Multilocus genome-wide association studies (GWAS) have become the state-of-the-art procedure to identify quantitative trait nucleotides (QTNs) associated with complex traits. However, implementation of multilocus model in GWAS is still difficult. In this study, we integrated least angle regression with empirical Bayes to perform multilocus GWAS under polygenic background control. We used an algorithm of model transformation that whitened the covariance matrix of the polygenic matrix K and environmental noise. Markers on one chromosome were included simultaneously in a multilocus model and least angle regression was used to select the most potentially associated single-nucleotide polymorphisms (SNPs), whereas the markers on the other chromosomes were used to calculate kinship matrix as polygenic background control. The selected SNPs in multilocus model were further detected for their association with the trait by empirical Bayes and likelihood ratio test. We herein refer to this method as the pLARmEB (polygenic-background-control-based least angle regression plus empirical Bayes). Results from simulation studies showed that pLARmEB was more powerful in QTN detection and more accurate in QTN effect estimation, had less false positive rate and required less computing time than Bayesian hierarchical generalized linear model, efficient mixed model association (EMMA) and least angle regression plus empirical Bayes. pLARmEB, multilocus random-SNP-effect mixed linear model and fast multilocus random-SNP-effect EMMA methods had almost equal power of QTN detection in simulation experiments. However, only pLARmEB identified 48 previously reported genes for 7 flowering time-related traits in Arabidopsis thaliana.

Epistasis has been frequently observed in all types of mapping populations. However, relatively little is known about the effect of epistatic distorted markers on linkage group construction. In this study, a new approach was proposed to correct the recombination fraction between epistatic distorted markers in backcross and F 2 populations under the framework of fitness and liability models. The information for three or four markers flanking with an epistatic segregation distortion locus was used to estimate the recombination fraction by the maximum likelihood method, implemented via an expectation-maximisation algorithm. A set of Monte Carlo simulation experiments along with a real data analysis in rice was performed to validate the new method. The results showed that the estimates from the new method are unbiased. In addition, five statistical properties for the new method in a backcross were summarised and confirmed by theoretical, simulated and real data analyses.