Simple hierarchical and general nonlinear growth modeling in sheep
Differential equations and advanced statistical models have been used to predict growth phenomena. In the present study,
general nonlinear growth functions such as von Bertalanffy, Gompertz, logistic, and Brody, along with hierarchical modeling were
applied to investigate the phenotypic growth pattern of Iranian Lori-Bakhtiari sheep. Growth data from 1410 Lori- Bakhtiari lambs
were used in the present study. The results showed that the Brody function outperformed the other three nonlinear growth functions.
In addition, including hierarchical growth modeling results allowed the adoption of many random effect structures, suggesting that
hierarchical growth modeling has a useful role in growth data modeling. This method provides an estimation of growth parameters
based on individual animals, improving individual growth selection. The results suggest this approach for growth modeling. Combining
the strength of individual growth modeling with general growth modeling, e.g., von Bertalanffy, Gompertz, logistic, and Brody would
be deeply appealing in the future. In this regard, dealing with sheep growth phenomenon using pure mathematical models, i.e. grey
system theory models that could be new powerful prediction tools for breeders and experts, has not been done yet. However, running
the analysis on large datasets will require significantly higher computational power than is ordinarily available.
___
- Blasc A, Gomes E. A note on growth curves of rabbit lines
selected on growth rate or litter size. Anim Prod 1993; 57: 332-
334.
- Molina A, Menéndez-Buxadera A, Valera M, Serradilla M.
Random regression model of growth during the first three
months of age in Spanish merino sheep. J Anim Sci 2007; 85:
2830-2839.
- Kume K, Hagno L. Study of growth curve variations for kids
0-6 months old of Alpine goat breed in Albania. Arch Zootec
2010; 13: 54-62.
- Bathaei SS, Leroy PL. Genetic and phenotypic aspects of the
growth curve characteristics in Mehraban Iranian fat-tailed
sheep. Small Ruminant Res 1998; 29: 261-269.
- Lewis RM, Brotherstone S. A genetic evaluation of growth in
sheep using random regression techniques. Anim Sci 2002; 74:
63-70.
- Topal M, Ozdemir M, Aksakal V, Yildiz N, Dogru U.
Determination of the best non-linear function in order to
estimate growth in Morkaraman and Awassi lambs. Small
Ruminant Res 2004; 55: 229-232.
- Gbangboche AB, Adamou-Ndiaye M, Youssao AKI, Farnir F,
Detilleux J, Abiola FA, Leroy PL. Non-genetic factors affecting
the reproduction performance, lamb growth and productivity
indices of Djallonke sheep. Small Ruminant Res 2006; 64: 133-
142.
- Gbangboche AB, Youssao AKI, Senou M, Adamou-Ndiaye
M, Ahissou F, Farnir F, Michaux FA, Abiola FA, Leroy PL.
Examination of non-genetic factors affecting the growth
performance of Dejallonke sheep in Soudanian zone at the
Okpara breeding farm of Benin. Trop Anim Health Pro 2006;
38: 55-64.
- Abegaz S, Vanwyk JB, Olivira JJ. Estimation of genetic and
phenotypic parameters of growth curve and their relationship
with early growth and productivity in Herro sheep. Arch
Tierzucht 2010; 53: 85-94.
- Bahreini Behzadi MR, Aslaminejad AA, Sharifi AR, Simianer
H. Comparison of mathematical models for describing the
growth of Baluchi sheep. J Agric Sci Technol 2006; 14: 57-68.
- Donnet S, Foulley JL, Samson A. Bayesian analysis of growth
curves using mixed models defined by stochastic differential
equations. Biometrics 2010; 66: 733-741.
- Safaei M, Fallah-Khair AR, Seyed-Sharifi R, Haghbin H,
Nazarpak H, Sobhabi A, Yalchi T. Estimation of covariance
functions for growth trait from birth to 180 days of age in
Iranian Baluchi sheep. J Food Agric Environ 2010; 8: 659-663.
- Mota R, Luiz F, Aarão M, Paulo S, Lopes L, Pinheiro AM,
Hidalgo C, Suguimoto L. Random regression models in the
evaluation of the growth curve of Simbrasil beef cattle. Genet
Mol Res 2013; 12: 528-536.
- Deng JL. Properties of relational space for Grey Systems. In:
Grey System. Beijing, China: China Ocean Press, 1988. pp. 1-13
- Jing W, Yuesong H, Weilin L, Wenhui C. Application of grey
system theory to tree growth prediction. J Forestry Res 2000;
11: 34-36.
- Gbangboche AB, Glele-Kakai R, Salifou S, Albuquerque LG.
Comparison of non-linear growth models to describe the
growth curve in West African Dwarf sheep. Animal 2008; 2:
1003-1012.
- Lambe NR, Navajas EA, Simm G, Bunger L. A genetic
investigation of various growth models to describe of lamb of
two contrasting breeds. J Anim Sci 2006; 84: 2642-2654.
- Statistical Analysis System (SAS). SAS/STAT 9.2 User’s Guide:
The MIXED Procedure. Cary, NC, USA: SAS Institute Inc;
2009.
- Malhado CHM, Carneiro PLS, Mello P. Growth curves in
Dorper sheep crossed with the local Brazilian breeds, Morada
Nova, Rabo Largo, and Santa Inês. Small Ruminant Res 2009;
84: 16-21.
- Wilson RT, Peacock C, Sayers AR. Livestock production on
Masai Group Ranches. 2. Growth and live
weight in goats and
sheep at Elangata Wuas and the factors influencing them. J Agr
Rural Dev Trop 1982; 21: 191-198.
- Sarmento JLR, Rezazzi AJ, Souza WH, Torres RA, Breda FC,
Menezes GRO. Analysis of the growth curve of Santa Ines
sheep. Rev Bras Zootecn 2006; 35: 435-442.
- Waheed A, SajjadKhan M, Safdar A, Sarwar M. Estimation of
growth curve parameters in Beetal goats. Arch Tierzucht 2011;
54: 287-296.
- Forni S, Piles M, Blasco A, Varona L, Oliveira HN, Lôbo RB,
Albuquerque LG. Comparison of different nonlinear functions
to describe Nelore cattle growth. J Anim Sci 2009; 87: 496-506.
- Salehi Broujeni M, Ghaderi-Zefrehei M, Ghane-
Golmohammadi F, Ansari-Mahyari S. A novel LSSVM based
algorithm to increase accuracy of bacterial growth modeling.
Iran J Biotechnol 2018; 16: e1542.
- Sifeng L, Jeffrey F, Yingjie Y. A brief introduction to grey
systems theory. Grey Systems: Theory and Application 2012;
2: 89-104.
- Kayacan E, Ulutas B, Kaynak O. Grey system theory-based
models in time series prediction. Expert Syst Appl 2010; 37:
1784-1789.