Academic journal article Genetics

Needles: Toward Large-Scale Genomic Prediction with Marker-by-Environment Interaction

Academic journal article Genetics

Needles: Toward Large-Scale Genomic Prediction with Marker-by-Environment Interaction

Article excerpt

(ProQuest: ... denotes formulae omitted.)

GENOMIC prediction methods most often rely on a linear mixed-model framework that models at the same time fixed effects and random genetic effects (Meuwissen et al. 2001). These genetic effects are modeled by assigning a small effect to markers, which are used to genotype the individuals. Introducing a large number of genome-wide markers in the analysis has already proven to be beneficial instead of using only pedigree information or a few markers that are known to have a significant effect (so-called marker-assisted selection) in animal breeding (VanRaden et al. 2009; Aguilar et al. 2010) as well as in plant breeding (Bernardo and Yu 2007; Crossa et al. 2010; Burgueño et al. 2012). From an animal breeding perspective, environmental effects are mostly not modeled and regarded only as a nuisance because environmental effects are either negligible (König et al. 2005) or can be under the control of the breeders by creating selection environments that are very close to commercial environments (Mulder and Bijma 2005). Using this assumption, a distributed average information restricted maximum likelihood (AI-REML) ridge regression best linear unbiased prediction (DAIRRy-BLUP) framework (De Coninck et al. 2014) was developed to employ the computing power of supercomputing clusters for analyzing data sets with a large number of genotyped individuals based solely on dense linear algebra because genetic marker information is mainly dense.

However, when cultivating plants, the environment and some specific environmental conditions (e.g., soil moisture, solar radiation, and air humidity) can have a much stronger impact on the phenotypic trait, and the effects of markers may vary in different environments. It is thus recommended to also include genotype-by-environment interaction (G 3 E) effects for genomic prediction in plant breeding (Denis et al. 1997; Cooper et al. 2005). Different models have been presented to account for these interaction effects in genomic prediction, and most of these models apply a two-stage approach, where in the first stage an adjusted genotype mean is computed across environments, which is then used in the second stage to predict breeding values for untested plants based on their marker genotypes (Schulz-Streeck et al. 2013b). Actually, this two-stage approach commonly includes a preliminary step in which the intraenvironmental effects, such as block, row, and column effects, are taken into account when computing the genotypic mean per environment. These intraenvironmental effects can be modeled together with a location effect and the G 3 E effects to immediately obtain the genotypic means across the environments in the first step of a two-step approach (Schulz-Streeck et al. 2013b). However, in recent single-stage analyses, where the computation of genotypic means across environments is avoided and the interaction effects are explicitly modeled, the phenotypic records are mostly already corrected for spatial variations inside the environment (Burgueño et al. 2012; Heslot et al. 2014; Lopez-Cruz et al. 2015). Nonetheless, the single-stage approach may include the modeling of these intraenvironmental effects to enable the direct analysis of the raw phenotypic data (Schulz-Streeck et al. 2013a). The genetic effects can be assumed to follow a wide range of distributions. The most widely used choice is the assumption that genetic effects come from a normal distribution, and while other assumptions may lead to better predictions of the genomic breeding values, the normality assumption is a viable alternative because of its simplicity and computational efficiency (Crossa et al. 2010; Heslot et al. 2012). This assumption leads to the so-called best linear unbiased predictors (BLUP) for the random genetic effects (Henderson 1973).

When genetic marker information is applied for calculating correlations between individuals, this is referred to as GBLUP, where the G stands for use of a genomic relationship matrix instead of a relationship matrix based on pedigree data (Habier et al. …

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