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Background  Inbreeding is caused by mating between related individuals and its most common consequence is inbreeding depression. Several studies have detected heterogeneity in inbreeding depression among founder individuals, and recently a procedure for predicting hidden inbreeding depression loads associated with founders and the Mendelian sampling of non-founders has been developed. The objectives of our study were to expand this model to predict the inbreeding loads for all individuals in the pedigree and to estimate the covariance between the inbreeding loads and the additive genetic effects for the trait of interest. We tested the proposed approach with simulated data and with two datasets of records on weaning weight from the Spanish Pirenaica and Rubia Gallega beef cattle breeds.    Results  The posterior estimates of the variance components with the simulated datasets did not differ significantly from the simulation parameters. In addition, the correlation between the predicted and simulated inbreeding loads were always positive and ranged from 0.27 to 0.82. The beef cattle datasets comprised 35,126 and 75,194 records on weights between 170 and 250 days of age, and pedigrees of 308,836 and 384,434 individual-sire-dam entries for the Pirenaica and Rubia Gallega breeds, respectively. The posterior mean estimates of the variance of inbreeding depression loads were 29,967.8 and 28,222.4 for the Pirenaica and Rubia Gallega breeds, respectively. They were larger than those of the additive variance (695.0 and 439.8 for Pirenaica and Rubia Gallega, respectively), because they should be understood as the variance of the inbreeding depression achieved by a fully inbred (100%) descendant. Therefore, the inbreeding loads have to be rescaled for smaller inbreeding coefficients. In addition, a strong negative correlation (− 0.43 ± 0.10) between additive effects and inbreeding loads was detected in the Pirenaica, but not in the Rubia Gallega breed.    Conclusions  The results of the simulation study confirmed the ability of the proposed procedure to predict inbreeding depression loads for all individuals in the populations. Furthermore, the results obtained from the two real datasets confirmed the variability in the inbreeding depression loads in both breeds and suggested a negative correlation of the inbreeding loads with the additive genetic effects in the Pirenaica breed.

A multivariate analysis with direct additive and inbreeding depression load effects