Adaptation of Nonlinear Mathematical Models to Take into Consideration the Date of Conception of Animal Species

Abstract

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.