Mean (SD) of estimates of genomic heritability by simulation scenario (rows) and information used for analysis.

<p><i>h</i>²: trait heritability; </p><p></p><p></p><p></p><p><mi>h</mi></p><p><mi>G</mi></p><p><mn>2</mn></p><p></p><p></p><p></p>: genomic heritability; Short/Long refer to the length of the LD blocks. Fixed/Rand define whether the LD patterns were the same (Fixed) or varied (Rand.) between blocks (Rand). QTL (only QTL), QTL+MRK.LD (QTL and markers in LD with QTL), ALL (all loci), MRK.LD (only markers in LD with QTL), MRK.LD+MRK.LE (only markers, no QTL) and MRK.LE (only markers in LE with QTL) were used to compute the genomic relationship matrix.<p></p><p>Mean (SD) of estimates of genomic heritability by simulation scenario (rows) and information used for analysis.</p

Boxplot of estimated genomic heritability (3,000 MC replicates) by simulation and analysis scenario.

<p>Each plot presents results for one simulation scenario (5/10K 10 thousand LD blocks with 5 loci each; 50/1K one thousand LD blocks, each with 50 loci; FTP, ‘fixed transition probability, indicates that the LD patterns were the same across LD blocks, RTP, random transition probability, is a scenario where LD patterns changed between blocks). The labels in the horizontal axis indicate what information was used to compute the G-matrix (QTL = genotypes at causal loci, MRK.LD = markers in LD with QTL, MRK.LE = markers in LE with QTL, ALL = all loci).</p

Density plot of estimated genomic heritability (1,000 MC replicates) by analysis scenario (Simulation 2).

<p>The vertical dashed line gives the simulated heritability (QTL, MRK, MRK+QTL indicate whether QTL genotypes, or marker genotypes, MRK, or both, MRK+QTL, were used to compute genomic relationships).</p

Image_4_Prediction of Complex Traits: Robust Alternatives to Best Linear Unbiased Prediction.TIFF

<p>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.</p

Image_6_Prediction of Complex Traits: Robust Alternatives to Best Linear Unbiased Prediction.TIFF

<p>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.</p

Image_1_Prediction of Complex Traits: Robust Alternatives to Best Linear Unbiased Prediction.TIFF

<p>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.</p

Image_7_Prediction of Complex Traits: Robust Alternatives to Best Linear Unbiased Prediction.TIFF

<p>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.</p

Image_5_Prediction of Complex Traits: Robust Alternatives to Best Linear Unbiased Prediction.TIFF

<p>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.</p

Image_2_Prediction of Complex Traits: Robust Alternatives to Best Linear Unbiased Prediction.TIFF

<p>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.</p

Data_Sheet_1_Prediction of Complex Traits: Robust Alternatives to Best Linear Unbiased Prediction.pdf

<p>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.</p