Fast and flexible linear mixed models for genome-wide genetics

Runcie, Daniel E.; Crawford, Lorin

doi:10.1101/373902

Cited by 14 publications

(15 citation statements)

References 64 publications

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“…Many previous studies in genomic prediction, variance component analyses or GWAS took the Hadamard product matrix as the approximation of EGRM and focused only on low-degree epistasis (Muñoz et al 2014;Vitezica et al 2018;Runcie and Crawford 2019). Although when the degree of epistasis is low and the number of markers is large, the quality of approximation is expected to be good for any coding system according to a criterion suggested in Martini et al (2020), we still do not know whether the Hadamard product matrix approaches the genuine EGRM in a strict mathematical sense (Martini et al 2020).…”

Section: Outlook For Further Applicationsmentioning

confidence: 99%

“…The EGRM has been extensively applied in genome-wide prediction exploiting epistatic effects (Xu et al 2014;Jiang and Reif 2015;Zhao et al 2015). In the area of GWAS, EGRM has also been popularly exploited as a control of epistatic background effects in addition to additive background effects (Xu 2013;Jiang et al 2017;Runcie and Crawford 2019;Santantonio et al 2019). Recently, a fast GWAS algorithm for an exhaustive scan of digenic additive-by-additive interaction effects was developed by constructing the test statistic of epistatic effects from the EGRM (Ning et al 2018).…”

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confidence: 99%

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Efficient Algorithms for Calculating Epistatic Genomic Relationship Matrices

Jiang

Reif

2020

Genetics

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The genomic relationship matrix plays a key role in the analysis of genetic diversity, genomic prediction and genome-wide association studies. The epistatic genomic relationship matrix is a natural generalization of the classic genomic relationship matrix in the sense that it implicitly models the epistatic effects among all markers. Calculating the exact form of the epistatic relationship matrix requires high computational load and is hence not feasible when the number of markers is large or when high-degree of epistasis is in consideration. Currently, many studies use the Hadamard product of the classic genomic relationship matrix as an approximation. However, the quality of the approximation is difficult to investigate in the strict mathematical sense. In this study, we derived iterative formulas for the precise form of the epistatic genomic relationship matrix for arbitrary degree of epistasis including both additive and dominance interactions. The key to our theoretical results is the observation of an interesting link between the elements in the genomic relationship matrix and symmetric polynomials, which motivated the application of the corresponding mathematical theory. Based on the iterative formulas, efficient recursive algorithms were implemented. Compared with the approximation by the Hadamard product, our algorithms provided a complete solution to the problem of calculating the exact epistatic genomic relationship matrix. As an application, we showed that our new algorithms easily relieved the computational burden in a previous study on the approximation behavior of two limit models.

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Section: Outlook For Further Applicationsmentioning

confidence: 99%

mentioning

confidence: 99%

Efficient Algorithms for Calculating Epistatic Genomic Relationship Matrices

Jiang

Reif

2020

Genetics

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“…We used the posterior means of the line GxE effects as phenotypes for QTL mapping (posterior means in File S2). QTL mapping was run using the GridLMM package (Runcie and Crawford 2019). GridLMM provides the flexibility of joint QTL mapping in multi-parent populations using linear mixed models, and can also prevent proximal contamination of markers, which improves QTL mapping power (Lippert et al 2011).…”

Section: Statistical Analyses: Qtl Mappingmentioning

confidence: 99%

Multiple Loci Control Variation in Plasticity to Foliar Shade Throughout Development in Arabidopsis thaliana

Palmer

Brock

et al. 2020

G3 Genes|Genomes|Genetics

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The shade avoidance response is a set of developmental changes exhibited by plants to avoid shading by competitors, and is an important model of adaptive plant plasticity. While the mechanisms of sensing shading by other plants are well-known and appear conserved across plants, less is known about the developmental mechanisms that result in the diverse array of morphological and phenological responses to shading. This is particularly true for traits that appear later in plant development. Here we use a nested association mapping (NAM) population of Arabidopsis thaliana to decipher the genetic architecture of the shade avoidance response in late-vegetative and reproductive plants. We focused on four traits: bolting time, rosette size, inflorescence growth rate, and inflorescence size, found plasticity in each trait in response to shade, and detected 17 total QTL; at least one of which is a novel locus not previously identified for shade responses in Arabidopsis. Using path analysis, we dissected each colocalizing QTL into direct effects on each trait and indirect effects transmitted through direct effects on earlier developmental traits. Doing this separately for each of the seven NAM populations in each environment, we discovered considerable heterogeneity among the QTL effects across populations, suggesting allelic series at multiple QTL or interactions between QTL and the genetic background or the environment. Our results provide insight into the development and variation in shade avoidance responses in Arabidopsis, and emphasize the value of directly modeling the relationships among traits when studying the genetics of complex developmental syndromes.

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“…Approaches for estimating variance components typically search for parameter values that maximize the likelihood or the restricted maximum likelihood (REML) 11 . Despite a number of algorithmic improvements 2 , 4 , 12 – 16 , computing REML estimates of the variance components on data sets such as the UK Biobank 17 (≈500,000 individuals genotyped at nearly one million SNPs) remains challenging. The reason is that methods for computing these estimators typically perform repeated computations on the input genotypes.…”

Section: Introductionmentioning

confidence: 99%

Efficient variance components analysis across millions of genomes

Pazokitoroudi¹,

Wu²,

Burch

et al. 2020

Nat Commun

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While variance components analysis has emerged as a powerful tool in complex trait genetics, existing methods for fitting variance components do not scale well to large-scale datasets of genetic variation. Here, we present a method for variance components analysis that is accurate and efficient: capable of estimating one hundred variance components on a million individuals genotyped at a million SNPs in a few hours. We illustrate the utility of our method in estimating and partitioning variation in a trait explained by genotyped SNPs (SNPheritability). Analyzing 22 traits with genotypes from 300,000 individuals across about 8 million common and low frequency SNPs, we observe that per-allele squared effect size increases with decreasing minor allele frequency (MAF) and linkage disequilibrium (LD) consistent with the action of negative selection. Partitioning heritability across 28 functional annotations, we observe enrichment of heritability in FANTOM5 enhancers in asthma, eczema, thyroid and autoimmune disorders.

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Fast and flexible linear mixed models for genome-wide genetics

Cited by 14 publications

References 64 publications

Efficient Algorithms for Calculating Epistatic Genomic Relationship Matrices

Efficient Algorithms for Calculating Epistatic Genomic Relationship Matrices

Multiple Loci Control Variation in Plasticity to Foliar Shade Throughout Development in Arabidopsis thaliana

Efficient variance components analysis across millions of genomes

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