SUMMARY
Received: 2016-11-09 | Accepted: 2016-12-03 | Available online: 2017-12-31http://dx.doi.org/10.15414/afz.2017.20.04.90-94The objective of this study was to predict breeding values for single- and multi-trait animal models and compute their reliabilities using a direct inversion method (DIM), and single- (ST-APM) and multi-trait approximate methods (MT-APM). Variance and covariance components of lean meat (LM) content, average daily gain (ADG) from birth until the end of the field test, and number of piglets born alive at first (NBA1) and second and subsequent parities (NBA2), were estimated for the analyses of Czech Large White pigs (390,734 records), using single- and four-trait animal models. The average reliabilities estimated by DIM for all considered animals were 0.514 ±0.069, 0.406 ±0.070, 0.050 ±0.044, and 0.321 ±0.090 for LM, ADG, NBA1, and NBA2, respectively. Values of 0.576 ±0.087, 0.150 ±0.078, 0.228 ±0.078, and 0.323 ±0.099, were obtained for the ST-APM for LM, ADG, NBA1, and NBA2, respectively. The use of MT-APM slightly increases the reliability of breeding values by 4 %, 6 %, 14 %, and 8 % for LM, ADG, NBA1, and NBA2, respectively. In addition, the dependence of the reliability values on the number of offspring of breeding boars is obtained; the reliability increases from 0.215 for less than 5 offspring to 0.989 for more than 400 offspring for the LM trait. Calculated Pearson’s and Spearman’s correlation coefficients between the employed methods were, in general, high, positive, and highly statistically significant. The multi-trait approximation method can be used for the calculation of reliabilities of breeding values as an alternative for direct inversion method that has computational limitations Keywords: pig, breeding value, reliability, direct inversion, approximationReferencesBAUER J., PRIBYL J. and VOSTRÝ L. (2015) Contribution of domestic and Interbull records to reliabilities of single-step genomic breeding values in dairy cattle. Czech J. Anim. Sci., 60, 6, pp. 263-267GROENEVELD, E., M. KOVAC, and N. MIELENZ. (2008) VCE User’s Guide and Reference Manual, Version 6.0. Available from ftp://ftp.tzv.fal.de/pub/latest_vce/doc/ (accessed Aug 1, 2011).GROENEVELD E., KOVAC M. and WANG T. (1990) PEST, a general purpose BLUP package for multivariate prediction and estimation. In: Proc. 4th World Congr. Genet. Appl. Livest. Prod., Edinburgh, 13, pp. 488-491.KRUPA, E. and WOLF, J. (2013) Simultaneous estimation of genetic parameters for production and litter size traits in Czech Large White and Czech Landrace pigs. Czech J. Anim. Sci., vol. 58, pp. 429–436.KRUPA, E., E. ŽÁKOVÁ, and Z. KRUPOVÁ. (2015) Evaluation of inbreeding and genetic variability of five pig breeds in Czech Republic. Asian–Australas. J. Anim. Sci. vol. 28, pp. 25–36.MISZTAL, I., T. J. LAWLOR, and T. H. SHORT. (1993) Implementation of single- and multiple-trait animal models for genetic evaluation of Holstein type traits. J. Dairy Sci., vol. 76, pp. 1421–1432.MISZTAL, I., and WIGGANS, G. R.. (1988) Approximation of prediction error variance in large-scale animal models. J. Dairy Sci., 71(Suppl. 2), pp. 27–32.MISZTAL, I. and PEREZ-ENCISO, P. (1993) Sparse Matrix Inversion for Restricted Maximum Likelihood Estimation of Variance Components by Expectation-Maximization. J. Dairy Sci., 76, 5, pp. 1479-1483MISZTAL I. et al. (2013) Methods to approximate reliabilities in single-step genomic evaluation. J. Dairy Sci., vol. 96, pp. 647–654.MRODE R. A. (2005) Linear Models for the Prediction of Animal Breeding Values. 2nd Edition. Wallingford: CABI.MRODE R. A. (2014) Linear Models for the Prediction of Animal Breeding Values. 3rd Edition. Wallingford: CABI.NEUMAIER A., and GROENEVELD, E.. (1998) Restricted maximum likelihood estimation of covariances in sparse linear models. Genet. Sel. Evol., vol. 30, pp. 3-26.SÁNCHEZ, J. P., MISZTAL, I. and J. K. BERTRAND. (2008) Evaluation of methods for computing approximate accuracies in maternal random regression models for growth trait in beef. J. Anim. Sci., vol. 86, pp. 1057–1066.STRABEL, T., MISZTAL, I. and J. K. BERTRAND. (2001) Approximation of reliabilities for multiple-trait models with maternal effects. J. Anim. Sci., vol. 79, pp. 833–839.TIER, B. and MEYER, K. (2004) Approximating prediction error covariances among additive genetic effects within animals in multiple-trait and random regression models. J. Anim. Breed. Genetics, vol. 121, no. 2, pp. 77-89.VanRADEn P.M. (2008) Efficient methods to compute genomic predictions. J. of Dairy Sci., vol. 91, pp. 4414–4423.VanRADEN, P. M., and WIGGANS, G. R. (1991) Derivation, calculation, and use of national animal model information. J. Dairy Sci., vol. 74, pp. 2737–2746.WIGGANS, G. R., MISZTAL, I. and van VLECK, L. D. (1988) Animal model evaluation of Ayrshire milk yield with all lactations, herd-sire interaction, and groups based on unknown parents. J. Dairy Sci., vol. 71, pp. 1319–1329.