Vol 49 (11) ◽  
Author(s):  
Pollyane Vieira da Silva ◽  
Taciana Villela Savian
Keyword(s):  
Bayesian Information Criterion ◽  
Logistic Model ◽  
Nonlinear Modeling ◽  
Gompertz Model ◽  
Information Criterion ◽  
Coefficient Of Determination ◽  
Residual Standard Deviation ◽  
Statistical Measures ◽  
Quality Of Fit

ABSTRACT: The growth of plants and animals can be described through a growth curve. This curve is given by the equation of a nonlinear model, such as the Logistic model and the Gompertz model. The objective of this study was to adjust the Chanter model, as well as Logistic and Gompertz, using a set of cocoa (clone Sial-105) fruit whose length and diameter measurements were evaluated from 30 to 180 days after pollination, every 15 days. The Chanter model is a hybrid between the Logistic model and Gompertz model whose parameters can be interpreted similarly. A comparison of the quality of fit between the models was made using the following statistical measures: the Akaike’s information criterion (AIC), the Akaike’s weights criterion, Bayesian information criterion (BIC), residual standard deviation (RSD),the adjusted coefficient of determination (R²aj) and the measures of non-linearity Box’s bias and curvature of Bates and Watts. It was verified that the Chanter model is the most suitable one among the studied models for modeling the cocoa data.

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 Nonlinear modeling growth body weight of Mangalarga Marchador horses

2017 ◽  
Vol 47 (4) ◽  
Author(s):  
Felipe Amorim Caetano Souza ◽  
Tales Jesus Fernandes ◽  
Raquel Silva de Moura ◽  
Sarah Laguna Conceição Meirelles ◽  
Rafaela Aparecida Ribeiro ◽  
...  
Keyword(s):  
Body Weight ◽  
Linear Models ◽  
Nonlinear Modeling ◽  
Growth Curves ◽  
Live Weight ◽  
Information Criterion ◽  
Coefficient Of Determination ◽  
Cross Sectional ◽  
Adult Body Weight ◽  
The Cross

ABSTRACT: The analysis of the growth and development of various species has been done using the growth curves of the specific animal based on non-linear models. The objective of the current study was to evaluate the fit of the Brody, Gompertz, Logistic and von Bertalanffy models to the cross-sectional data of the live weight of the MangalargaMarchador horses to identify the best model and make accurate predictions regarding the growth and maturity in the males and females of this breed. The study involved recording the weight of 214 horses, of which 94 were males and 120 were non-pregnant females, between 6 and 153 months of age. The parameters of the model were estimated by employing the method of least squares, using the iteratively regularized Gauss-Newton method and the R software package. Comparison of the models was done based on the following criteria: coefficient of determination (R²); Residual Standard Deviation (RSD); corrected Akaike Information Criterion (AICc). The estimated weight of the adult horses by the models ranged between 431kg and 439kg for males and between 416kg and 420kg for females. The growth curves were studied using the cross-sectional data collection method. For males the von Bertalanffymodel was found to be the most effective in expressing growth, while in females the Brody model was more suitable. The MangalargaMarchador females achieve adult body weight earlier than the males.

scholarly journals Description of blackberry fruit growth by nonlinear regression models

2020 ◽  
Vol 42 (2) ◽  
Author(s):  
Édipo Menezes da Silva ◽  
Maraísa Hellen Tadeu ◽  
Victor Ferreira da Silva ◽  
Rafael Pio ◽  
Tales Jesus Fernandes ◽  
...  
Keyword(s):  
Statistical Models ◽  
Regression Models ◽  
Least Squares Method ◽  
Growth Curves ◽  
Gompertz Model ◽  
Information Criterion ◽  
Financial Return ◽  
Nonlinear Regression Models ◽  
Small Fruit ◽  
Small Producers

Abstract Blackberry is a small fruit with several properties beneficial to human health and its cultivation is an alternative for small producers due to its fast and high financial return. Studying the growth of fruits over time is extremely important to understand their development, helping in the most appropriate crop management, avoiding post-harvest losses, which is one of the aggravating factors of blackberry cultivation, being a short shelf life fruit. Thus, growth curves are highlighted in this type of study and modeling through statistical models helps understanding how such growth occurs. Data from this study were obtained from an experiment conducted at the Federal University of Lavras in 2015. The aim of this study was to adjust nonlinear, double Logistic and double Gompertz models to describe the diameter growth of four blackberry cultivars (‘Brazos’, ‘Choctaw’, ‘Guarani’ and ‘Tupy’). Estimations of parameters were obtained using the least squares method and the Gauss-Newton algorithm, with the “nls” and “glns” functions of the R statistical software. The comparison of adjustments was made by the Akaike information criterion (AICc), residual standard deviation (RSD) and adjusted determination coefficient (R2 aj). The models satisfactorily described data, choosing the Logistic double model for ‘Brazos’ and ‘Guarani’ cultivars and the double Gompertz model for ‘Tupy’ and ‘Choctaw’ cultivars.

scholarly journals Fitting mathematical models to lactation curves from holstein cows in the southwestern region of the state of Parana, Brazil

2015 ◽  
Vol 87 (1) ◽  
pp. 503-517 ◽  
Author(s):  
Abílio G.T. Ferreira ◽  
Douglas S. Henrique ◽  
Ricardo A.M. Vieira ◽  
Emilyn M. Maeda ◽  
Altair A. Valotto
Keyword(s):  
Mathematical Models ◽  
Milk Production ◽  
Information Criterion ◽  
The State ◽  
Holstein Cows ◽  
Suitable Model ◽  
Almost All ◽  
Quality Of Fit ◽  
Wood Model

The objective of this study was to evaluate four mathematical models with regards to their fit to lactation curves of Holstein cows from herds raised in the southwestern region of the state of Parana, Brazil. Initially, 42,281 milk production records from 2005 to 2011 were obtained from "Associação Paranaense de Criadores de Bovinos da Raça Holandesa (APCBRH)". Data lacking dates of drying and total milk production at 305 days of lactation were excluded, resulting in a remaining 15,142 records corresponding to 2,441 Holstein cows. Data were sorted according to the parity order (ranging from one to six), and within each parity order the animals were divided into quartiles (Q25%, Q50%, Q75% and Q100%) corresponding to 305-day lactation yield. Within each parity order, for each quartile, four mathematical models were adjusted, two of which were predominantly empirical (Brody and Wood) whereas the other two presented more mechanistic characteristics (models Dijkstra and Pollott). The quality of fit was evaluated by the corrected Akaike information criterion. The Wood model showed the best fit in almost all evaluated situations and, therefore, may be considered as the most suitable model to describe, at least empirically, the lactation curves of Holstein cows raised in Southwestern Parana.

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 The Standard Deviation Structure as a New Approach to Growth Analysis in Weight and Length Data of Farmed Lutjanus guttatus

Fishes ◽  
2021 ◽  
Vol 6 (4) ◽  
pp. 60
Author(s):  
Sergio G. Castillo-Vargasmachuca ◽  
Eugenio Alberto Aragón-Noriega ◽  
Guillermo Rodríguez-Domínguez ◽  
Leonardo Martínez-Cárdenas ◽  
Eulalio Arámbul-Muñoz ◽  
...  
Keyword(s):  
Standard Deviation ◽  
Growth Parameters ◽  
Growth Models ◽  
Growth Curves ◽  
Gompertz Model ◽  
Information Criterion ◽  
Weight Growth ◽  
Length Data ◽  
Size At Age ◽  
The Right

In the present study, size-at-age data (length and weight) of marine cage-reared spotted rose snapper Lutjanus guttatus were analyzed under four different variance assumptions (observed, constant, depensatory, and compensatory variances) to analyze the robustness of selecting the right standard deviation structure to parametrize the von Bertalanffy, Logistic, and Gompertz models. The selection of the best model and variance criteria was obtained based on the Bayesian information criterion (BIC). According to the BIC results, the observed variance in the present study was the best way to parametrize the three abovementioned growth models, and the Gompertz model best represented the length and weight growth curves. Based on these results, using the observed error structure to calculate the growth parameters in multi-model inference analyses is recommended.

scholarly journals Deep Learning-Based Optimal Smart Shoes Sensor Selection for Energy Expenditure and Heart Rate Estimation

Sensors ◽  
2021 ◽  
Vol 21 (21) ◽  
pp. 7058
Author(s):  
Heesang Eom ◽  
Jongryun Roh ◽  
Yuli Sun Hariyani ◽  
Suwhan Baek ◽  
Sukho Lee ◽  
...  
Keyword(s):  
Heart Rate ◽  
Deep Learning ◽  
Energy Expenditure ◽  
Mean Squared Error ◽  
Pressure Sensors ◽  
Absolute Error ◽  
Coefficient Of Determination ◽  
Proposed Model ◽  
Point Pressure

Wearable technologies are known to improve our quality of life. Among the various wearable devices, shoes are non-intrusive, lightweight, and can be used for outdoor activities. In this study, we estimated the energy consumption and heart rate in an environment (i.e., running on a treadmill) using smart shoes equipped with triaxial acceleration, triaxial gyroscope, and four-point pressure sensors. The proposed model uses the latest deep learning architecture which does not require any separate preprocessing. Moreover, it is possible to select the optimal sensor using a channel-wise attention mechanism to weigh the sensors depending on their contributions to the estimation of energy expenditure (EE) and heart rate (HR). The performance of the proposed model was evaluated using the root mean squared error (RMSE), mean absolute error (MAE), and coefficient of determination (R2). Moreover, the RMSE was 1.05 ± 0.15, MAE 0.83 ± 0.12 and R2 0.922 ± 0.005 in EE estimation. On the other hand, and RMSE was 7.87 ± 1.12, MAE 6.21 ± 0.86, and R2 0.897 ± 0.017 in HR estimation. In both estimations, the most effective sensor was the z axis of the accelerometer and gyroscope sensors. Through these results, it is demonstrated that the proposed model could contribute to the improvement of the performance of both EE and HR estimations by effectively selecting the optimal sensors during the active movements of participants.

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