Resumo

CERON-ROJAS, J. Jesus  e  SAHAGUN-CASTELLANOS, Jaime. Multivariate empirical Bayes to predict the plant breeding values. Agrociencia [online]. 2016, vol.50, n.5, pp.633-648. ISSN 2521-9766.

The plant breeding value is inheritable and determines phenotypic characteristics such as plant height, and grain yield, and it can be predicted by means of univariate or multivariate Bayesian models based on the phenotypic or genomic plants information. These models control the uncertainty associated to prediction better, but this comes at a high computational cost, so less demanding alternative models are required. Empirical Bayes is a prediction method in which the expectation of the posterior distribution is the estimator of the breeding value. This is a variant of the standard Bayesian estimator and is efficient; it is robust to the erroneous specifications of the a priori distribution of parameters, and the parameter covariances can be estimated through restricted maximum likelihood. A multivariate linear model was proposed to predict the breeding value within the empirical Bayes context. This model incorporates the genetic correlations between traits, pedigree information, genomic information, and contains the multivariate genomic linear model and the multivariate standard linear model as particular cases. The genomic model uses only genomic information, whereas the standard model uses only information from the pedigree in the prediction. To compare numerically the efficiency of each of the three models, the correlations between the predicted and observed values obtained with the data from two maize (Zea mays) F2 populations and one double haploid wheat (Triticum aestivum L.) population, each of them with three characteristics and a particular set of molecular markers and genotypes, were used. In the three populations, the numerical results indicated that the model proposed provides more precise predictions than the other two. We concluded that the results were due to the fact that the model proposed used the genetic correlations between traits and the phenotypic, as well as genomic information, in the prediction.

Palavras-chave : Joint posterior distribution; molecular markers; multivariate linear model; Triticum aestivum; restricted likelihood; Zea mays.

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