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

Mohammed Balafrej

doi:doi:10.11648/j.ijssam.20190403.13

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

Mohammed Balafrej

Published in International Journal of Systems Science and Applied Mathematics (Volume 4, Issue 3)

Received: 1 October 2019 Accepted: 15 October 2019 Published: 23 October 2019

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Abstract

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 (t_bm) corresponding to the age t_bm 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 (t_bm) 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 (t_bm) from a biological point of view that is corporal and morphological compositions for different breeds and production systems.

Published in	International Journal of Systems Science and Applied Mathematics (Volume 4, Issue 3)
DOI	10.11648/j.ijssam.20190403.13
Page(s)	38-46
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2019. Published by Science Publishing Group

Keywords

Slaughter Age, Slaughter Weight, Inflection Point, Nonlinear Model, Brody, Logistic, Gompertz, Richards, Von Bertalanffy

References

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APA Style

Mohammed Balafrej. (2019). Determination of a New Characterization Point for Nonlinear Mathematical Models Applied to Sheep. International Journal of Systems Science and Applied Mathematics, 4(3), 38-46. https://doi.org/10.11648/j.ijssam.20190403.13

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ACS Style

Mohammed Balafrej. Determination of a New Characterization Point for Nonlinear Mathematical Models Applied to Sheep. Int. J. Syst. Sci. Appl. Math. 2019, 4(3), 38-46. doi: 10.11648/j.ijssam.20190403.13

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AMA Style

Mohammed Balafrej. Determination of a New Characterization Point for Nonlinear Mathematical Models Applied to Sheep. Int J Syst Sci Appl Math. 2019;4(3):38-46. doi: 10.11648/j.ijssam.20190403.13

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@article{10.11648/j.ijssam.20190403.13,
  author = {Mohammed Balafrej},
  title = {Determination of a New Characterization Point for Nonlinear Mathematical Models Applied to Sheep},
  journal = {International Journal of Systems Science and Applied Mathematics},
  volume = {4},
  number = {3},
  pages = {38-46},
  doi = {10.11648/j.ijssam.20190403.13},
  url = {https://doi.org/10.11648/j.ijssam.20190403.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijssam.20190403.13},
  abstract = {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.},
 year = {2019}
}

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TY  - JOUR
T1  - Determination of a New Characterization Point for Nonlinear Mathematical Models Applied to Sheep
AU  - Mohammed Balafrej
Y1  - 2019/10/23
PY  - 2019
N1  - https://doi.org/10.11648/j.ijssam.20190403.13
DO  - 10.11648/j.ijssam.20190403.13
T2  - International Journal of Systems Science and Applied Mathematics
JF  - International Journal of Systems Science and Applied Mathematics
JO  - International Journal of Systems Science and Applied Mathematics
SP  - 38
EP  - 46
PB  - Science Publishing Group
SN  - 2575-5803
UR  - https://doi.org/10.11648/j.ijssam.20190403.13
AB  - 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.
VL  - 4
IS  - 3
ER  -

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Mohammed Balafrej

Department of Agriculture, Production Chains Development Directorate, Rabat, Morocco

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Mohammed Balafrej. (2019). Determination of a New Characterization Point for Nonlinear Mathematical Models Applied to Sheep. International Journal of Systems Science and Applied Mathematics, 4(3), 38-46. https://doi.org/10.11648/j.ijssam.20190403.13

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ACS Style

Mohammed Balafrej. Determination of a New Characterization Point for Nonlinear Mathematical Models Applied to Sheep. Int. J. Syst. Sci. Appl. Math. 2019, 4(3), 38-46. doi: 10.11648/j.ijssam.20190403.13

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AMA Style

Mohammed Balafrej. Determination of a New Characterization Point for Nonlinear Mathematical Models Applied to Sheep. Int J Syst Sci Appl Math. 2019;4(3):38-46. doi: 10.11648/j.ijssam.20190403.13

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@article{10.11648/j.ijssam.20190403.13,
  author = {Mohammed Balafrej},
  title = {Determination of a New Characterization Point for Nonlinear Mathematical Models Applied to Sheep},
  journal = {International Journal of Systems Science and Applied Mathematics},
  volume = {4},
  number = {3},
  pages = {38-46},
  doi = {10.11648/j.ijssam.20190403.13},
  url = {https://doi.org/10.11648/j.ijssam.20190403.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijssam.20190403.13},
  abstract = {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.},
 year = {2019}
}

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TY  - JOUR
T1  - Determination of a New Characterization Point for Nonlinear Mathematical Models Applied to Sheep
AU  - Mohammed Balafrej
Y1  - 2019/10/23
PY  - 2019
N1  - https://doi.org/10.11648/j.ijssam.20190403.13
DO  - 10.11648/j.ijssam.20190403.13
T2  - International Journal of Systems Science and Applied Mathematics
JF  - International Journal of Systems Science and Applied Mathematics
JO  - International Journal of Systems Science and Applied Mathematics
SP  - 38
EP  - 46
PB  - Science Publishing Group
SN  - 2575-5803
UR  - https://doi.org/10.11648/j.ijssam.20190403.13
AB  - 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.
VL  - 4
IS  - 3
ER  -

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