scholarly journals Modeling the Growth of Forage Legumes

2020 ◽  
Vol 12 (5) ◽  
pp. 139
Author(s):  
Brunna R. Rezende ◽  
Michelane S. S. Lima ◽  
Hygor A. Santana ◽  
Wilhan V. dos Santos ◽  
Anderson R. da Silva
Keyword(s):  
Growth Curve ◽  
Goodness Of Fit ◽  
Nonlinear Models ◽  
Accumulation Rate ◽  
Growth Curves ◽  
Biomass Accumulation ◽  
Information Criterion ◽  
Dry Mass ◽  
Von Bertalanffy ◽  
Forage Legumes

Modeling the growth curve of agricultural crops is of paramount importance so that management tasks such as fertilization and irrigation can be carried out at the appropriate time, increasing the vegetal yield. With this purpose, nonlinear models are commonly employed. The objective of this work was to fit some of the main nonlinear models that best describe the growth curve of some of the main species of forage legumes, namely: Crotalaria juncea, Canavalia ensiformis, Cajanus cajan and Dolichos lablab L. A randomized block experiment was conducted in field conditions between November 2015 and February 2016 in southeastern Goiás, Brazil. The variables plant height, stem diameter, fresh and dry mass were measured after 15, 30, 45, 60 and 90 days from sowing. The following models were fitted: Gompertz, Logistic, Brody and von Bertalanffy. The following goodness-of-fit criteria were calculated: R2 (normal and adjusted), AIC (Akaike Information Criterion) and absolute mean error. The growth curves of morphological variables are easier to model than the biomass curves. The von Bertalanffy and Gompertz models presented in general the best fit. The species C. juncea has an expressive biomass accumulation rate.

scholarly journals Sigmoid growth curves, a new approach to study the dynamics of the epicotyl emergence of oak

2019 ◽  
Vol 61 (1) ◽  
pp. 30-41
Author(s):  
Joanna Ukalska ◽  
Szymon Jastrzębowski
Keyword(s):  
Growth Curve ◽  
Goodness Of Fit ◽  
Nonlinear Models ◽  
Germination Rate ◽  
Growth Curves ◽  
Model Parameters ◽  
Residual Variance ◽  
Nonlinear Behaviour ◽  
Pedunculate Oak ◽  
Growth Phenomenon

Abstract Three of the most frequently used sigmoidal growth curves from the Richards family are the logistic model, Gompertz model and Richards model. They are used in the analysis of organismal growth over time in many disciplines/studies and were proposed in many parameterisations. Choosing the right parameterisation is not easy. The correct parameterisation of the model should take into account such parameters that are useful to describe the analysed growth phenomenon and are biologically relevant without additional calculations. In addition, each parameter of the model only affects one shape characteristic of each growth curve, which makes it possible to determine standard errors and confidence intervals using statistical software. Growth curves in germination dynamics studies should provide information on topics such as the length of the lag in onset of germination, the maximum germination rate and, when it occurs, the time at which 50% of seeds will germinate and the final germination proportion. In this article, we present three parameterisations of the logistic, Gompertz and Richards models and indicate two parameterisations for each model, corresponding to the above-mentioned issues. Our proposition is parameterisation by taking into account the maximum absolute growth rate. Parameterisations indicated as useful for germination dynamics are characterised by the fact that each parameter has the same meaning in every model, so its estimates can be compared directly amongst the models. We also discussed the goodness-of-fit measures for nonlinear models and in particular measures of nonlinear behaviour of a model’s individual parameters as well as overall measures of nonlinearity. All described models were used to study the dynamics of the epicotyl emergence of pedunculate oak. After checking the close-to-linear behaviour of the studied model parameters and by taking into account the criteria of model selection (AICc of each growth curve and the residual variance [RV]), the best model describing the dynamics of epicotyl appearance of pedunculate oak was the Richards curve.

scholarly journals NONLINEAR MODELS BASED ON QUANTILES IN THE FITTING OF GROWTH CURVES OF PEPPER GENOTYPES

2021 ◽  
Vol 39 (3) ◽  
Author(s):  
Ana Carolina Ribeiro de OLIVEIRA ◽  
Paulo Roberto CECON ◽  
Guilherme Alves PUIATTI ◽  
Maria Eduarda da Silva GUIMARÃES ◽  
Cosme Damião CRUZ ◽  
...  
Keyword(s):  
Regression Models ◽  
Nonlinear Models ◽  
Growth Curves ◽  
Information Criterion ◽  
Ordinary Least Squares ◽  
Von Bertalanffy ◽  
Absolute Deviation ◽  
Nonlinear Regression Models ◽  
Curvature Measurements ◽  
Best Fit

This study aimed to fit nonlinear regression models to model the growth of the characters fruit length (FL) and fruit width (FW) of pepper genotypes (Capsicum annuum L.) over time using the method of ordinary least squares (OLS); and identify the model with the best fit and compare it to the model obtained via nonlinear quantile regression (QR) in the 0.25, 0.5, and 0.75 quantiles. Three regression models (Logistic, Gompertz, and von Bertalanffy) and four fit quality evaluators were adopted: Akaike information criterion, residual mean absolute deviation, and parametric and intrinsic curvature measurements. Five commercial genotypes of pepper were evaluated. Characters FL and FW were evaluated weekly from seven days after flowering, totaling ten measurements. In the estimation by OLS, the Logistic and von Bertalanffy models were considered adequate according to the quality evaluators. In the comparison between the models above by OLS and QR, the superiority of models obtained by QR was verified for the character FL. For the character FW, QR was efficient in three out of the five genotypes, being a valuable alternative in the study of fruit growth.

scholarly journals A COMPARISON OF NONLINEAR MODELS FOR DESCRIBING WEIGHT-AGE DATA IN ANGLO-NUBIAN DOES

2019 ◽  
Vol 32 (1) ◽  
pp. 251-258 ◽  
Author(s):  
Francisco Arthur Arré ◽  
José Elivalto Guimarães Campelo ◽  
José Lindenberg Rocha Sarmento ◽  
Luiz Antônio Silva Figueiredo Filho ◽  
Diego Helcias Cavalcante
Keyword(s):  
Goodness Of Fit ◽  
Mean Squared Error ◽  
Nonlinear Models ◽  
Age Groups ◽  
Coefficient Of Determination ◽  
Group Model ◽  
Age Group ◽  
Von Bertalanffy ◽  
Absolute Deviation ◽  
Model Interaction

ABSTRACT The objective of this study was to determine the optimum age at last weighing and compare the goodness of fit of nonlinear models used to fit longitudinal weight-age data to describe the growth pattern of Anglo-Nubian does. Weights of 104 animals from birth to 60 months of age were grouped into 10 age groups at six-month intervals. In each age group, parameters A (asymptotic weight), B (integration constant), and K (maturity index) were estimated using the Brody, Gompertz, logistic, and von Bertalanffy models. Data were analyzed using analysis of variance in a factorial design (10 age groups × 4 nonlinear models). The age group × model interaction was not significant. Mean estimates of A, B, and K were significantly different between age groups up to 30 months (p < 0.05), indicating that the estimated curve is affected by weights taken before this age independent of the model. The values of mean squared error (MSE), mean absolute deviation (MAD), coefficient of determination (R2) and Rate of convergence (RC) at each age group up to 30 months were compared to determine the goodness of fit of nonlinear models. The ranking of fit was logistic, Brody, von Bertalanffy, and Gompertz. The logistic and Brody models respectively estimated the smallest and largest asymptotic weight. Longitudinal weight records taken until 30 months of age are most appropriate for estimating the growth of Anglo-Nubian does using nonlinear models.

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 Describing the growth curve of local turkey using non-linear models

2018 ◽  
pp. 7104-7107
Author(s):  
Aureliano Juárez-Caratachea ◽  
Iván Delgado-Hurtado ◽  
Ernestina Gutiérrez-Vázquez ◽  
Guillermo Salas-Razo ◽  
Ruy Ortiz-Rodríguez ◽  
...  
Keyword(s):  
Growth Curve ◽  
Visual Analysis ◽  
Linear Models ◽  
Logistic Models ◽  
Information Criterion ◽  
Von Bertalanffy ◽  
Commercial Feed ◽  
Non Linear ◽  
Best Fitting ◽  
Multiple Determination

Objective. Determine the best non-linear model to fit the growth curve of local turkeys managed under confinement in Michoacan, Mexico. Material and methods. Twenty-four and 43 female and male turkeys, reared under commercial conditions were given commercial feed. Birds were weighed weekly from hatch to 29 weeks of age. The Gompertz, Brody, Richards, von Bertalanffy and Logistic models were chosen to describe the age-weight relationship. Results. The best fitting model was selected based on the multiple determination coefficient (R2), the Akaike information criterion (AIC) and visual analysis of the observed and predicted curves. In both female and male, von Bertalanffy was the best model. The highest estimates of parameter A (mature weight) for both females and males were obtained with the von Bertalanffy model followed by the Gompertz and Logistic. The estimates of A were higher for males than for females. The highest estimates of parameter k (rate of maturity) for both females and males were, in decreasing order, for the Logistic, Gompertz, and von Bertalanffy models. k values for female turkeys was higher than for males. The age at the point of inflection (TI) and body weight at the age of point of inflection (WI) varied with the model used. The largest values of TI and WI corresponded to the Logistic model. Between sexes, the largest TI and WI values corresponded to males. Conclusions. The best models to describe turkey growth was the von Bertalanffy because it present the highest R2 and lowest AIC values.

scholarly journals Growth Curves of Texel Male Lambs

2018 ◽  
Vol 44 (1) ◽  
pp. 6
Author(s):  
Michelli De Fátima Sieklicki ◽  
Victor Breno Pedrosa ◽  
Caroline Gomes Rocha ◽  
Raphael Patrick Moreira ◽  
Paula Roberta Falcão ◽  
...  
Keyword(s):  
Growth Rate ◽  
Mean Square Error ◽  
Nonlinear Models ◽  
Growth Curves ◽  
Coefficient Of Determination ◽  
Good Growth ◽  
Von Bertalanffy ◽  
Mean Square ◽  
The Mean ◽  
Best Fit

Background: The consumption of lamb meat is growing due to improved farming methods. However, to be economically feasible, the animal should stand out for its precocity, fast finishing and muscular force, such as seen in Texel breed. Besides, knowledge about weight gain and development can facilitate the selection of the best animals, and allow a better fitting to farming systems. Growth curves are an effective method that describes animal development, modeling the relationship between weight and age and help to predict the growth rate. Thus, this study aimed to analyze which nonlinear model, including Brody, Gompertz, Von Bertalanffy and Logistic best describe the growth curve of Texel sheep.Materials, Methods & Results: In this experiment, the lambs were kept in confined system while the ewes, in a semi-extensive system. This study followed 42 Texel male lambs, which were confined from birth to slaughter, and fed concentrated feed (3% of body weight) and corn silage (average 1.5 kg/animal/day), 4 times a day. The lambs were weighed fortnightly, in different classes considered as follows, weight at birth (BW), 15 days (P15), 30 days (P30), 45 days (P45), 60 days (P60), 75 days (P75), 90 days (P90), 105 days (P105), and 120 days (P120), which was defined as the slaughtering weight. The growth curves were determined using the nonlinear models of Brody, Von Bertalanffy, Gompertz and Logistic. The following parameters were used in the curves, Y, slaughtering weight; A, asymptotic weight; k, growth rate, t, animal age; B, constant related to the initial weight; and, m, constant of the curve shape. The criteria used for selecting the model that best described the curve were the mean square error (MSE), which was calculated by dividing the sum of squared error by the number of observations, and also the coefficient of determination (R²), calculated as the square of the correlation between the observed and estimated weights. The average weights observed were as follows, 4.02 kg at birth, 21.68 kg at weaning (P60) and 32.55 kg at slaughtering (P120). The solution of the nonlinear models allows, thru the parameters, establish specific feeding programs and define the optimal slaughtering age. Furthermore, the coefficients of determination, with values close to 97.3%, showed good fits for all models. Still, considering the mean square error, where the lower value indicates the best fit to the data evaluated, the results were 13.1564 (Brody), 13.3421 (Von Bertalanffy), 13.4876 (Gompertz) and 13.6717 (Logistic). The results showed that Brody could be considered the model that best describes the growth rate up to 120 days old of Texel lambs.Discussion: Compared to other studies, the average weights obtained in the experiment varied widely. This large variation can be explained by the used rearing system that might favor or not the performance of lambs. However, the average weaning weight obtained was similar to several studies in the literature, confirming the potential of Texel breed. This breed demonstrated to be capable to provide a precocious animal, with good growth results from the early developmental stage until the slaughtering age. Regarding the growth curves, the Brody model was the best fit for the estimated and observed weights. Moreover, the coefficient of determination indicated good fits for all models. However, an important aspect is the negative correlation between the A and k parameters, demonstrating that the higher the animal growth rate, the lower its asymptotic size.

BODY TEMPERATURE AFFECTS THE SHAPE OF AVIAN GROWTH CURVES

1993 ◽  
Vol 01 (04) ◽  
pp. 363-374 ◽  
Author(s):  
C. ZONNEVELD ◽  
S.A.L.M. KOOIJMAN
Keyword(s):  
Body Temperature ◽  
Growth Curve ◽  
Time Course ◽  
Growth Curves ◽  
The Body ◽  
Growth Equation ◽  
Von Bertalanffy ◽  
Gradual Development ◽  
Mathematical Equations ◽  
Von Bertalanffy Growth Equation

Growth of birds is described by a variety of mathematical equations. These equations generally lack a biological motivation. As a result, it remains unclear why growth in different species should be described by different equations. In this article, we argue that the gradual development of endothermy affects the growth of birds. Hence, differences in the growth curve may result from differences in the thermal ontogeny. We assume that birds would grow according to the von Bertalanffy growth equation, if their temperature were constant. Using the deviations from this growth curve, we reconstruct the time course of the temperature of growing birds. This reconstruction well describes data on the ontogeny of the body temperature in birds.

scholarly journals Growth curves on females of the Caracu breed

2016 ◽  
Vol 37 (4Supl1) ◽  
pp. 2749 ◽  
Author(s):  
Raphael Patrick Moreira ◽  
Maria Eugênia Zerlotti Mercadante ◽  
Victor Breno Pedrosa ◽  
Joslaine Noely dos Santos Gonçalves Cyrillo ◽  
Wignez Henrique
Keyword(s):  
Growth Traits ◽  
Nonlinear Models ◽  
Average Daily Gain ◽  
Growth Curves ◽  
Coefficient Of Determination ◽  
Von Bertalanffy ◽  
Mean Square ◽  
The Mean ◽  
Best Fit ◽  
Daily Gain

The objective of the study was to analyze nonlinear models that best fit the growth of Caracu cows. The experiment was conducted at the Instituto de Zootecnia, Centro APTA Bovinos de Corte, Sertãozinho, SP. Data of weight at birth to 63 months of age, from 500 females of the Caracu breed were used. The mean weight at birth (BW), weaning weight (W7), weight at 26 months (W26) and weight at 63 months (W63) were, respectively, 32 kg, 198 kg, 354 kg and 488 kg, providing an average daily gain (ADG) of 0.241 kg/day. The nonlinear models used were: Brody, Von Bertalanffy, Logistic and Gompertz. All of the models tended to describe accordingly the growth curve of these animals, but, according to the mean square residual and coefficient of determination adopted to select the most appropriate model, Brody showed the best fit. All models presented a high and negative correlation between the A and k parameters, indicating that the most precocious animals are less likely to reach elevated weights at 63 months of age. The effect of year of birth significantly affected (P &lt; 0.01) the parameters A and k, concluding that the animal selection based on growth traits favored the increase of mature weight and growth precocity over the generations.

scholarly journals Nonlinear models in the height description of the Rhino sunflower cultivar

2022 ◽  
Vol 52 (3) ◽  
Author(s):  
Anderson Chuquel Mello ◽  
Marcos Toebe ◽  
Rafael Rodrigues de Souza ◽  
João Antônio Paraginski ◽  
Junior Carvalho Somavilla ◽  
...  
Keyword(s):  
Growth Curve ◽  
Critical Points ◽  
Nonlinear Models ◽  
Information Criterion ◽  
Coefficient Of Determination ◽  
Maximum Acceleration ◽  
Inflection Points ◽  
Best Fitting ◽  
Microsoft Office

ABSTRACT: Sunflower produces achenes and oil of good quality, besides serving for production of silage, forage and biodiesel. Growth modeling allows knowing the growth pattern of the crop and optimizing the management. The research characterized the growth of the Rhino sunflower cultivar using the Logistic and Gompertz models and to make considerations regarding management based on critical points. The data used come from three uniformity trials with the Rhino confectionery sunflower cultivar carried out in the experimental area of the Federal University of Santa Maria - Campus Frederico Westphalen in the 2019/2020 agricultural harvest. In the first, second and third trials 14, 12 and 10 weekly height evaluations were performed on 10 plants, respectively. The data were adjusted for the thermal time accumulated. The parameters were estimated by ordinary least square’s method using the Gauss-Newton algorithm. The fitting quality of the models to the data was measured by the adjusted coefficient of determination, Akaike information criterion, Bayesian information criterion, and through intrinsic and parametric nonlinearity. The inflection points (IP), maximum acceleration (MAP), maximum deceleration (MDP) and asymptotic deceleration (ADP) were determined. Statistical analyses were performed with Microsoft Office Excel® and R software. The models satisfactorily described the height growth curve of sunflower, providing parameters with practical interpretations. The Logistics model has the best fitting quality, being the most suitable for characterizing the growth curve. The estimated critical points provide important information for crop management. Weeds must be controlled until the MAP. Covered fertilizer applications must be carried out between the MAP and IP range. ADP is an indicator of maturity, after reaching this point, the plants can be harvested for the production of silage without loss of volume and quality.

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