Exploring the Use of Random Regression Models withLegendre Polynomials to Analyze Clutch Sizein Iranian Native Fowl

Document Type : Research Article


1 Department of Animal Science, Faculty of Agriculture, Ferdowsi University of Mashhad, Mashhad, Iran

2 Department of Animal Science, Faculty of Agriculture and Natural Resources, University of Tehran, Karaj, Iran


Random regression models (RRM) have become common for the analysis of longitudinal data or repeated records on individual over time. The goal of this paper was to explore the use of random regression models with orthogonal / Legendre polynomials (RRL) to analyze new repeated measures called clutch size (CS) as a meristic trait for Iranian native fowl. Legendre polynomial functions of increasing order 0 (no covariate) to 4 were fitted to the age at sexual maturity (ASM) and 1 to 10 to the additive genetic and permanent environmental effects. Days in production (clutch) were used as time variables. Homogeneity of residual variance through the time was assumed. Analyses were carried out within restricted maximum likelihood algorithm (REML) using WOMBAT software. Adequacy of models was checked by Bayesian information criterion (BIC). The resulted BICs suggested a model composed of the second order polynomial for ASM and 8th order polynomial for additive genetic and permanent environmental effect was the most suitable for adjusting the present records. The highest phenotypic and permanent environmental variance of CS was at the beginning of the production period. Additive genetic variance was fairly consistent during 210 and 265 days of age (d 210-d265). Estimates of heritability for CS ranged from 0.033 to 0.199 for d 161 and d 242 in the first cycle of egg production, respectively. The ratio of animal permanent environmental variance to phenotypic variance was in the range of 0.01 and 0.264. The estimated ranges for additive genetic and permanent environmental correlations were -0.18 to 0.99 and -0.5 to 0.99, respectively and were high between the adjacent ages and they tended to decrease at nonadjacent ages.


Akbas Y., Takma Ç. and Yaylak E. (2004). Genetic parameters for quail body weights using a random regression model. Southern African J. Anim. Sci. 34(2), 104-109.
Akbas Y., Ünver Y., Oguz I. and Altan O. (2002). Estimation of genetic parameters for clutch traits in laying hens. Proc. 7th World Cong. Genet. Appl. Livest. Prod., Montpellier, France.
Anang A., Mielenz N. and Schüler L. (2002). Monthly model for genetic evaluation of laying hens. II. Random regression. Br. Poult. Sci. 43(3), 384-390.
Anang A., Mielenz N., Schüler L. and Preisinger D.R. (2001). The use of monthly egg production records for genetic evaluation of laying hens. J. Ilmu. Ternak dan Vet. 6(4), 230-234.
Arango J., Cundiff L.V. and Van Vleck L.D. (2004). Covariance functions and random regression models for cow weight in beef cattle. J. Anim. Sci. 82(1), 54-67.
Crow F. and Dove W.F. (2000). Perspectives on Genetics: Anecdotal, Historical and Critical Commentaries. The University of Wisconsin Press. 2537 Daniels Street, Madison, Wisconsin.
Farzin N., Vaez Torshizi R., Kashan N. and Gerami A. (2010). Estimation of genetic and phenotypic correlations between monthly and cumulative egg productions in a commercial broiler female line. Glob. Vet. 5(3), 164-167.
Grossman M., Grossman T.N. and Koops W.J. (2000). A model for persistency of egg production. Poult. Sci. 79, 1715-1724.
Jensen J. (2001). Genetic evaluation of dairy cattle using test-day models. J. Dairy Sci. 84, 2803-2812.
Kirkpatrick M., Lofsvold D. and Bulmer M. (1990). Analysis of the inheritance, selection and evolution of growth trajectories. Genetics. 124, 979-993.
Komprej A., Malovrh Š., Gorjanc G., Kompan D. and KovacM. (2013). Genetic and environmental parameters estimation for milk traits in Slovenian dairy sheep using random regression mode. Czech J. Anim. Sci. 58(3), 125-135.
Koops W.J. and Grossman M. (1992). Characterization of poultry egg production using a multiphasic approach. Poult. Sci. 71, 399-405.
Kranis A., Su G., Sorensen D. and Woolliams J.A. (2007). The application of random regression models in the genetic analysis of monthly egg production in turkeys and a comparison with alternative longitudinal models. Poult. Sci. 86(3), 470-475.
Lukovic Z., Uremovic M., Konjacic M., Uremovic Z. and Vincek D. (2007). Genetic parameters for litter size in pigs using random regression model. Asian-australs J. Anim. Sci. 20(2), 160-165.
Lukovic Z., Malovrh S., Gorjanc G. and KovacM. (2004). A random regression model in analysis of litter size in pigs. Southern African J. Anim. Sci. 34(4), 241-248.
Lukovic Z., Malovrh S., Gorjanc G. and KovacM. (2003). Genetic parameters for number of piglets born alive using random regression model. Agric. Cons. Sci. 68(2), 105-108.
Meyer K. (2006). WOMBAT.University of New England. Australia.
Meyer K. (1998). Estimating covariance functions for longitudinal data using a random regression model. Genet. Sel. Evol. 30, 221-240.
Minvielle F., Kayang B.B., Inoue-Murayama M., Miwa M., Vignal A., Gourichon D., Neau A., Monvoisin L. and Ito S.I. (2006). Search for QTL affecting the shape of the egg laying curve of the Japanese quail. BMC Genet. 7, 26-31.
Miyoshi S., Luc K.M. and Kuchida K. (1996). Application of non-linear models to egg production curves in chickens. Japans Poult. Sci. 33, 178-184.
Pool M.H. and Meuwissen T.H.E. (1999). Prediction of daily milk yields from a limited number of test days using test day models. J. Dairy Sci. 82, 1555-1564.
Rawling J.O., Pantula S.G. and Dickey D.A. (1998). Applied Regression Analysis: A Research Tool. Springer Texts in Statisitcs. Springer-Verlag, Inc., New York.
Rowland H.D. and Weller S.G. (1996). The Gist of Genetics: Guide to Learning and Review. Jones and Barlett Publishers, London, UK.
Strabel T., Szyda J., Ptak E. and Jamrozik J. (2005). Comparison random regression test-day model for polish black and white cattle. J. Dairy Sci. 88, 3688-3699.
Van der Werf J. (2001). Random Regression in Animal Breeding. Course Notes. University of New England. Armindale. Australia.
Venturini G.C., Grossi D.A., Ramos S.B., Cruz V.A.R., Souza C.G., Ledur M.C., Faro L.El., Schmidt G.S. and Munari D.P. (2012). Estimation of genetic parameters for partial egg production periods by means of random regression models. Genet. Mol. Res. 11(3), 1819-1829.
Wolc A., Arango J., Settar P., Fulton J.E., O’Sullivan N.P., Preisinger R., Fernando R., Garrick D.J. and Dekkers J.C.M. (2013). Analysis of egg production in layer chickens using random regression model with genomic relationships. Poult. Sci. 92(6), 1486-1491.
Wolc A., Arango J., Settar P., O’Sullivan N.P. and Dekkers J.C.M. (2011). Evaluation of egg production in layers using random regression models. Poult. Sci. 90(1), 30-34.
Wolc A., Bednarczyk M., Lisowski M. and Szwaczkowski T. (2010). Genetic relationships among time of egg formation, clutch traits and traditional selection traits in laying hens. J. Anim. Feed Sci. 19, 452-459.
Wolc A. and Szwaczkowski T. (2009). Estimation of genetic parameters for monthly egg production in laying hens based on random regression models. J. Appl. Genet. 50(1), 41-46.
Wolc A., Lisowski M. and Szwaczkowski T. (2007). Heritability of egg production in laying hens under cumulative, multitrait and repeated measurement animal models. Czech J. Anim. Sci. 52(8), 254-259.