Methodological implementation of mixed linear models in multi-locus genome-wide association studies

Abstract

The mixed linear model has been widely used in genome-wide association studies (GWAS), but its application to multi-locus GWAS analysis has not been explored and assessed. Here, we implemented a fast multi-locus random-SNP-effect EMMA (FASTmrEMMA) model for GWAS. The model is built on random single nucleotide polymorphism (SNP) effects and a new algorithm. This algorithm whitens the covariance matrix of the polygenic matrix K and environmental noise, and specifies the number of nonzero eigenvalues as one. The model first chooses all putative quantitative trait nucleotides (QTNs) with ≤ 0.005 P-values and then includes them in a multi-locus model for true QTN detection. Owing to the multi-locus feature, the Bonferroni correction is replaced by a less stringent selection criterion. Results from analyses of both simulated and real data showed that FASTmrEMMA is more powerful in QTN detection and model fit, has less bias in QTN effect estimation and requires a less running time than existing single- and multi-locus methods, such as empirical Bayes, settlement of mixed linear model under progressively exclusive relationship (SUPER), efficient mixed model association (EMMA), compressed MLM (CMLM) and enriched CMLM (ECMLM). FASTmrEMMA provides an alternative for multi-locus GWAS.

Metabolic GWAS‐based dissection of genetic bases underlying the diversity of plant metabolism

“…However, for complex traits determined by several large‐effect loci, this approach may not be appropriate, especially in the presence of population structure. The application of multi‐locus mixed models could lead to the identification of new causative loci with promising performance (Segura et al ., ; Wen et al ., ). Despite the contribution of single nucleotide polymorphism (SNP)‐based GWAS to the dissection of genetic bases underlying complex traits in various species, SNP‐based GWAS incurs a severe penalty for multi‐testing due to the overlooked interactions between SNPs within a gene and weak signals aggregating within related SNP sets.…”

Genomic Prediction Accuracy of Seven Breeding Selection Traits Improved by QTL Identification in Flax

“…Thus, alternative multi-locus methods have been proposed [14], including the multi-locus random-SNP-effect mixed linear model (mrMLM) [9,15], the FAST multi-locus random-SNP-effect EMMA (FASTmrEMMA) [16], the polygene-background-control-based least angle regression plus empirical Bayes (pLARmEB) [17], the iterative modified-sure independence screening EM-Bayesian LASSO (ISIS EM-BLASSO) [18], and the integration of the Kruskal-Wallis test with empirical Bayes under polygenic background control (pKWmEB). These methods adapt statistical models that simultaneously test multiple markers and, doing so, substantially increase the statistical power while simultaneously reducing Type 1 errors and running time [9,[15][16][17][18][19]. These methods also usually adapt LOD scores (usually LOD ≥ 3), rather than the stringent Bonferroni correction (0.05/number of SNPs) [19], thus empowering the detection of more large and small effect QTNs [10].…”

A fast mrMLM algorithm for multi-locus genome-wide association studies

“…Finally, some matrix transformations and identities are adopted. One such matrix transformation is spectral decomposition, which lets target functions and derivatives be expressed by simple forms, such as in Kang et al [6] and Wen et al [18]. The first stage of the new method (FASTmrMLM) considers a QTN effect as random.…”

“…Previous studies have reported higher power of QTN detection in multi-locus models as compared to the singlemarker GWAS analysis [17,16]. Bonferroni multiple test correction in the single-marker analysis is replaced by a less stringent selection criterion in multi-locus GWAS analysis [16,18]. Therefore significant loci for complex traits are not missed out.…”

“…Initially, many statistical approaches were used to estimate all the SNP effects in multi-locus model, such as Bayesian LASSO [19], penalized logistic regression [20,21], adaptive mixed LASSO [22], elastic net [23], empirical Bayes [24], and empirical Bayes LASSO [25]. If the number of SNPs is large, [16], FASTmrEMMA [18] and ISIS EM-BLASSO [29]. In the first stage, single-locus methods are used to scan all the markers on the genome.…”