Parameterizations of the Von Bertalanffy Model for Description of Growth Curves

Abstract


 
 
 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.
 
 

Cross-sectional and longitudinal method for describing growth curve of rabbits

“…where represents the weight of the animal as a function of time ; α and β are anabolism and catabolism constants, respectively, and is an exponent that indicates the last values proportional to some body weight power (Bertalanffy, 1957;Fernandes et al, 2020).…”

“…Rabbits have a high growth rate (Marín-García et al, 2020), and in the post-weaning phase (from the 28th day of age) is the time Corresponding author: fernandesfelipest@gmail.com Submitted: September 7, 2021. Accepted: March 17, 2022. when the greatest influence of daily management occurs, which is directly correlated with animal breed, food quality, health and thermal environment in which the animals will be submitted throughout the breeding period (Ferreira et al, 2012). Thus, it is important to evaluate methods that can model the growth traits of these animals in view of the importance of management in rabbit in http://dx.doi.org/10.1590/1678-4162-12534 Arq.…”

Bertalanffy-Pütter models for avian growth

“…It is represented by exponent-pairs of the form ( a , a +1). Assuming exponents a = 1 or b = 1, as for the above-mentioned models, then the differential Eq ( 1 ) could be solved by means of elementary functions [ 46 , 48 , 49 ]. For general exponent-pairs the solution of differential Eq ( 1 ) was expressed in terms of the Gaussian hypergeometric function 2 F 1 [ 45 , 50 ], which is not an elementary function [ 51 ].…”

Estimation of Fishing Mortality Rate and Exploitation Status of Yellowstrip Scad (Selaroides leptolepis) in Tomini Bay using Von Bertalanffy Growth Model Approach

“…Von Bertalanffy mathematical model has been applied widely to plot growth for numerous biota (Lee et al, 2020), such as in fishes (Ogle and Isermann, 2017;Du Pontavice et al, 2018;Harris et al, 2018;Vahabnezhad et al, 2020;Wang et al, 2021), mollusks (López-Rocha et al, 2018;Ford et al, 2020;Prato et al, 2020) , sea turtle (Ramirez et al, 2021), and poultry (Mata-Estrada et al, 2020;Del Norte-Campos et al, 2021). It even started to be attempted in several study areas (Fernandes et al, 2020), including Covid-19 outbreak (Brahma et al, 2021). It indicates that Von Bertalanffy Growth Function is a tool that is still demonstrative to be used.…”