The proportion of explained genetic variance across QTLs was found to be related to the number of detected QTLs for each trait and environment. In particular, traits with more detected QTLs explained a higher proportion of genetic variation. YLD, in particular, showed a tendency to have higher proportion of explained genetic variance for increasing numbers of detected QTLs, which should not be surprising given the findings of large effect loci for this trait (Mueller and Gai 2011). The observed increase in variance explained was partly due to genetic effects that were consistent across environments, which are not taken into account in the model. For example, a QTL with a moderate effect on YLD can be expressed only under a specific environmental condition (e.g. a long-day photoperiod) and a QTL with a large effect on ASI can be expressed in both short- and long-day photoperiods, but in different magnitudes.
Our main aim was to study to what extent the genotype × environment interaction (GEI) could be described by a model without any QTL effects. The model without any QTL effect (model 7) was able to well capture the observed genetic variance in most traits and environments. Only the traits YLD and ASI in the summer and winter season showed a high proportion of genetic variance that could not be fitted by the model without QTLs (Fig. 3). The observed GEI was captured by the QTLs (model 3) for most traits and environments. It is worth pointing out that our findings of the main QTL effects are not in contradiction with recent findings of Seo et al. (2014) who detected three loci of large effect (explaining more than 10% of genetic variance) for flowering time in two environments in the same population. However, those loci were detected as the main QTL effects without the inclusion of an environment-specific QTL effect. In our study, we were also able to detect additional loci of small effect (explaining less than 10% of genetic variance) in addition to the main QTL effects, although in different environments in most traits. This illustrates the power of having complete phenotyping data in multiple environments. However, the amount of genetic variance explained by the detected QTLs was quite low, in particular for MFLW and PH (14% and 17%, respectively) and YLD (15%).
The mixed model approach is the most widely used method to analyze MTME data in plant biology. However, if the fixed multiplicative model is not a suitable approach for a given trait, the mixed model approach comes with the burden of model complexity and the need to use a multi-trait experimental design with the corresponding costs of repeated measures. The aim of the current study was to make use of the data collected in this project and to provide a methodology that can be used in the analysis of any genotype by environment (G x E) situation. The mixed model approach is a powerful tool for the analysis of MTME data. In addition, it provides a framework to model the complexity of the interaction structure of GEI and thus it allows for a well defined analysis of GEI. We use a linear mixed model (LMM) to analyse the data. This LMM includes a model for fixed additive effects, including the main effect of genotypes, and the interaction effect of genotypes and environments. As the fixed effect of genotypes is only an average effect, it was necessary to model GEI for each genotype and environment, which involves the estimation of two parameters, namely the variance of the genotype and genotype by environment interaction (G x E). The estimation of these parameters was performed by maximum likelihood (ML) estimation. More specifically, the linear mixed model for the MTME data was given by: 827ec27edc