scholarly journals PARAMETERIZATIONS OF THE VON BERTALANFFY MODEL FOR DESCRIPTION OF GROWTH CURVES

2020 ◽  
Vol 38 (3) ◽  
pp. 369
Author(s):  
Felipe Augusto FERNANDES ◽  
Édipo Menezes SILVA ◽  
Kelly Pereira LIMA ◽  
Sérgio Alberto JANE ◽  
Tales Jesus FERNANDES ◽  
...  
Keyword(s):  
Regression Models ◽  
Growth Curves ◽  
Von Bertalanffy ◽  
Growth Data ◽  
Nonlinear Regression Models ◽  
Von Bertalanffy Model ◽  
Estimated Parameters ◽  
Biological Interpretation ◽  
Curvature Measurements ◽  
Nonlinearity Measures

The growth curves of animals, in general, have an “S” shape, also known as sigmoidal curves. This type of   curve is well fitted by nonlinear regression models, including von Bertalanffy’s model, which has been widely  applied in several areas, being presented in literature through different parameterizations, which in practice, can complicate its understanding, affect nonlinearity measures and inferences about parameters. To quantify  the nonlinearity present in a Bates and Watts model, a geometric concept of curvature has been used. The aim of this work was to analytically develop three parameterizations of the von Bertalanffy’s nonlinear model  referring to its nonlinearity, implications for inferences and to establish relationships between parameters in the different ways of expressing the models. These parameterizations were adjusted to the growth data of sheep. For each parameterization, the intrinsic and parametric curvature measurements described by Bates and Watts were calculated. The parameterization choice affects nonlinearity measures, consequently, influences the reliability and inferences about estimated parameters. The forms most used in literature showed the greatest deviations from linearity, showing the importance of analyzing these measures in any growth curve study. Parameterization should be used in which the b estimate represents the abscissa of the inflection point, as it presents minor linearity deviations and direct biological interpretation for all parameters.

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 Growth of the tambaqui Colossoma macropomum (Cuvier) (Characiformes: Characidae): which is the best model?

2005 ◽  
Vol 65 (1) ◽  
pp. 129-139 ◽  
Author(s):  
M. A. H Penna ◽  
M. A Villacorta-Corrêa ◽  
T. Walter ◽  
M. Petrere-JR
Keyword(s):  
Growth Model ◽  
Negative Correlation ◽  
The Other ◽  
Data Sources ◽  
Von Bertalanffy ◽  
Data Set ◽  
Colossoma Macropomum ◽  
Von Bertalanffy Model ◽  
Estimated Parameters ◽  
Schnute Model

In order to decide which is the best growth model for the tambaqui Colossoma macropomum Cuvier, 1818, we utilized 249 and 256 length-at-age ring readings in otholiths and scales respectively, for the same sample of individuals. The Schnute model was utilized and it is concluded that the Von Bertalanffy model is the most adequate for these data, because it proved highly stable for the data set, and only slightly sensitive to the initial values of the estimated parameters. The phi' values estimated from five different data sources presented a CV = 4.78%. The numerical discrepancies between these values are of not much concern due to the high negative correlation between k and L<FONT FACE=Symbol>¥</FONT> viz, so that when one of them increases, the other decreases and the final result in phi' remains nearly unchanged.

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 Methods to verify parameter equality in nonlinear regression models

2010 ◽  
Vol 67 (2) ◽  
pp. 218-222 ◽  
Author(s):  
Lídia Raquel de Carvalho ◽  
Sheila Zambello de Pinho ◽  
Martha Maria Mischan
Keyword(s):  
Nonlinear Regression ◽  
Regression Models ◽  
Growth Curves ◽  
Original Data ◽  
Minimum Variance ◽  
Ratio Method ◽  
Parameter Estimates ◽  
Nonlinear Regression Models ◽  
Sample Data ◽  
Parameter Estimators

In biologic experiments, in which growth curves are adjusted to sample data, treatments applied to the experimental material can affect the parameter estimates. In these cases the interest is to compare the growth functions, in order to distinguish treatments. Three methods that verify the equality of parameters in nonlinear regression models were compared: (i) developed by Carvalho in 1996, performing ANOVA on estimates of parameters of individual fits; (ii) suggested by Regazzi in 2003, using the likelihood ratio method; and (iii) constructing a pooled variance from individual variances. The parametric tests, F and Tukey, were employed when the parameter estimators were near to present the properties of linear model estimators, that is, unbiasedness, normal distribution and minimum variance. The first and second methods presented similar results, but the third method is simpler in calculations and uses all information contained in the original data.

Dynamic child growth prediction: A comparative methods approach

2017 ◽  
Vol 17 (6) ◽  
pp. 468-493 ◽  
Author(s):  
Andrada E Ivanescu ◽  
Ciprian M Crainiceanu ◽  
William Checkley
Keyword(s):  
Regression Models ◽  
Prediction Models ◽  
Growth Curves ◽  
Child Growth ◽  
Prediction Performance ◽  
Model Parameters ◽  
Supplementary File ◽  
Functional Regression ◽  
Growth Data ◽  
Missing Data Imputation

Abstract: We introduce a class of dynamic regression models designed to predict the future of growth curves based on their historical dynamics. This class of models incorporates both baseline and time-dependent covariates, start with simple regression models and build up to dynamic function-on-function regressions. We compare the performance of the dynamic prediction models in a variety of signal-to-noise scenarios and provide practical solutions for model selection. We conclude that (a) prediction performance increases substantially when using the entire growth history relative to using only the last and first observation; (b) smoothing incorporated using functional regression approaches increases prediction performance; and (c) the interpretation of model parameters is substantially improved using functional regression approaches. Because many growth curve datasets exhibit missing and noisy data, we propose a bootstrap of subjects approach to account for the variability associated with the missing data imputation and smoothing. Methods are motivated by and applied to the CONTENT dataset, a study that collected monthly child growth data on 197 children from birth until month 15. R code describing the fitting approaches is provided in a supplementary file.

Statistical Properties of Alternative Parameterizations of the von Bertalanffy Growth Curve

1986 ◽  
Vol 43 (4) ◽  
pp. 742-747 ◽  
Author(s):  
D. A. Ratkowsky
Keyword(s):  
Linear Model ◽  
Growth Curve ◽  
Asymptotic Properties ◽  
Statistical Properties ◽  
Data Sets ◽  
Von Bertalanffy ◽  
Marine Animals ◽  
Nonlinear Regression Models ◽  
Linear Behavior ◽  
Biological Interpretation

The von Bertalanffy growth curve is often used in fisheries research to describe the relationship between the weight or length of a fish and its age. The equation is also encountered in various other branches of science and applied science in a variety of different parameterizations and names; for example, it is also known as the asymptotic regression equation or the three-parameter exponential equation. Since these equations are all nonlinear regression models, the properties of the least squares estimators of the parameters of these models may be very different from their large-sample properties, where the estimators are unbiased, have the minimum attainable variance, and are normally distributed, the conditions that pertain in a linear model. Different parameterizations will have estimators which approximate the asymptotic properties to varying degrees of closeness. My study of eight parameterizations shows that one of them, a generalization which allows unequal age increments of a parameterization proposed by Schnute and Fournier, is far superior to any of the other models, which include the most commonly used parameterization, in that it exhibits close-to-linear behavior. Two of the three parameters in this model represent the expected mean lengths corresponding to the youngest and oldest ages, respectively, in the sample, and thus have a ready biological interpretation. I discuss why it is important to have a close-to-linear model when one wishes to make comparisons between two or more data sets. Methodology is briefly described for carrying out such comparisons, and some further remarks are made about why biologists should be concerned about the statistical properties of the models that they use. Although most data sets I used for illustration are obtained from marine animals, the conclusions are general and apply to all disciplines which make use of the von Bertalanffy model in whichever guise or form it appears.

scholarly journals Gender on the growth of Criollo foals from birth to three years of age

2017 ◽  
Vol 47 (1) ◽  
Author(s):  
Anelise Maria Hammes Pimentel ◽  
Walvonvitis Baes Rodrigues ◽  
Charles Ferreira Martins ◽  
Nathanael Ramos Montanez ◽  
Arione Augusti Boligon ◽  
...  
Keyword(s):  
Regression Models ◽  
Nonlinear Models ◽  
Body Height ◽  
Growth Curves ◽  
Experimental Period ◽  
Future Research ◽  
First Year ◽  
Nonlinear Regression Models ◽  
Rate Of Increase ◽  
First Year Of Life

ABSTRACT: The objective of the present study was to evaluate the effect of gender on the growth of Criollo foals, in order to use this information as a reference for breeding as well as in future research. Body height, thoracic perimeter, and cannon bone perimeter of 75 foals were measured from two farms in Rio Grande do Sul, Brazil (Lat. 32°, 33′, 58″, Long. 53°, 22′, 33″) and from three generations over three years. In both farms, animals were kept under the same range and feeding conditions. Nonlinear regression models were applied to describe the growth curves for the three traits over the experimental period. Cannon bone perimeter was greater in males than in females (P<0.001) but the predicted curves for body height and thoracic perimeter did not differ between genders. For all traits, the highest rate of increase was achieved in the first year of life (body height = 74%, thoracic perimeter = 76%, and cannon bone perimeter = 63% for males and 83% for females). Results of this study indicated that changes in body height and thoracic perimeter can be predicted using nonlinear models in both male and female foals, until they reach three years of age; whereas, changes in cannon bone perimeter should be modeled separately for each gender.

scholarly journals Combined Effects of pH and Sugar on Growth Rate ofZygosaccharomyces rouxii, a Bakery Product Spoilage Yeast

1999 ◽  
Vol 65 (11) ◽  
pp. 4921-4925 ◽  
Author(s):  
Jeanne-Marie Membré ◽  
Martine Kubaczka ◽  
Christine Chéné
Keyword(s):  
Growth Rate ◽  
Synthetic Medium ◽  
Growth Curves ◽  
Estimated Parameters ◽  
Spoilage Yeast ◽  
Effects Of Ph ◽  
Biological Interpretation ◽  
Collection Strain ◽  
Ph Range ◽  
Counting Cell

ABSTRACT The effects of citric acid-modified pH (pH 2.5, 2.75, 3, 3.5, 4, 4.5, 5, and 5.5) and a 30% glucose–70% sucrose mixture (300, 400, 500, 600, 700, 800, 875, and 900 g/liter) on an osmophilic yeast,Zygosaccharomyces rouxii, were determined by using synthetic medium. One hundred experiments were carried out; 50-ml culture flasks were inoculated with 103 CFU ml−1 by using a collection strain and a wild-type strain cocktail. The biomass was measured by counting cell colonies, and growth curves were fitted by using a Baranyi equation. The growth rate decreased linearly with sugar concentration, while the effect of pH was nonlinear. Indeed, the optimal pH range was found to be pH 3.5 to 5, and pH 2.5 resulted in a 30% reduction in the growth rate. Finally, we evaluated the performance of two nonlinear predictive models developed previously to describe bacterial contamination. Equations derived from the Rosso and Ratkowsky models gave similar results; however, the model that included dimensionless terms based on the Ratkowsky equation was preferred because it contained fewer estimated parameters and also because biological interpretation of the results was easier.

Growth of two species of tiger prawn, Penaeus esculentus and P. semisulcatus, in the western Gulf of Carpentaria

1984 ◽  
Vol 35 (6) ◽  
pp. 703 ◽  
Author(s):  
GP Kirkwood ◽  
IF Somers
Keyword(s):  
Confidence Regions ◽  
Type Model ◽  
Von Bertalanffy ◽  
Growth Data ◽  
Von Bertalanffy Model ◽  
Lack Of Fit ◽  
Significant Difference ◽  
Tiger Prawn ◽  
Males And Females ◽  
Least Squares Estimates

Growth data were obtained for the two tiger prawn species P. esculentus and P. semisulcatus from a tagging experiment carried out in February 1981 in waters adjacent to Groote Eylandt in the western Gulf of Carpentaria. A von Bertalanffy growth curve was fitted to these data and least squares estimates of the parameters L∞ and K and joint 95% confidence regions were calculated for males and females of both species. Tests on the residuals from the fitted curve were carried out to check the adequacy of the fit of the von Bertalanffy model, and differences in the parameters L∞ and K between sexes and species were examined. An alternative von Bertalanffy-type model was used to test the consistency between the estimated L∞ values and the carapace leilgths of the largest individuals observed in samples from the populations. For males of each species, the fit of the von Bertalanffy model was satisfactory, and the estimates of L∞ were consistent with the largest observed carapace lengths in catch samples. For females, however, the fit of the von Bertalanffy model was not entirely satisfactory, especially for P. semisulcatus, for which additionally the estimated L∞ was much higher than the largest carapace length in catch samples. Possible reasons for this lack of fit are discussed. Estimates of L∞ all differed significantly, with the exception of P. esculentus males and P. semisulcatus males. No significant difference was found in estimates of K for P. esculentus males and females, and only a marginally significant difference in K between P. esculentus males and females and P. semisulcatus males. Presence of a bopyrid parasite in P. semisulcatus did not affect growth.

An empirical regression function suitable for modelling spore germination subject to temperature threshold

1980 ◽  
Vol 58 (8) ◽  
pp. 936-941 ◽  
Author(s):  
Bijan Payandeh ◽  
D. R. Wallace ◽  
D. M. MacLeod
Keyword(s):  
Nonlinear Regression ◽  
Spore Germination ◽  
Full Range ◽  
Regression Function ◽  
Temperature Threshold ◽  
Approximation Techniques ◽  
Nonlinear Regression Models ◽  
Estimated Parameters ◽  
Proposed Model ◽  
Biological Interpretation

Nonlinear regression analysis and least squares approximation techniques were employed to express percent spore germination as a function of time and temperature. Two sets of spore germination data under varying temperatures were used. A seven-parameter nonlinear regression model was found to fit the data equally as well as previously used mixed linear and two-stage nonlinear regression models. The proposed model is very flexible and allows for the expression of temperature threshold effects. In addition to providing a common set of parameters applicable to the full range of temperatures under consideration, such estimated parameters are amenable to biological interpretation.

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