Prediction of Complex Traits: Robust Alternatives to Best Linear Unbiased Prediction.

A widely used method for prediction of complex traits in animal and plant breeding is "genomic best linear unbiased prediction" (GBLUP). In a quantitative genetics setting, BLUP is a linear regression of phenotypes on a pedigree or on a genomic relationship matrix, depending on the type of input information available. Normality of the distributions of random effects and of model residuals is not required for BLUP but a Gaussian assumption is made implicitly. A potential downside is that Gaussian linear regressions are sensitive to outliers, genetic or environmental in origin. We present simple (relative to a fully Bayesian analysis) to implement robust alternatives to BLUP using a linear model with residual or Laplace distributions instead of a Gaussian one, and evaluate the methods with milk yield records on Italian Brown Swiss cattle, grain yield data in inbred wheat lines, and using three traits measured on accessions of . The methods do not use Markov chain Monte Carlo sampling and model hyper-parameters, viewed here as regularization "knobs," are tuned via some cross-validation. Uncertainty of predictions are evaluated by employing bootstrapping or by random reconstruction of training and testing sets. It was found (e.g., test-day milk yield in cows, flowering time and FRIGIDA expression in ) that the best predictions were often those obtained with the robust methods. The results obtained are encouraging and stimulate further investigation and generalization.