A compressed variance component mixed model framework for detecting small and linked QTL-by-environment interactions.

Detecting small and linked quantitative trait loci (QTLs) and QTL-by-environment interactions (QEIs) for complex traits is a difficult issue in immortalized F2 and F2:3 design, especially in the era of global climate change and environmental plasticity research. Here we proposed a compressed variance component mixed model. In this model, a parametric vector of QTL genotype and environment combination effects replaced QTL effects, environmental effects and their interaction effects, whereas the combination effect polygenic background replaced the QTL and QEI polygenic backgrounds. Thus, the number of variance components in the mixed model was greatly reduced. The model was incorporated into our genome-wide composite interval mapping (GCIM) to propose GCIM-QEI-random and GCIM-QEI-fixed, respectively, under random and fixed models of genetic effects. First, potentially associated QTLs and QEIs were selected from genome-wide scanning. Then, significant QTLs and QEIs were identified using empirical Bayes and likelihood ratio test. Finally, known and candidate genes around these significant loci were mined. The new methods were validated by a series of simulation studies and real data analyses. Compared with ICIM, GCIM-QEI-random had 29.77 ± 18.20% and 24.33 ± 10.15% higher average power, respectively, in 0.5-3.0% QTL and QEI detection, 43.44 ± 9.53% and 51.47 ± 15.70% higher average power, respectively, in linked QTL and QEI detection, and identified 30 more known genes for four rice yield traits, because GCIM-QEI-random identified more small genes/loci, being 2.69 ± 2.37% for additional genes. GCIM-QEI-random was slightly better than GCIM-QEI-fixed. In addition, the new methods may be extended into backcross and genome-wide association studies. This study provides effective methods for detecting small-effect and linked QTLs and QEIs.