Growth Models of Female Dairy Cattle

Different methods of representing animal growth are possible and are defined for different animal categories. In this paper, weight measuring of female dairy cattle will be modelled by several nonlinear models. The most commonly used methods for describing the growth of animals are: Gompertz function, logistic function, Schmalhausen function, Brody function, Weibull function, Wood function and Von Bertalanffy function. Measured weight values and estimated parameters of growth curves will be analyzed using regression analysis methods. We will work with the weight measurements of 10 calves under 25 months of age from cowsheds in village Zaluži in the Czech Republic. A comparison of several growth curves will be done. The suitability of individual models will be evaluated not only by the index of determination, but also by the intrinsic curvature according to Bates and Watts. This curvature affects the size of the linearization areas in which initial solution will ensure convergence of nonlinear regression.

[1]  A. Goshu,et al.  Generalized Mathematical Model for Biological Growths , 2013 .

[2]  Deniz Ünal,et al.  Gompertz, logistic and brody functions to model the growth of fish species Siganus rivulatus , 2017 .

[3]  Lubomír Kubáček,et al.  On a linearization of regression models , 1995 .

[4]  J. Schmalhausen Beiträge zur quantitativen Analyse der Formbildung , 1927, Wilhelm Roux' Archiv für Entwicklungsmechanik der Organismen.

[5]  C. Winsor,et al.  The Gompertz Curve as a Growth Curve. , 1932, Proceedings of the National Academy of Sciences of the United States of America.

[6]  L. Martyushev,et al.  Universal Model of Ontogenetic Growth: Substantiation and Development of Schmalhausen's Model , 2014, 1404.4318.

[7]  L. Bertalanffy Quantitative Laws in Metabolism and Growth , 1957 .

[8]  Boris Zeide,et al.  Analysis of Growth Equations , 1993 .

[9]  I. Schmalhausen Das Wachstumsgesetz und die Methode der Bestimmung der Wachstumskonstante , 1928, Wilhelm Roux' Archiv für Entwicklungsmechanik der Organismen.

[10]  Samuel Brody,et al.  Bioenergetics and growth. With special reference to the efficiency complex in domestic animals. , 1946 .

[11]  F. J. Richards A Flexible Growth Function for Empirical Use , 1959 .

[12]  D. G. Watts,et al.  Relative Curvature Measures of Nonlinearity , 1980 .

[13]  Benjamin Gompertz,et al.  XXIV. On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies. In a letter to Francis Baily, Esq. F. R. S. &c , 1825, Philosophical Transactions of the Royal Society of London.