A dynamic model with QTL covariables for predicting flowering time of common bean (Phaseolus vulgaris) genotypes

Multi-genotype multi-environment trials, associated with characterization of the environment, marker information for the genotypes and measurements of the phenotypic traits of interest can potentially provide the basis for models to predict the behavior of untested genotypes in new environments. However, there is as yet no clear indication of the best form of such models, nor how to parameterize them. The purpose of this study was to propose and test an approach to crop-QTL modeling, applied to prediction of time to flowering in common bean (Phaseolus vulgaris), which avoids the pitfall of estimating separately the parameters for each genotype. The environmental model is a dynamic model with development rates that depend on daily temperature and day length. Three of the model parameters are expressed as linear functions of the QTLs for time to flowering, resulting in a model that combines environmental variables and QTLs. An innovative approach to parameter estimation is proposed, based on least squares, which makes it quite easy to estimate all the parameters of this model simultaneously, using all the data. The parameterized model explains most of the genotypic and environmental variability in the data, and 47% of the genotype by environment (GxE) interaction. Cross validation shows that the model extrapolates well to new genotypes in the same environments as those of the data, and also to new environments if they are similar in terms of temperature and photoperiod to those in the training data.