Many important traits in plant breeding are polygenic and therefore recalcitrant to traditional marker-assisted selection. Genomic selection addresses this complexity by including all markers in the prediction model. A key method for the genomic prediction of breeding values is ridge regression (RR), which is equivalent to best linear unbiased prediction (BLUP) when the genetic covariance between lines is proportional to their similarity in genotype space. This additive model can be broadened to include epistatic effects by using other kernels, such as the Gaussian, which represent inner products in a complex feature space. To facilitate the use of RR and nonadditive kernels in plant breeding, a new software package for R called rrBLUP has been developed. At its core is a fast maximum-likelihood algorithm for mixed models with a single variance component besides the residual error, which allows for effi cient prediction with unreplicated training data. Use of the rrBLUP software is demonstrated through several examples, including the identifi cation of optimal crosses based on superior progeny value. In cross-validation tests, the prediction accuracy with nonadditive kernels was signifi cantly higher than RR for wheat (Triticum aestivum L.) grain yield but equivalent for several maize (Zea mays L.) traits. THE ABILITY TO PREDICT COMPLEX TRAITS from marker data is becoming increasingly important in plant breeding (Bernardo, 2008). Th e earliest attempts, now over 20 years old, involved fi rst identifying signifi cant markers and then combining them in a multiple regression model (Lande and Th ompson, 1990). Th e focus over the last decade has been on genomic selection methods, in which all markers are included in the prediction model (Bernardo and Yu, 2007; Heff ner et al., 2009; Jannink et al., 2010). One of the fi rst methods proposed for genomic selection was ridge regression (RR), which is equivalent to best linear unbiased prediction (BLUP) in the context of mixed models (Whittaker et al., 2000; Meuwissen et al., 2001). Th e basic RR-BLUP model is

Ridge Regression and Other Kernels for Genomic Selection with R Package rrBLUP

Despite important strides in marker technologies, the use of marker-assisted selection has stagnated for the improvement of quantitative traits. Biparental mating designs for the detection of loci affecting these traits (quantitative trait loci [QTL]) impede their application, and the statistical methods used are ill-suited to the traits' polygenic nature. Genomic selection (GS) has been proposed to address these deficiencies. Genomic selection predicts the breeding values of lines in a population by analyzing their phenotypes and high-density marker scores. A key to the success of GS is that it incorporates all marker information in the prediction model, thereby avoiding biased marker effect estimates and capturing more of the variation due to small-effect QTL. In simulations, the correlation between true breeding value and the genomic estimated breeding value has reached levels of 0.85 even for polygenic low heritability traits. This level of accuracy is sufficient to consider selecting for agronomic performance using marker information alone. Such selection would substantially accelerate the breeding cycle, enhancing gains per unit time. It would dramatically change the role of phenotyping, which would then serve to update prediction models and no longer to select lines. While research to date shows the exceptional promise of GS, work remains to be done to validate it empirically and to incorporate it into breeding schemes.

Genomic Selection for Crop Improvement

We intuitively believe that the dramatic drop in the cost of DNA marker information we have experienced should have immediate benefits in accelerating the delivery of crop varieties with improved yield, quality and biotic and abiotic stress tolerance. But these traits are complex and affected by many genes, each with small effect. Traditional marker-assisted selection has been ineffective for such traits. The introduction of genomic selection (GS), however, has shifted that paradigm. Rather than seeking to identify individual loci significantly associated with a trait, GS uses all marker data as predictors of performance and consequently delivers more accurate predictions. Selection can be based on GS predictions, potentially leading to more rapid and lower cost gains from breeding. The objectives of this article are to review essential aspects of GS and summarize the important take-home messages from recent theoretical, simulation and empirical studies. We then look forward and consider research needs surrounding methodological questions and the implications of GS for long-term selection.

/pdf/genomic-selection-in-plant-breeding-from-theory-to-practice-4lgte3tnhg.pdf

Genomic selection in plant breeding: from theory to practice.

Genomic Selection in Plant Breeding: Methods, Models, and Perspectives

The use of genomic selection in breeding programs may increase the rate of genetic improvement, reduce the generation time, and provide higher accuracy of estimated breeding values (EBVs). A number of different methods have been developed for genomic prediction of breeding values, but many of them assume that all animals have been genotyped. In practice, not all animals are genotyped, and the methods have to be adapted to this situation. In this paper we provide an extension of a linear mixed model method for genomic prediction to the situation with non-genotyped animals. The model specifies that a breeding value is the sum of a genomic and a polygenic genetic random effect, where genomic genetic random effects are correlated with a genomic relationship matrix constructed from markers and the polygenic genetic random effects are correlated with the usual relationship matrix. The extension of the model to non-genotyped animals is made by using the pedigree to derive an extension of the genomic relationship matrix to non-genotyped animals. As a result, in the extended model the estimated breeding values are obtained by blending the information used to compute traditional EBVs and the information used to compute purely genomic EBVs. Parameters in the model are estimated using average information REML and estimated breeding values are best linear unbiased predictions (BLUPs). The method is illustrated using a simulated data set. The extension of the method to non-genotyped animals presented in this paper makes it possible to integrate all the genomic, pedigree and phenotype information into a one-step procedure for genomic prediction. Such a one-step procedure results in more accurate estimated breeding values and has the potential to become the standard tool for genomic prediction of breeding values in future practical evaluations in pig and cattle breeding.

/pdf/genomic-prediction-when-some-animals-are-not-genotyped-3n91sc80gp.pdf

Genomic prediction when some animals are not genotyped

Reproducing kernel Hilbert spaces regression procedures for prediction of total genetic value for quantitative traits, which make use of phenotypic and genomic data simultaneously, are discussed from a theoretical perspective. It is argued that a nonparametric treatment may be needed for capturing the multiple and complex interactions potentially arising in whole-genome models, i.e., those based on thousands of single-nucleotide polymorphism (SNP) markers. After a review of reproducing kernel Hilbert spaces regression, it is shown that the statistical specification admits a standard mixed-effects linear model representation, with smoothing parameters treated as variance components. Models for capturing different forms of interaction, e.g., chromosome-specific, are presented. Implementations can be carried out using software for likelihood-based or Bayesian inference.

https://www.genetics.org/content/genetics/178/4/2289.full.pdf

Reproducing Kernel Hilbert Spaces Regression Methods for Genomic Assisted Prediction of Quantitative Traits

The objective of this study was to estimate genetic parameters for growth, feed intake and greenhouse gasses emission traits in Italian Holstein, using data collected on young bulls undergoing performance test. The phenotypic information was recorded on 189 bulls, for which genomic information was obtained using SNP chips. Data were analysed using a linear mixed model, which included an additive genetic effect using a genomic relationship matrix. Results show high heritability estimates for growth traits, moderate to high estimates for emission and feed intake traits. Selection for reduced emissions appears possible and reducing methane will also reduce carbon dioxide emissions (genetic correlation of 0.96). Feed intake traits could serve as indicators, because the genetic correlations range between 0.58 and 0.85. Growth traits showed strong positive correlations with emission traits (0.66 to 0.81), selection indices built at reducing emissions should carefully consider these traits as well. 

36. Genetic parameters for growth, feed intake and greenhouse gasses emissions in Italian Holstein-Friesian bulls

The aim of this study is to propose a new approach for the collection of data from genetic traits and milk proteins and to manage this information in a unique virtual environment. Information about genetic traits and milk proteins can come from different sources and can be determined using different types of genetic tests. All input data are recorded in the database with a priority that is defined by the database update algorithm, taking into account the source of the data and the type of genetic test. In this way, the most reliable information is considered official herd book data, according to the established priorities. In conclusion, this new management of genetic traits and milk proteins aims to lay the foundations for a process of harmonization that supports international exchanges of data and that makes the interpretation of genetic traits clearer, in particular for breeders and for the livestock industry. 

804. An ontology approach for the collection and management of genetic traits and milk protein data

Age at first calving (AFC) is around a 2-years non-productive period (on average in Holstein cows) which plays a relevant role in the cost of rearing replacements in dairy herds. In the present study we aimed at evaluating the heritability of AFC and estimating breeding value of the trait in the Italian Holstein population. A linear animal model was used and heritability was 0.03 (Posterior Standard Deviation of 0.005). Further analyses will be performed to obtain a genomic evaluation of AFC and to evaluate the economic importance of this trait. 

702. Genetic aspects of age at first calving in Italian Holstein dairy cows

Gestation length (GL) affects both the cow and the newborn calf. Genetic components of GL are both direct and maternal, meaning that both the calf (direct effect) and the cow (maternal effect) genotypes contribute to determine it. The objective of this study was to define how much of the direct and maternal components is heritable in the Italian Holstein population and to estimate breeding values. A multiple-trait repeatability linear animal model was defined, considering first and later parities as different traits. The heritability of the direct effect was 0.44 (posterior standard deviation: 0.004) for first parities and 0.36 (0.003) for later. The heritability of maternal effect was 0.09 (0.001) for first parities and 0.06 (0.001) for later. In conclusion, the possibility of selecting for GL was confirmed. Further analyses will be performed in order to quantify the economic importance of GL and to identify its relationship with other traits. 

Johannes B. C. H. M. van Kaam

Papers

Reproducing Kernel Hilbert Spaces Regression Methods for Genomic Assisted Prediction of Quantitative Traits

36. Genetic parameters for growth, feed intake and greenhouse gasses emissions in Italian Holstein-Friesian bulls

804. An ontology approach for the collection and management of genetic traits and milk protein data

702. Genetic aspects of age at first calving in Italian Holstein dairy cows

113. Genetic evaluation of gestation length in Italian Holstein breed