This is the first large-scale experimental study on genome-based prediction of testcross values in an advanced cycle breeding population of maize. The study comprised testcross progenies of 1,380 doubled haploid lines of maize derived from 36 crosses and phenotyped for grain yield and grain dry matter content in seven locations. The lines were genotyped with 1,152 single nucleotide polymorphism markers. Pedigree data were available for three generations. We used best linear unbiased prediction and stratified cross-validation to evaluate the performance of prediction models differing in the modeling of relatedness between inbred lines and in the calculation of genome-based coefficients of similarity. The choice of similarity coefficient did not affect prediction accuracies. Models including genomic information yielded significantly higher prediction accuracies than the model based on pedigree information alone. Average prediction accuracies based on genomic data were high even for a complex trait like grain yield (0.72-0.74) when the cross-validation scheme allowed for a high degree of relatedness between the estimation and the test set. When predictions were performed across distantly related families, prediction accuracies decreased significantly (0.47-0.48). Prediction accuracies decreased with decreasing sample size but were still high when the population size was halved (0.67-0.69). The results from this study are encouraging with respect to genome-based prediction of the genetic value of untested lines in advanced cycle breeding populations and the implementation of genomic selection in the breeding process.

High-throughput genotyping and large scale phenotyping produces massive amounts of data. In this vignette, we present a novel R package named synbreed for the analysis of such data to derive genome-based predictions. It contains a collection of functions required to fit and validate genomic prediction models in plant and animal breeding. This covers data processing, data visualization and data analysis. Thereby a versatile analysis pipeline is established within one software package. All functions are embedded within the framework of a single, unified data object. The implementation is flexible with respect to a wide range of data formats and models. The package fills an existing gap in the availability of software for next-generation genetics research. Where necessary, the package provides gateways to other software programs to extend the field of applications. The utility of the package is demonstrated in this document using three large-scale example data sets provided by the synbreedData R package: a simulated data set representing a maize breeding program, a publicly available mice data set and a dairy cattle data set.

Models based on additive marker effects and on epistatic interactions can be translated into genomic relationship models. This equivalence allows to perform predictions based on complex gene interaction models and reduces computational effort significantly. In the theory of genome-assisted prediction, the equivalence of a linear model based on independent and identically normally distributed marker effects and a model based on multivariate Gaussian distributed breeding values with genomic relationship as covariance matrix is well known. In this work, we demonstrate equivalences of marker effect models incorporating epistatic interactions and corresponding mixed models based on relationship matrices and show how to exploit these equivalences computationally for genome-assisted prediction. In particular, we show how models with epistatic interactions of higher order (e.g., three-factor interactions) translate into linear models with certain covariance matrices and demonstrate how to construct epistatic relationship matrices for the linear mixed model, if we restrict the model to interactions defined a priori. We illustrate the practical relevance of our results with a publicly available data set on grain yield of wheat lines growing in four different environments. For this purpose, we select important interactions in one environment and use this knowledge on the network of interactions to increase predictive ability of grain yield under other environmental conditions. Our results provide a guide for building relationship matrices based on knowledge on the structure of trait-related gene networks.

In genome-based prediction there is considerable uncertainty about the statistical model and method required to maximize prediction accuracy. For traits influenced by a small number of quantitative trait loci (QTL), predictions are expected to benefit from methods performing variable selection [e.g., BayesB or the least absolute shrinkage and selection operator (LASSO)] compared to methods distributing effects across the genome [ridge regression best linear unbiased prediction (RR-BLUP)]. We investigate the assumptions underlying successful variable selection by combining computer simulations with large-scale experimental data sets from rice (Oryza sativa L.), wheat (Triticum aestivum L.), and Arabidopsis thaliana (L.). We demonstrate that variable selection can be successful when the number of phenotyped individuals is much larger than the number of causal mutations contributing to the trait. We show that the sample size required for efficient variable selection increases dramatically with decreasing trait heritabilities and increasing extent of linkage disequilibrium (LD). We contrast and discuss contradictory results from simulation and experimental studies with respect to superiority of variable selection methods over RR-BLUP. Our results demonstrate that due to long-range LD, medium heritabilities, and small sample sizes, superiority of variable selection methods cannot be expected in plant breeding populations even for traits like FRIGIDA gene expression in Arabidopsis and flowering time in rice, assumed to be influenced by a few major QTL. We extend our conclusions to the analysis of whole-genome sequence data and infer upper bounds for the number of causal mutations which can be identified by LASSO. Our results have major impact on the choice of statistical method needed to make credible inferences about genetic architecture and prediction accuracy of complex traits. G ENOME-BASED prediction of genotypic values from marker or sequence information has been shown to be a valuable tool in plant and animal breeding (Meuwissen et al. 2001;Meuwissen and Goddard 2010;Albrecht et al. 2011). A series of statistical methods mainly differing in the extent of regularization and variable selection has been proposed in the literature (a review is in de los Campos et al. 2013). Simulation studies revealed clear differences between methods with respect to their predictive ability. Several factors affecting the prediction performance of these methods such as genetic trait architecture, span of linkage disequilibrium (LD), sample size, trait heritability, and marker density have been identified (Zhong et al. 2009;Daetwyler et al. 2010;Habier et al. 2010). However, how these methods account for the respective factors is still not fully understood, causing uncertainty about the best choice of method for a given population and trait.High-throughput genotyping platforms deliver data sets where the number of available observations n is typically smaller than the number of markers p. In these high-dimensional data sets...

The calibration data for genomic prediction should represent the full genetic spectrum of a breeding program. Data heterogeneity is minimized by connecting data sources through highly related test units. One of the major challenges of genome-enabled prediction in plant breeding lies in the optimum design of the population employed in model training. With highly interconnected breeding cycles staggered in time the choice of data for model training is not straightforward. We used cross-validation and independent validation to assess the performance of genome-based prediction within and across genetic groups, testers, locations, and years. The study comprised data for 1,073 and 857 doubled haploid lines evaluated as testcrosses in 2 years. Testcrosses were phenotyped for grain dry matter yield and content and genotyped with 56,110 single nucleotide polymorphism markers. Predictive abilities strongly depended on the relatedness of the doubled haploid lines from the estimation set with those on which prediction accuracy was assessed. For scenarios with strong population heterogeneity it was advantageous to perform predictions within a priori defined genetic groups until higher connectivity through related test units was achieved. Differences between group means had a strong effect on predictive abilities obtained with both cross-validation and independent validation. Predictive abilities across subsequent cycles of selection and years were only slightly reduced compared to predictive abilities obtained with cross-validation within the same year. We conclude that the optimum data set for model training in genome-enabled prediction should represent the full genetic and environmental spectrum of the respective breeding program. Data heterogeneity can be reduced by experimental designs that maximize the connectivity between data sources by common or highly related test units.