Inferences from Genomic Models in Stratified Populations

Abstract

Unaccounted population stratification can lead to spurious associations in genome-wide association studies (GWAS) and in this context several methods have been proposed to deal with this problem. An alternative line of research uses whole-genome random regression (WGRR) models that fit all markers simultaneously. Important objectives in WGRR studies are to estimate the proportion of variance accounted for by the markers, the effect of individual markers, prediction of genetic values for complex traits, and prediction of genetic risk of diseases. Proposals to account for stratification in this context are unsatisfactory. Here we address this problem and describe a reparameterization of a WGRR model, based on an eigenvalue decomposition, for simultaneous inference of parameters and unobserved population structure. This allows estimation of genomic parameters with and without inclusion of markerderived eigenvectors that account for stratification. The method is illustrated with grain yield in wheat typed for 1279 genetic markers, and with height, HDL cholesterol and systolic blood pressure from the British 1958 cohort study typed for 1 million SNP genotypes. Both sets of data show signs of population structure but with different consequences on inferences. The method is compared to an advocated approach consisting of including eigenvectors as fixed-effect covariates in a WGRR model. We show that this approach, used in the context of WGRR models, is ill posed and illustrate the advantages of the proposed model. In summary, our method permits a unified approach to the study of population structure and inference of parameters, is computationally efficient, and is easy to implement.

Genome-enabled methods for predicting litter size in pigs: a comparison

“…Daetwyler et al (2012) stated that a large part of prediction accuracy was because of population structure, with LD between markers and QTL playing a smaller role. Methods for accounting for population structure in prediction were investigated by Janss et al (2012).…”

Meta‐analysis of genome‐wide association from genomic prediction models

“…In particular, we followed the approach proposed by Lans et al . (2012), which consists of including eigenvectors of the G matrix as covariates. After studying the variance explained by the principal components of G (Fig.…”

“…(2012), who suggested that, when eigenvectors are included in the GBLUP model, a ‘double counting’ is observed given that the effect of the eigenvector is already included in the genomic relationship matrix used to estimate the variance components and subsequent SNP effects (Lans et al . 2012). Consequently, we dropped the eigenvectors of G and kept the model represented by equation (1) throughout the analysis.…”

“…However, it has been reported that including the whole G matrix through a pertinent random animal effect may account for all structure, making it unnecessary to fit individual components (Lans et al . 2012). To confirm this, we compared SNP effects estimated from GBLUP models including and ignoring the principal components as fixed effects but keeping the background additive effect with the variance–covariance matrix proportional to G , following Lans et al .…”

“…To confirm this, we compared SNP effects estimated from GBLUP models including and ignoring the principal components as fixed effects but keeping the background additive effect with the variance–covariance matrix proportional to G , following Lans et al . (2012). To determine the number of principal components, we factorized G using the eigenvalue decomposition given by G  =  UDU ’, where U ( n  ×  n , with n the number of genotyped animals) is a matrix of eigenvectors of G and D is a diagonal matrix with elements equal to eigenvalues.…”