Variable Reduction Stage

A number of studies have illustrated that most quantitative traits are controlled by a small portion of genes, including a few genes with large effects and polygenes with minor effects (Zhang et al., 2017; Wen et al., 2019). It is critical to dissect all associated loci from large-scale genetic markers. Herein, we conduct a variable reduction stage, whose purpose is dimension reduction. At this stage, the FastRR algorithm detects a subset of putative variables associated with the phenotype, and thus avoids the intractable computational problems of high-dimensional datasets analysis.

We calculate the marginal correlation coefficients between Z_c (variables after polygenic background correction) and y_c (phenotype after polygenic background correction) under model (5), R function cor.test returns the p-value of the correlation test. The critical value for significance was set at p-value < 0.01 (Tamba et al., 2017). For the threshold of 0.01, even the slight correlations between predictors and the response will be captured (Tamba et al., 2017), and the unassociated loci will be removed. All the most potential QTNs are selected to construct the reduced multi-locus model for the next stage. Essentially, this marginal correlation step is similar to the single marker scanning, which combined with the polygenic background without considering variance components σγ2.