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 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 Comparison of growth curves of two genotypes of dairy goats using nonlinear mixed models

2013 ◽  
Vol 152 (5) ◽  
pp. 829-842 ◽  
Author(s):  
J. G. L. REGADAS FILHO ◽  
L. O. TEDESCHI ◽  
M. T. RODRIGUES ◽  
L. F. BRITO ◽  
T. S. OLIVEIRA
Keyword(s):  
Random Effects ◽  
Growth Curve ◽  
Mixed Model ◽  
Growth Curves ◽  
Growth Patterns ◽  
Dairy Goat ◽  
Residual Variance ◽  
Nonlinear Mixed Model ◽  
Error Structure ◽  
Mixed Model Methodology

SUMMARYThe objective of the current study was to assess the use of nonlinear mixed model methodology to fit the growth curves (weightv.time) of two dairy goat genotypes (Alpine, +A and Saanen, +S). The nonlinear functions evaluated included Brody, Von Bertalanffy, Richards, Logistic and Gompertz. The growth curve adjustment was performed using two steps. First, random effectsu1,u2andu3were linked to the asymptotic body weight (β1), constant of integration (β2) and rate constant of growth (β3) parameters, respectively. In addition to a traditional fixed-effects model, four combinations of models were evaluated using random variables: all parameters associated with random effects (u1,u2andu3), onlyβ1andβ2(u1andu2), onlyβ1andβ3(u1andu3) and onlyβ1(u1). Second, the fit of the best adjusted model was refined by using the power variance and modelling the error structure. Residual variance ($\sigma _e^2 $) and the Akaike information criterion were used to evaluate the models. After the best fitting model was chosen, the genotype curve parameters were compared. The residual variance was reduced in all scenarios for which random effects were considered. The Richards (u1andu3) function had the best fit to the data. This model was reparameterized using two isotropic error structures for unequally spaced data, and the structure known in the literature as SP(MATERN) proved to be a better fit. The growth curve parameters differed between the two genotypes, with the exception of the constant that determines the proportion of the final size at which the inflection point occurs (β4). The nonlinear mixed model methodology is an efficient tool for evaluating growth curve features, and it is advisable to assign biologically significant parameters with random effects. Moreover, evaluating error structure modelling is recommended to account for possible correlated errors that may be present even when using random effects. Different Richard growth curve parameters should be used for the predominantly Alpine and Saanen genotypes because there are differences in their growth patterns.

scholarly journals Predicting the Digestive Tract Development and Growth Performance of Goat Kids Using Sigmoidal Models

Animals ◽  
2021 ◽  
Vol 11 (3) ◽  
pp. 757
Author(s):  
Mahmoud Abdelsattar ◽  
Yimin Zhuang ◽  
Kai Cui ◽  
Yanliang Bi ◽  
Naifeng Zhang
Keyword(s):  
Body Weight ◽  
Digestive Tract ◽  
Goodness Of Fit ◽  
Pearson Correlation ◽  
Body Height ◽  
Growth Curves ◽  
The Body ◽  
Quadratic Model ◽  
Model Parameters ◽  
Poor Growth

The transition from monogastric to rumination stage is crucial in ruminants’ growth to avoid stressors—weaning and neonatal mortalities. Poor growth of the digestive tract could adversely affect the performance of the animal. Modeling informative growth curves is of great importance for a better understanding of the effective development pattern, in order to optimize feeding management system, and to achieve more production efficiency. However, little is known about the digestive tract growth curves. For this reason, one big goat farm of Laiwu black breed was chosen as a basis of this study. Forty-eight kids belonging to eight-time points (1, 7, 14, 28, 42, 56, 70, and 84 d; 6 kids for each) were selected and slaughtered. The body weight, body size indices, rumen pH, and stomach parts were determined and fitted to the polynomial and sigmoidal models. In terms of goodness of fit criteria, the Gompertz model was the best model for body weight, body oblique length, tube, and rumen weight. Moreover, the Logistic model was the best model for carcass weight, body height, and chest circumference. In addition, the Quadratic model showed the best fit for dressing percentage, omasum weight, abomasum weight, and rumen volume. Moreover, the cubic model best fitted the ruminal pH and reticulum percentage. The Weibull model was the best model for the reticulum weight and omasum percentage, while the MMF model was the best model describing the growth of chest depth, rumen percentage, and abomasum percentage. The model parameters, R squared, inflection points, area under curve varied among the different dependent variables. The Pearson correlation showed that the digestive tract development was more correlated with age than body weight, but the other variables were more correlated with body weight than age. The study demonstrated the use of empirical sigmoidal and polynomial models to predict growth rates of the digestive tract at relevant age efficiently.

scholarly journals Growth curves in meat-type and laying quail: a Bayesian perspective

2017 ◽  
Vol 38 (4Supl1) ◽  
pp. 2743
Author(s):  
Robson Marcelo Rossi ◽  
Daiane De Oliveira Grieser ◽  
Vagner De Almeida Conselvan ◽  
Simara Márcia Marcato
Keyword(s):  
Body Weight ◽  
Bayesian Approach ◽  
Goodness Of Fit ◽  
Nonlinear Models ◽  
Growth Curves ◽  
Gompertz Model ◽  
Body Growth ◽  
Coturnix Coturnix ◽  
Body Weight Data ◽  
Meat Type

The aim of this study was to assess the goodness of fit for nonlinear models, using the best model to describe body growth curves, comparing the parameters obtained for gender and one meat-type (Coturnix coturnix coturnix) and two laying (Coturnix coturnix japonica) quail strains, as well as nesting via MCMC (Markov chain Monte Carlo processes) methods under a Bayesian approach. A total of 1,350 one-day-old mixed quail were used: 400 of meat-type, 450 of yellow laying, and 500 of red laying strains distributed in a completely randomized design with three treatments (each treatment corresponded to one strain) and five replications. The experimental period consisted of 1 to 42 days of age. At 21 days of age, quail sexing was performed by means of sexual dimorphism, being individually identified at one day of age with numbered rings, allowing determining growth curves by gender. Birds were reared in a conventional system, fed ad libitum with diets formulated to meet nutritional requirements. Body weight was determined weekly and assessed using nonlinear models: Logistic, Brody, Von Bertalanffy, and Gompertz, whose parameters were estimated under a Bayesian approach via MCMC algorithm by means of BRugs package from the software R. DIC (Deviance Information Criterion) criterion was used to select the best nonlinear model, i.e. the lower the DIC value is, the better the model goodness of fit to the data. Gompertz model was better adjusted to the data regardless the gender or strain. Meat-type quail had the highest asymptotic weights and the highest age at which growth rate was maximum, followed by red and yellow strains. All nestings presented significant differences (p < 0.05) between gender for contrasted parameters. Meat-type, yellow, and red females presented values significantly (p < 0.05) higher for asymptotic weight (370, 203, and 215 g, respectively) when compared to males (274, 131, and 143 g, respectively), which were earlier in body growth. Gompertz model was better adjusted to body weight data of quail regardless the gender or strain and the Bayesian approach allowed obtaining accurate estimations. Meat-type strain presented the highest body asymptotic weight, followed by red and yellow laying strains. Females presented higher asymptotic weight than that found for males of their respective strains but were later in growth.

scholarly journals Adjusting the growth curve of sugarcane varieties using nonlinear models

2020 ◽  
Vol 50 (3) ◽  
Author(s):  
Sérgio Alberto Jane ◽  
Felipe Augusto Fernandes ◽  
Edilson Marcelino Silva ◽  
Joel Augusto Muniz ◽  
Tales Jesus Fernandes ◽  
...  
Keyword(s):  
Growth Curve ◽  
Least Squares Method ◽  
Nonlinear Models ◽  
Height Growth ◽  
Coefficient Of Determination ◽  
Model Parameters ◽  
Suitable Model ◽  
Software Environment ◽  
Phenological Stages ◽  
Sugarcane Varieties

ABSTRACT: Assessing sugarcane (Saccharum spp.) stalk growth helps to adequately manage the phenological stages of the crop. The aim of this study was to describe the height-growth curve of four sugarcane varieties (RB92579, RB93509, RB931530 and SP79-1011), in irrigated plant-cane and ratoon cane plantations, using the Logistic and Gompertz nonlinear models, while considering all deviations from assumptions. The model parameters were estimated based on the least squares method using the Gauss-Newton algorithm. To select the most suitable model, nonlinear measures, adjusted coefficient of determination (R2 adj), residual standard deviation (RSD), and corrected Akaike information criterion (AICc) were used. Based on the best models, stalk height growth rates and crop phenological stages were determined using critical points. All tests were performed in the free software environment for statistical computing and graphics, R. In general, the Logistic and Gompertz models without AR(1) better described the plant-cane and ratoon cane stalk height, respectively. All varieties showed early growth, and the RB92579 variety presented higher rates in both cycles.

scholarly journals Growth curves in meat-type and laying quail: a Bayesian perspective

2017 ◽  
Vol 38 (4Supl1) ◽  
pp. 2743 ◽  
Author(s):  
Robson Marcelo Rossi ◽  
Daiane De Oliveira Grieser ◽  
Vagner De Almeida Conselvan ◽  
Simara Márcia Marcato
Keyword(s):  
Body Weight ◽  
Bayesian Approach ◽  
Goodness Of Fit ◽  
Nonlinear Models ◽  
Growth Curves ◽  
Gompertz Model ◽  
Body Growth ◽  
Coturnix Coturnix ◽  
Body Weight Data ◽  
Meat Type

The aim of this study was to assess the goodness of fit for nonlinear models, using the best model to describe body growth curves, comparing the parameters obtained for gender and one meat-type (Coturnix coturnix coturnix) and two laying (Coturnix coturnix japonica) quail strains, as well as nesting via MCMC (Markov chain Monte Carlo processes) methods under a Bayesian approach. A total of 1,350 one-day-old mixed quail were used: 400 of meat-type, 450 of yellow laying, and 500 of red laying strains distributed in a completely randomized design with three treatments (each treatment corresponded to one strain) and five replications. The experimental period consisted of 1 to 42 days of age. At 21 days of age, quail sexing was performed by means of sexual dimorphism, being individually identified at one day of age with numbered rings, allowing determining growth curves by gender. Birds were reared in a conventional system, fed ad libitum with diets formulated to meet nutritional requirements. Body weight was determined weekly and assessed using nonlinear models: Logistic, Brody, Von Bertalanffy, and Gompertz, whose parameters were estimated under a Bayesian approach via MCMC algorithm by means of BRugs package from the software R. DIC (Deviance Information Criterion) criterion was used to select the best nonlinear model, i.e. the lower the DIC value is, the better the model goodness of fit to the data. Gompertz model was better adjusted to the data regardless the gender or strain. Meat-type quail had the highest asymptotic weights and the highest age at which growth rate was maximum, followed by red and yellow strains. All nestings presented significant differences (p < 0.05) between gender for contrasted parameters. Meat-type, yellow, and red females presented values significantly (p < 0.05) higher for asymptotic weight (370, 203, and 215 g, respectively) when compared to males (274, 131, and 143 g, respectively), which were earlier in body growth. Gompertz model was better adjusted to body weight data of quail regardless the gender or strain and the Bayesian approach allowed obtaining accurate estimations. Meat-type strain presented the highest body asymptotic weight, followed by red and yellow laying strains. Females presented higher asymptotic weight than that found for males of their respective strains but were later in growth.

scholarly journals Growth curves of meat-producing mammals by von Bertalanffy’s model

2019 ◽  
Vol 54 ◽  
Author(s):  
Felipe Augusto Fernandes ◽  
Tales Jesus Fernandes ◽  
Adriele Aparecida Pereira ◽  
Sarah Laguna Conceição Meirelles ◽  
Adriano Carvalho Costa
Keyword(s):  
Growth Curve ◽  
Nonlinear Models ◽  
Growth Curves ◽  
Research Institutions ◽  
Direct Interpretation ◽  
Curvature Measurements

Abstract: The objective of this work was to evaluate how the parameterization and the application of different allometric values affect the obtention of the most adequate fit of von Bertalanffy’s model, in the description of the growth curve of meat-producing mammals (bovine, pigs, rabbits, and sheep). Among the nonlinear models, von Bertalanffy’s has been very often applied in several areas, with different parameterizations. This model has been commonly used with an allometric value of m = 2/3; however, for mammals, it is believed that this value can be m = 3/4. The analyzed data referring to the mass of meat-producing mammals according to their age were obtained from research institutions and from the literature. The results showed that von Bertalanffy’s model, with the allometric value of m = 3/4 and the used parameterization, provided better adjustments to quality evaluators. Besides, the model softened the overestimation of parameter a, giving a direct interpretation of parameter b, with the lowest values for curvature measurements, mainly for the parametric ones, and provided more reliable adjustments. Von Bertalanffy’s model can be used in the description of the growth curves of meat-producing mammals.

Nonlinear models to describe the testicular size growth curve of Mangalarga Marchador stallions

2021 ◽  
pp. 103422
Author(s):  
Danielle Estanislau Coelho Silva ◽  
Jurandy Mauro Penitente-Filho ◽  
Domingos Lollobrigida Souza Neto ◽  
Bruna Waddington ◽  
Renan Reis de Oliveira ◽  
...  
Keyword(s):  
Growth Curve ◽  
Nonlinear Models ◽  
Size Growth ◽  
Testicular Size

scholarly journals A Hybrid Modeling Technique of Epidemic Outbreaks with Application to COVID-19 Dynamics in West Africa

Biology ◽  
2021 ◽  
Vol 10 (5) ◽  
pp. 365
Author(s):  
Chénangnon Frédéric Tovissodé ◽  
Jonas Têlé Doumatè ◽  
Romain Glèlè Kakaï
Keyword(s):  
West Africa ◽  
Growth Curve ◽  
Exponential Growth ◽  
Latency Period ◽  
Growth Curves ◽  
Exponential Growth Phase ◽  
Model Framework ◽  
Logistic Regression Models ◽  
Containment Measures ◽  
Reporting Data

The widely used logistic model for epidemic case reporting data may be either restrictive or unrealistic in presence of containment measures when implemented after an epidemic outbreak. For flexibility in epidemic case reporting data modeling, we combined an exponential growth curve for the early epidemic phase with a flexible growth curve to account for the potential change in growth pattern after implementation of containment measures. We also fitted logistic regression models to recoveries and deaths from the confirmed positive cases. In addition, the growth curves were integrated into a SIQR (Susceptible, Infective, Quarantined, Recovered) model framework to provide an overview on the modeled epidemic wave. We focused on the estimation of: (1) the delay between the appearance of the first infectious case in the population and the outbreak (“epidemic latency period”); (2) the duration of the exponential growth phase; (3) the basic and the time-varying reproduction numbers; and (4) the peaks (time and size) in confirmed positive cases, active cases and new infections. The application of this approach to COVID-19 data from West Africa allowed discussion on the effectiveness of some containment measures implemented across the region.

scholarly journals A generalized Gompertz growth model with applications and related birth-death processes

2020 ◽  
Author(s):  
Majid Asadi ◽  
Antonio Di Crescenzo ◽  
Farkhondeh A. Sajadi ◽  
Serena Spina
Keyword(s):  
Growth Model ◽  
Growth Curve ◽  
Goodness Of Fit ◽  
Gompertz Model ◽  
Death Process ◽  
Birth Process ◽  
Failure Data ◽  
First Case ◽  
Gompertz Growth Model ◽  
Birth Death

AbstractIn this paper, we propose a flexible growth model that constitutes a suitable generalization of the well-known Gompertz model. We perform an analysis of various features of interest, including a sensitivity analysis of the initial value and the three parameters of the model. We show that the considered model provides a good fit to some real datasets concerning the growth of the number of individuals infected during the COVID-19 outbreak, and software failure data. The goodness of fit is established on the ground of the ISRP metric and the $$d_2$$ d 2 -distance. We also analyze two time-inhomogeneous stochastic processes, namely a birth-death process and a birth process, whose means are equal to the proposed growth curve. In the first case we obtain the probability of ultimate extinction, being 0 an absorbing endpoint. We also deal with a threshold crossing problem both for the proposed growth curve and the corresponding birth process. A simulation procedure for the latter process is also exploited.

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