Determination of a New Characterization Point for Nonlinear Mathematical Models Applied to Sheep

Improvement of sheep productivity requires selection, the use of nonlinear mathematical models provides a good means of condensing information and facilitates the interpretation and understanding of the growth phenomenon. However, few studies have addressed the optimal age of slaughter and focused on determining which models fit best with their sheep growth data. This age should meet the production objectives which differ upstream according to the production systems and downstream according to the nature of the demands expressed by all the actors in the sector, namely from slaughter to consumption. Some studies have concluded that it corresponds to the age of inflection where the growth rate is at its maximum. But according to the findings, for some production systems, this age is not suitable since it is very far from the slaughter age with the risk of hasty decision making about the judgment of the growth potential of animals. Therefore, the objective of this study is to develop a new landmark located further down the growth curve than the inflection point and that meets the specific needs of these systems. To do this, we have calculated for the models Logistic, Gompertz, Richards and Von Bertalanffy, the point f (tbm) corresponding to the age tbm which satisfies two conditions namely the third derivative which is cancelled and the second derivative which is negative. For the function of Brody this point does not exist. The weights at this point represent 79%, 68% and 61% of the asymptotic weight respectively for the models Logistic, Gompertz and Von Bertalanffy. Subsequently, this point was compared with the inflection point for slaughter statistics (live slaughtering weights), using the Von Bertalanffy model as an example and then illustrating the changes in trends that may occur during animal growth and may bias judgments about precocity if decision-making is hasty about growth potential. It can be concluded that the point f (tbm) could provide a better assessment of the growth potential relative to the inflection point for some sheep production systems and therefore, efforts should be made by researchers in the countries concerned by this problematic, in order to characterize the point f (tbm) from a biological point of view that is corporal and morphological compositions for different breeds and production systems.