Parametric and Nonparametric Statistical Methods for Genomic Selection of Traits with Additive and Epistatic Genetic Architectures

Howard, Réka; Carriquiry, Alicia L.; Beavis, William D.

doi:10.1534/g3.114.010298

Cited by 167 publications

(208 citation statements)

References 101 publications

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“…Confirming the results reported by Crossa et al (2014), Howard et al (2014) found that the parametric methods studied (e.g., Bayes A, Bayes B, Bayes C, Bayes LASSO, BRR, G-BLUP, Least Squares) performed slightly better in terms of predictive ability when only additive effects were present. In the presence of epistasis, nonparametric methods (e.g., RKHS, neural networks) exceeded the parametric methods.…”

Section: Discussionsupporting

confidence: 82%

“…Since Meuwissen et al (2001), many studies have compared the predictive performance of additive models in genomic selection and concluded that there is no great discrepancy among models and that when there is, it varies depending on the species and the genetic trait architecture Howard et al, 2014). However, the models tested only considered additive effects.…”

Section: Discussionmentioning

confidence: 99%

See 1 more Smart Citation

Genome-wide prediction of maize single-cross performance, considering non-additive genetic effects

Santos¹,

Pereira²,

Pinho³

et al. 2015

Genet. Mol. Res.

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ABSTRACT. The prediction of single-cross hybrids in maize is a promising technique for optimizing the use of financial resources in a breeding program. This study aimed to evaluate Genomic Best Linear Unbiased Predictors models for hybrid prediction and compare them with the Bayesian Ridge Regression, Bayes A, Bayesian LASSO, Bayes C, Bayes B, and Reproducing Kernel Hilbert Spaces Regression models, with inclusion or absence of non-additive effects under three heritability scenarios. Data from a maize germplasm bank belonging to USDA were used to determine the effects of molecular markers, which were considered to be parametric, to build 400 single-cross hybrids between two line groups via simulation. The following parameters were used to compare the models: predictive ability, estimation of variance components, heritability of genetic effects present in all situations, and the sum of squares of the predicted errors. The models responded positively when dominance effects were included in non-additive models, with all models tending to show an increase in the values of heritability parameters under all scenarios. Differences occur between models depending on the heritability range considered. Estimates of additive and dominant effects were better than estimates of epistatic effects. Estimates increased in accuracy for all models when non-additive effects for maize cob weight were considered.

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Section: Discussionsupporting

confidence: 82%

Section: Discussionmentioning

confidence: 99%

Genome-wide prediction of maize single-cross performance, considering non-additive genetic effects

Santos¹,

Pereira²,

Pinho³

et al. 2015

Genet. Mol. Res.

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“…populations with known pedigrees (Oakey et al 2007), but marker-based estimation of epistatic effects for natural populations appears possible only with more advanced statistical methodology, for example semiparametric mixed models and reproducing kernel Hilbert spaces (Gianola and Van Kaam 2008;Howard et al 2014). Another direction for future research is the estimation of heritability in the presence of additional random effects, which would increase the applicability to agricultural field trials (where the raw data are usually at plot rather than individual plant level).…”

Section: Discussionmentioning

confidence: 99%

Marker-Based Estimation of Heritability in Immortal Populations

et al. 2014

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Heritability is a central parameter in quantitative genetics, from both an evolutionary and a breeding perspective. For plant traits heritability is traditionally estimated by comparing within-and between-genotype variability. This approach estimates broad-sense heritability and does not account for different genetic relatedness. With the availability of high-density markers there is growing interest in marker-based estimates of narrow-sense heritability, using mixed models in which genetic relatedness is estimated from genetic markers. Such estimates have received much attention in human genetics but are rarely reported for plant traits. A major obstacle is that current methodology and software assume a single phenotypic value per genotype, hence requiring genotypic means. An alternative that we propose here is to use mixed models at the individual plant or plot level. Using statistical arguments, simulations, and real data we investigate the feasibility of both approaches and how these affect genomic prediction with the best linear unbiased predictor and genome-wide association studies. Heritability estimates obtained from genotypic means had very large standard errors and were sometimes biologically unrealistic. Mixed models at the individual plant or plot level produced more realistic estimates, and for simulated traits standard errors were up to 13 times smaller. Genomic prediction was also improved by using these mixed models, with up to a 49% increase in accuracy. For genome-wide association studies on simulated traits, the use of individual plant data gave almost no increase in power. The new methodology is applicable to any complex trait where multiple replicates of individual genotypes can be scored. This includes important agronomic crops, as well as bacteria and fungi.KEYWORDS marker-based estimation of heritability; GWAS; genomic prediction; Arabidopsis thaliana; one-vs. two-stage approaches N ARROW-SENSE heritability is an important parameter in quantitative genetics, determining the response to selection and representing the proportion of phenotypic variance that is due to additive genetic effects (Jacquard 1983;Ritland 1996;Visscher et al. 2006Visscher et al. , 2008Holland et al. 2010;Sillanpaa 2011). This definition of heritability goes back to Fisher (1918) and Wright (1920) almost a century ago. In plant species for which replicates of the same genotype are available (inbred lines, doubled haploids, clones), a different form of heritability, broadsense heritability, is traditionally estimated by the intraclass correlation coefficient for genotypic effects, using estimates for within-and between-genotype variance. Broad-sense heritability is also referred to as repeatability and gives the proportion of phenotypic variance explained by heritable (additive) and nonheritable (dominance, epistasis) genetic variance.With the arrival of high-density genotyping there is growing interest in marker-based estimation of narrow-sense heritability (WTCCC 2007;Yang et al. 2010Yang et al. , 2011Vatti...

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“…The use of semiparametric reproducing kernel Hilbert space (RKHS) regression models has been promoted as an alternative powerful option to capture epistasis in genomic selection (Gianola et al 2006;Gianola and Van Kaam 2008). The RKHS model outperformed linear models that focused exclusively on marker main effects in a number of studies based on simulated data (e.g., Gianola et al 2006;Howard et al 2014) and empirical data (e.g., Perez-Rodriguez et al 2012;Crossa et al 2013). Choosing an appropriate kernel, which can be interpreted as a relationship matrix among genotypes (i.e., individuals), is a central element of model specification in RKHS regression .…”

mentioning

confidence: 99%

“…The RKHS model outperformed linear models that focused exclusively on marker main effects in a number of studies based on simulated data (e.g., Gianola et al 2006;Howard et al 2014) and empirical data (e.g., Perez-Rodriguez et al 2012;Crossa et al 2013). Choosing an appropriate kernel, which can be interpreted as a relationship matrix among genotypes (i.e., individuals), is a central element of model specification in RKHS regression .…”

mentioning

confidence: 99%

Modeling Epistasis in Genomic Selection

Jiang¹,

2015

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Modeling epistasis in genomic selection is impeded by a high computational load. The extended genomic best linear unbiased prediction (EG-BLUP) with an epistatic relationship matrix and the reproducing kernel Hilbert space regression (RKHS) are two attractive approaches that reduce the computational load. In this study, we proved the equivalence of EG-BLUP and genomic selection approaches, explicitly modeling epistatic effects. Moreover, we have shown why the RKHS model based on a Gaussian kernel captures epistatic effects among markers. Using experimental data sets in wheat and maize, we compared different genomic selection approaches and concluded that prediction accuracy can be improved by modeling epistasis for selfing species but may not for outcrossing species.KEYWORDS epistasis; genomic selection; genomic best linear unbiased prediction (G-BLUP); extended G-BLUP (EG-BLUP); reproducing kernel Hilbert space regression (RKHS); GenPred; shared data resource E PISTASIS has long been recognized as an important component in dissecting genetic pathways and understanding the evolution of complex genetic systems (Phillips 2008). It is hence a biologically influential component contributing to the genetic architecture of quantitative traits (Mackay 2014). The influence of epistasis on genome-wide QTL mapping ranges from limited (e.g., Buckler et al. 2009;Tian et al. 2011) to high (e.g., Carlborg et al. 2006;Würschum et al. 2011;Huang et al. 2014). These discrepancies can be explained by the complexities of the examined traits, which are controlled by many loci exhibiting small effects entailing a low QTL detection power. In addition, the estimation of QTL main and interaction effects is very likely biased (Beavis 1994), which makes it challenging to reliably elucidate the role of epistasis through genome-wide QTL mapping studies.Genomic selection has been suggested as an alternative to tackle complex traits that are regulated by many genes, each exhibiting a small effect (Meuwissen et al. 2001). Genomic selection approaches based on additive and dominance effects have been successfully applied to predict complex traits in human (Yang et al. 2010), animal (Hayes et al. 2009, and plant populations (Jannink et al. 2010;Zhao et al. 2015). Moreover, several genomic selection approaches have been developed to model both main and epistatic effects (Xu 2007;Cai et al. 2011;Wittenburg et al. 2011;Wang et al. 2012). While in some studies prediction accuracies increased (Hu et al. 2011), in others modeling epistasis adversely affected prediction accuracies (Lorenzana and Bernardo 2009).Despite these first attempts, epistasis is often ignored in genomic selection approaches using parametric models mainly because of the high associated computational load, especially if a large number of markers are available. An attractive solution to reduce the computational load is to extend genomic best linear unbiased prediction (G-BLUP) models (VanRaden 2008) by adding marker-based epistatic relationship matrices [extended genomic...

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Parametric and Nonparametric Statistical Methods for Genomic Selection of Traits with Additive and Epistatic Genetic Architectures

Cited by 167 publications

References 101 publications

Genome-wide prediction of maize single-cross performance, considering non-additive genetic effects

Genome-wide prediction of maize single-cross performance, considering non-additive genetic effects

Marker-Based Estimation of Heritability in Immortal Populations

Modeling Epistasis in Genomic Selection

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