Adaptation of Nonlinear Mathematical Models to Take into Consideration the Date of Conception of Animal Species
International Journal of Systems Science and Applied Mathematics
Volume 4, Issue 2, June 2019, Pages: 18-23
Received: Aug. 23, 2019; Accepted: Sep. 6, 2019; Published: Sep. 21, 2019
Views 506      Downloads 88
Mohammed Balafrej, Department of Agriculture, Production Chains Development Directorate, Rabat, Morocco
Article Tools
Follow on us
Nonlinear functions are of great interest in the field of livestock, particularly through the modeling of the relationship between weight and age in animal species, which facilitates both the interpretation and the understanding of the growth phenomenon. Adjustments to growth data allow the information to be condensed into a few parameters that are used for selection purposes and to improve production forecasts. However, these functions do not take into consideration the fixed nature of the conception date which is specific for each animal species. In principle, all observations should be based on this date. The purpose of this study is to adapt the most frequently used mathematical models to take into consideration the conception dates of animal species. To do this, four functions were studied namely those of Logistic, Gompertz, Richards and Von Bertalanffy. Afterwards, modified models were developed to determine their derivatives and inflection points. An example of an initial model and its adaptations were adjusted to the data of moroccan sheep "sardi" to observe the effects of adaptations on the growth curves for males and females of this species. The results obtained show that among these functions, only Richards and Von Bertalanffy could be adapted according to two methods to meet the aforementioned objective because the logistic and Gompertz models are strictly positive and do not cancel each other out. In addition, the comparison example between Richards' Model and its adaptations to sheep data shows that for the initial model, the conception dates are -24.07 days and -23.6 days for males and females, respectively. while modified models, whose adjustment results show similar results, have -150 day conception dates for both sexes. In conclusion, the modified models of Richards and Von Bertalanffy seem to represent at best the biology of animal species and therefore, could replace the initial models for future studies of animal species growth modeling.
Logistic, Gompertz, Richards, Von Bertalanffy, Conception Date, Inflexion Point, Growth Model
To cite this article
Mohammed Balafrej, Adaptation of Nonlinear Mathematical Models to Take into Consideration the Date of Conception of Animal Species, International Journal of Systems Science and Applied Mathematics. Vol. 4, No. 2, 2019, pp. 18-23. doi: 10.11648/j.ijssam.20190402.11
Copyright © 2019 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License ( which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Patricia Román-Román, Juan José Serrano-Pérez and Francisco Torres-Ruiz (2019). A Note on Estimation of Multi-Sigmoidal Gompertz Functions with Random Noise. Mathematics 2019, 7 (6), 541;
Irfan Daskiran et al. Growth caractéristics of indigenous Norduz female and male lambs. J. of Agricutural sciences (2010), v. 16, p. 62-69. Turkey.
Benjamin Gompertz. On the nature of the function of the law of human mortality, and on a new mode of determining the value of life contingencies. Philosophical transactions of the Royale Society of London. v. 115. (1825) p 513. 583.
Samuel Brody, 1945. Bioenergetics and Growth with special reference to the efficiency complex in domestic animals. Hafner publishing company (1945) Inc. New York 3. N. Y.
Ludwig von Bertalanfy. Quantitative lawsin metabolism and Growgh. The quarterly revew of biology (1957) vol. 32 n°3.
Fitzhugh Jr HA. Analysis of growth curves and strategies for altering their shape. J Anim Sci 1976; 42: 1036-1051.
Firat MZ, Karaman E, Basar EK, Narinc D. 2016. Bayesian analysis for the comparison of nonlinear negression model parameters: an application to the growth of Japanese quail. Braz J Poultry Sci. 18 (SI): 19–26.
Bathaei SS, Leroy PL. Growth and mature weight of Mehraban Iranian fat-tailed sheep. Small Rumin Res 1996; 22: 155-162.
Freitas AR. Curvas de crescimento na producão animal. R Bras Zootec 2005; 34: 786795.
Sariyel V, Aygun A, Keskin I. 2017. Comparison of growth curve models in partridge. Poult Sci. 96 (6): 1635–1640.
Yaya Wen, Ke Liu, Honghua Liu, Haiyue Cao, Haiguang Mao, Xinyang Dong & Zhaozheng Yin (2019) Comparison of nine growth curve models to describe growth of partridges (Alectoris chukar), Journal of Applied Animal Research, 47: 1, 195-200, DOI: 10.1080/09712119.2019.1599900.
J. C Pinheiro and D. M. Bates, Mixed-Effects Models in S and S-PLUS, Springer-Verlag, NewYork, 2000.
Nelder, J. A., “The fitting of a generalization of the logistic curve”, Biometrics Vol. 17 (1961), 89-110.
Winsor, C. P., “The Gompertz curve as a growth curve”, Proc. National Academy of Science, Vol. 18 (1932), No. 1.
Richards, F. J., “A flexible growth function for empirical use”, J. Exp. Bot. Vol. 10 (1959), 290-300.
Bertalanffy, von L., “Quantitative laws in metabolism and growth”, Quart. Rev. Biol. Vol. 3 (1957), No. 2, 218.
Brown, J. E., Fitzhugh Jr., H. A. and Cartwright, T. C. A Comparison of Non Linear 1976.
Malhado, C. H. M., Carneiro, P. L. S., Affonso, P. R. A. M., Souza Jr., A. A. O. and Sarmento, J. L. R.. Growth Curves in Dorper Sheep Crossed with the Local Brazilian Breeds, Morada Nova, Rabo Largo, and Santa Inês. Small Rumin. Res. 2009, 84: 16–21.
Science Publishing Group
1 Rockefeller Plaza,
10th and 11th Floors,
New York, NY 10020
Tel: (001)347-983-5186