Genome-Wide Association Studies with a Genomic Relationship Matrix: A Case Study with Wheat and Arabidopsis

Abstract

Standard genome-wide association studies (GWAS) scan for relationships between each of p molecular markers and a continuously distributed target trait. Typically, a marker-based matrix of genomic similarities among individuals (G) is constructed, to account more properly for the covariance structure in the linear regression model used. We show that the generalized least-squares estimator of the regression of phenotype on one or on m markers is invariant with respect to whether or not the marker(s) tested is(are) used for building G, provided variance components are unaffected by exclusion of such marker(s) from G. The result is arrived at by using a matrix expression such that one can find many inverses of genomic relationship, or of phenotypic covariance matrices, stemming from removing markers tested as fixed, but carrying out a single inversion. When eigenvectors of the genomic relationship matrix are used as regressors with fixed regression coefficients, e.g., to account for population stratification, their removal from G does matter. Removal of eigenvectors from G can have a noticeable effect on estimates of genomic and residual variances, so caution is needed. Concepts were illustrated using genomic data on 599 wheat inbred lines, with grain yield as target trait, and on close to 200 Arabidopsis thaliana accessions.

Invited review: Genome-wide association analysis for quantitative traits in livestock – a selective review of statistical models and experimental designs

“…These authors recommended the exclusion of all SNPs that are located on the same chromosome as the SNP to be tested from the GRM. However, a recent article by Gianola et al (2016) on GWASs with a GRM suggests that double-fitting the SNP effects (as fixed and random effects) is a less severe problem than previously thought. Another way of modeling population structure is to fit principal components (Patterson et al, 2006), but, as Hayes (2013) pointed out, it is not exactly traceable which variation source they actually remove.…”

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“…However, outcomes from GWAS are not strictly comparable with those from shrinkage-based procedures. In single-marker least-squares the estimator is potentially biased because other genomic regions are ignored in the model; further, short and long range linkage disequilibria create statistical ambiguity (Gianola et al 2016). In WGR, on the other hand, regressions are akin to partial derivatives, i.e., the coefficient gives the net effect of the marker given that the other markers are fitted; typically, regressions become smaller as p is increased at a fixed n .…”

“…The wheat yield data set in the package BGLR (Pérez and de los Campos 2014) was employed to contrast MBL with GBLUP and Bayes C π . This wheat data set has been studied extensively, e.g., by Crossa et al (2010), Gianola et al (2011), Long et al (2011) and Gianola et al (2016). There are n = 599 wheat inbred lines, each genotyped with p = 1279 DArT (Diversity Array Technology) markers and each planted in four environments.…”

“…Standard GWAS aims to find connections between markers and genomic regions having an effect on a single trait (e.g., Manolio et al 2009, Visscher et al 2012; Gianola et al 2016; Schaid et al 2018) A search for pleiotropy, on the other hand, focuses on markers having multi-trait effects. The latter can be viewed as a search for vectors of effects with non-null coordinates that are distant from a T –dimensional 0 origin.…”

“…Two main paradigms have been employed for investigating statistical associations between molecular markers and complex traits: marker-by-marker genome-wide association studies (GWAS) and whole-genome regression approaches (WGR). GWAS is dominant in human genetics; Visscher et al (2017) present a perspective and Gianola et al (2016) formulate a statistically orientated critique. WGR was developed mostly in animal and plant breeding (e.g., Lande and Thompson 1990; Meuwissen et al 2001; Gianola et al 2003) primarily for predicting future performance, but it has received some attention in human genetics as well (e.g., Lee et al 2011; Yang et al 2010; de los Campos et al 2011; Makowsky et al 2011; López de Maturana et al 2014).…”