The study of QTL × environment interaction (QEI) is important for understanding genotype × environment interaction (GEI) in many quantitative traits. For modeling GEI and QEI, factorial regression (FR) models form a powerful class of models. In FR models, covariables (contrasts) defined on the levels of the genotypic and/or environmental factor(s) are used to describe main effects and interactions. In FR models for QTL expression, considerable numbers of genotypic covariables can occur as for each putative QTL an additional covariable needs to be introduced. For large numbers of genotypic and/or environmental covariables, least square estimation breaks down and partial least squares (PLS) estimation procedures become an attractive alternative. In this paper we develop methodology for analyzing QEI by FR for estimating effects and locations of QTLs and QEI and interpreting QEI in terms of environmental variables. A randomization test for the main effects of QTLs and QEI is presented. A population of F2 derived F3 families was evaluated in eight environments differing in drought stress and soil nitrogen content and the traits yield and anthesis silking interval (ASI) were measured. For grain yield, chromosomes 1 and 10 showed significant QEI, whereas in chromosomes 3 and 8 only main effect QTLs were observed. For ASI, QTL main effects were observed on chromosomes 1, 2, 6, 8, and 10, whereas QEI was observed only on chromosome 8. The assessment of the QEI at chromosome 1 for grain yield showed that the QTL main effect explained 35.8% of the QTL + QEI variability, while QEI explained 64.2%. Minimum temperature during flowering time explained 77.6% of the QEI. The QEI analysis at chromosome 10 showed that the QTL main effect explained 59.8% of the QTL + QEI variability, while QEI explained 40.2%. Maximum temperature during flowering time explained 23.8% of the QEI. Results of this study show the possibilities of using FR for mapping QTL and for dissecting QEI in terms of environmental variables. PLS regression is efficient in accounting for background noise produced by other QTLs.
Theoretical and Applied Genetics (2006) 112 (6) 1009-1023 [doi: 10.1007/s00122-005-0204-z]