Simultaneous estimation of sire expected progeny differences and variance components using restricted maximum likelihood

The objective of this study was to develop, for breed associations of Argentina, the necessary Fortran programs to organize a National Sire Evaluation program. Therefore, using four different models, eight Fortran-WATFIV programs were developed to estimate simultaneously the best linear unbiased predictor (BLUP) of the sire expected progeny differences (EPDs), the standard error of prediction (SEP), variance components and heritability of weaning weight. The Cholesky\u27s method was used to solve the mixed model equations;Since the data set of this study was small, restricted maximum likelihood (REML) was the chosen method to estimate (sigma)(,s)(\u272) and (sigma)(,e)(\u272) using genetic groups and relationships among the sires. Basically, Model I, II, III and IV allowed one to point out the computational differences in estimates of (sigma)(,s)(\u272). Comparing the REML estimates for (sigma)(,s)(\u272) obtained with the different models, it could be concluded that the estimation of (sigma)(,s)(\u272), from the data set studied, was slightly affected by including genetic groups and/or the relationships among the sires. However, the REML estimates obtained for (sigma)(,s)(\u272) were greater in those models that took into account the additive genetic relationships among the sires. This seems to support the argument that the increment of the variance of sire may be due to the fact that the use of A(\u27-1) has the greatest effect on sires with small number of progeny; therefore, these sires would have their EPDs less regressed toward their mean or group mean. Consequently, the estimate of heritability was higher in those models that took into account the additive relationships among the sires;However, no general conclusions could be established due to the fact that the additional information that A(\u27-1) incorporates to the sire evaluation procedure in any other data set may show different patterns that the tendencies found with the data set analyzed. With the methodology developed, further research will be needed to see if general rules could be established about the effect that the incorporation of A(\u27-1) has on the estimation of variance components.(\u27);Sire EPDs obtained with the models studied were compared. The Pearson product moment correlation coefficients between individual sire EPDs over all the sires ranged from 0.94 to 0.97. The Spearman rank-order correlations for all the sires in the four evaluations ranged from 0.93 to 0.96