Estimation of Variance Components for Body Weight of Moghani Sheep Using B-Spline Random Regression Models

Document Type : Research Article


Department of Animal Science, Faculty of Agriculture, Bu Ali Sina University, Hamedan, Iran


The aim of the present study was the estimation of (co) variance components and genetic parameters for body weight of Moghani sheep, using random regression models based on B-Splines functions. The data set included 9165 body weight records from 60 to 360 days of age from 2811 Moghani sheep, collected between 1994 to 2013 from Jafar-Abad Animal Research and Breeding Institute, Ardabil province, Iran. Random regression models were employed to analyze the data. Contemporary groups (year-season of birth -sex-birth type-dam age at the birth) and fixed regression of body weight on age were considered as fixed parts of the models. Random regressions of direct additive genetic, permanent environment, maternal additive genetic and maternal environment were random parts of the models. Linear and quadratic B-Spline functions with two or three coefficients were fitted for fixed and random regressions of the models. A heterogeneous structure of residual variance was considered in five age classes. Variance components were estimated by average information algorithm of restricted maximum likelihood (AI-REML). Different models were compared based on Akaike information criterion (AIC) and Schwarz Bayesian information criterion (BIC). According to both criteria, the best model was a model with quadratic B-Spline functions with 3, 3, 3, 2 and 2 coefficients for fixed regression and random regressions of direct additive genetic, permanent environmental, maternal additive genetic and maternal environmental effects, respectively. According to this model, low to moderate estimates of direct heritability (0.135 to 0.330) and moderate to high estimates of coefficient of permanent environmental effects (0.229 to 0.613) were obtained, while estimates of maternal heritability (0.05 to 0.14) and coefficient of maternal environment (less than 0.01) were low or negligible in all ages.


Akaike H. (1974). A new look at the statistical model identification. IEEE Trans. Automat. Control. 19, 716-723.
Baldi F., Alencar M.M. and Albuquerque L.G. (2010). Random regression analyses using B-Splines functions to model growth from birth to adult age in Canchim cattle. J. Anim. Breed. Genet. 127, 433-441.
Boligon A.A., Mercadante M.E.Z., Lôbo R.B., Baldi F. and Albuquerque L.G. (2012). Random regression analyses using B-spline functions to model growth of Nellore cattle. Animal. 6(2), 212-220.
de Boor C. (200(. A Practical Guide to Splines. Vol. 27 of Springer Series in Applied Mathematics, Springer Verlag, New York.
Fischer T.M., Van der Werf J.H.J., Banks R.G. and Ball A.J. (2004). Description of lamb growth using random regression on field data. Livest. Prod. Sci. 89, 175-185.
Ghafouri-Kesbi F., Eskandarinasab M. and Shahir M. (2008). Estimation of direct and maternal effects on body weight in Mehraban sheep using random regression models. Arch. Tierz. 51, 235-246.
Kariuki C.M., Ilatsia E.D., Wasike C.B., Kosgey I.S. and Kahi A.K. (2010). Genetic evaluation of growth of Dorper sheep in semi-arid Kenya using random regression models. Small Rumin. Res. 93, 126-134.
Lewis R.M. and Brotherstone S. (2002). A genetic evaluation of growth in sheep using random regression techniques. Anim. Sci. 74, 63-70.
Meyer K. (2000). Random regressions to model phenotypic variation in monthly weights of Australian beef cows. Livest. Prod. Sci. 65, 19-38.
Meyer K. (2005). Random regression analyses using B-Splines to model growth of Australian Angus cattle. Genet. Sel. Evol. 37, 473-500.
Meyer K. (2007). WOMBAT- A program for mixed model analyses by restricted maximum likelihood. User notes, Animal Genetics and Breeding Unit, Armidale, Australia.
Misztal I. (2006). Properties of random regression models using linear splines. J. Anim. Breed. Genet. 123, 74-80.
Molina A., Menéndez-Buxadera A., Valera M. and Serradilla J.M. (2007). Random regression model of growth during the first three months of agein Spanish Merino sheep. J. Anim. Sci. 85, 2830-2839.
Najafi M.J., Lavvaf A., Hemmati B., Farahvash T. and Abdollahpoor R. (2011). Estimation of genetic parameters for growth traits in Moghani sheep using random regression. Res. Opin. Anim. Vet. Sci. 1(10), 677-685.
Rice J.A. and Wu C.O. (2001). Nonparametric mixed effects models for unequally sampled noisy curves. Biometrics. 57, 253-259.
Safaei M., Eskandarinasab M.P. and Shearbaftoosy A. (2006). Estimates of genetic parameters for growth traits in Baluchi sheep using random regression models. J. Agric. Sci. Technol. 20, 93-102.
Sarmento J.L.R., Torres R.A., Pereira C.S., Sousa W.H., Lopes P.S., Araujo C.V. and Euclydes R.F. (2006). Genetic evaluation of growth traits of SantaInes hair sheep using random regression models. Arq. Bras. Med. Vet. Zootec. 58, 68-77.
SAS Institute. (2004). SAS®/STAT Software, Release 9.1. SAS Institute, Inc., Cary, NC. USA.
Schwarz G. (1978). Estimating the dimension of a model. Ann. Stat. 6, 461-464.
Shodja J., Nosrati M., Alijani S. and Pirani N. (2006). Estimation of genetic and phenotypic parameters for body weight at different ages and yearly wool production in Moghani sheep. Knowl. Agric. 57, 153-162.
Vatankhah M. (2012). Genetic analysis of ewe body weight in Lori-Bakhtiari sheep using random regression models. J. Livest. Sci. Technol. 1(1), 48-53.
Vatankhah M., Moradi Sharebabak M., Nejati Javarami A., Miraei-Ashtiani S.R. and VaezTorshizi R. (2004). A review of sheep breeding in Iran. Pp. 591-597 in Proc. 1st Iranian Cong. Anim. Aqua. Sci. Tehran, Iran.
Wolca B., Barczaka E., Wójtowski J., Slósarzc P. and Szwaczkowskia T. (2011). Genetic parameters of body weight in sheep estimated via random regression and multi-trait animal models. Small Rumin. Res. 100, 15-18.