Sensitivity Analysis for Plant Models with Correlated Parameters: Application to the Characterization of Sun flower Genotypes

The understanding of gene-environment interaction is a crucial issue in plant breeding. For this objective, mechanistic models of plant growth can help disentangle the genotypic and environmental effects. Each genotype is characterized by a specific vector of model parameters and ideally, these parameters are stable for a certain range of environments. Each parameter can be seen as resulting from the influences of several genes (epistasis), while the same gene can influence several parameters (pleiotropy). As a consequence, in a family of genotypes (for a same species), there may be strong correlations between parameters. Moreover, in order to be able to use plant models to characterize and differentiate genotypes, the parametric estimation methods should be precise enough so that the estimation uncertainty remains small and so that statistically significant differences can be detected between the parameters of different genotypes. For this purpose, sensitivity analysis was shown to be a very helpful method in the estimation process, specifically for screening non influential parameters that can be fixed to some nominal values (thus common to all genotypes, the model parameter is thus considered as non-genotypic parameter). Therefore, when performing sensitivity analysis of plant growth models with the specific objective of characterization of genotypes, we need to use a method able to take into account correlated inputs. For example, the classical Sobol method can not be applied straightforwardly. The objective of this paper is thus to introduce a method adapted to the sensitivity analysis for correlated inputs and to apply it to a plant model. The SUNFLO model of sunflower growth is used for this purpose. The model parameters for a family of 20 genotypes have been estimated or measured with very heavy experimental work and this set of parameter vectors is used to compute the statistical distribution in the parameter space.