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

Daniel Gianola, Alessio Cecchinato, Hugo Naya, Chris-Carolin Schön

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 t 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 Arabidopsis thaliana. 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 Arabidopsis) that the best predictions were often those obtained with the robust methods. The results obtained are encouraging and stimulate further investigation and generalization.