Fast empirical Bayesian LASSO for multiple quantitative trait locus mapping

Cai, Xiaodong; Huang, Anhui; Xu, Shizhong

doi:10.1186/1471-2105-12-211

Cited by 80 publications

(89 citation statements)

References 24 publications

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“…The necessity of tuning the parameters remains even when the parameter l is analytically integrated out; in fact, the reduced hierarchy leads to increased sensitivity to the hyperpriors (Cai et al 2011).…”

Section: Discussionmentioning

confidence: 99%

Back to Basics for Bayesian Model Building in Genomic Selection

Kärkkäinen¹,

Sillanpää

2012

Genetics

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Numerous Bayesian methods of phenotype prediction and genomic breeding value estimation based on multilocus association models have been proposed. Computationally the methods have been based either on Markov chain Monte Carlo or on faster maximum a posteriori estimation. The demand for more accurate and more efficient estimation has led to the rapid emergence of workable methods, unfortunately at the expense of well-defined principles for Bayesian model building. In this article we go back to the basics and build a Bayesian multilocus association model for quantitative and binary traits with carefully defined hierarchical parameterization of Student's t and Laplace priors. In this treatment we consider alternative model structures, using indicator variables and polygenic terms. We make the most of the conjugate analysis, enabled by the hierarchical formulation of the prior densities, by deriving the fully conditional posterior densities of the parameters and using the acquired known distributions in building fast generalized expectation-maximization estimation algorithms.T HE availability of the genome-wide sets of molecular markers has opened new avenues to animal and plant breeders for estimating breeding values on the basis of molecular markers with and without pedigree information (Bernardo and Yu 2007;Hayes et al. 2009;Lorenzano and Bernando 2009). The same holds true for phenotype prediction in human genetics (Lee et al. 2008;de los Campos et al. 2010). There are clearly two very different model approaches to estimate genomic breeding values, the first of which applies simultaneous estimation and variable selection to multilocus association models, where all markers are included as potential explanatory variables (e.g., Meuwissen et al. 2001;Xu 2003). Multilocus association models assign different, possibly zero, effects to every marker allele or genotype and determine the genetic value of an individual as a sum of the marker effects. The second approach is to utilize the marker information for estimating realized relationships between individuals and use the marker-estimated genomic relationship matrix instead of the pedigree-based numerator relationship matrix in a mixed-model context (e.g., VanRaden 2008;Powell et al. 2010).In recent literature there are numerous Bayesian methods of phenotype prediction and breeding value estimation based on multilocus association models, from Meuwissen et al. (2001) BayesA and BayesB onward (e.g., Xu 2003;Yi et al. 2003;Yi and Xu 2008;de los Campos et al. 2009;Verbyla et al. 2009Verbyla et al. , 2010Mutshinda and Sillanpää 2010;Sun et al. 2010;Habier et al. 2011;Knürr et al. 2011). The Bayesian methods have proved workable, efficient, and flexible, but the tremendous number of markers in the modern SNP data sets makes the computational methods traditionally connected to Bayesian estimation, e.g., Markov chain Monte Carlo (MCMC), rather cumbersome or even infeasible. For the same models fast alternative estimation procedures have been proposed, most commonly ...

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Section: Discussionmentioning

confidence: 99%

Back to Basics for Bayesian Model Building in Genomic Selection

Kärkkäinen¹,

Sillanpää

2012

Genetics

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“…Again, characterization of the genetic effects and molecular mechanisms of the contributing genes is essential for resolving these issues. Furthermore, advanced statistical methods that are able to include and assess the magnitudes of all of the effects in a single model (42,43) would help quantitative understanding of the relative contributions of the various genetic components to heterosis.…”

Section: Discussionmentioning

confidence: 99%

Genetic composition of yield heterosis in an elite rice hybrid

Zhou

Chen

Yao

et al. 2012

Proc. Natl. Acad. Sci. U.S.A.

218

213

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Heterosis refers to the superior performance of hybrids relative to the parents. Utilization of heterosis has contributed tremendously to the increased productivity in many crops for decades. Although there have been a range of studies on various aspects of heterosis, the key to understanding the biological mechanisms of heterotic performance in crop hybrids is the genetic basis, much of which is still uncharacterized. In this study, we dissected the genetic composition of yield and yield component traits using data of replicated field trials of an "immortalized F 2 " population derived from an elite rice hybrid. On the basis of an ultrahigh-density SNP bin map constructed with population sequencing, we calculated single-locus and epistatic genetic effects in the whole genome and identified components pertaining to heterosis of the hybrid. The results showed that the relative contributions of the genetic components varied with traits. Overdominance/pseudo-overdominance is the most important contributor to heterosis of yield, number of grains per panicle, and grain weight. Dominance × dominance interaction is important for heterosis of tillers per plant and grain weight and has roles in yield and grain number. Single-locus dominance has relatively small contributions in all of the traits. The results suggest that cumulative effects of these components may adequately explain the genetic basis of heterosis in the hybrid. epistasis | recombinant inbred intercross H eterosis, or hybrid vigor, refers to the superior performance of the hybrids relative to the parents (1). Utilization of heterosis has tremendously increased productivity of many crops globally. However, the understanding of the underpinning biological mechanism is still fragmentary after a century of debate and quest. Although there have been a range of studies on various aspects of heterosis (2-5), the key to understanding the biological mechanisms of heterotic performance in crop hybrids is the genetic basis (6), much of which is still uncharacterized (7).Three classic genetic hypotheses-dominance (8-11), overdominance (12-15), and epistasis (16, 17)-were proposed as explanations for the genetic basis of heterosis. Although there have been a large number of genetic analyses in plants with results favoring one hypothesis or another (18-31), genetic composition pertaining to heterotic performance of crop hybrids has not been fully characterized in an experimental population. There has been no assessment about the relative contributions of these genetic components to heterosis in a crop hybrid.The following conditions should be met for complete genetic characterization of heterosis relevant to crop production: (i) the genetic materials are based on elite hybrids that have shown timehonored superiority in crop production; (ii) the targets are key traits of agronomic performance; (iii) the experimental population allows identification of all of the genetic components concerned, including dominance (d/a ≤1, where d is the dominant effect and a is the additiv...

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“…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).…”

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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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Fast empirical Bayesian LASSO for multiple quantitative trait locus mapping

Cited by 80 publications

References 24 publications

Back to Basics for Bayesian Model Building in Genomic Selection

Back to Basics for Bayesian Model Building in Genomic Selection

Genetic composition of yield heterosis in an elite rice hybrid

Modeling Epistasis in Genomic Selection

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