Section: Scientific Foundations

Methods for the Applications (in Genetics, Agronomy, Forestry and the Environmental Sciences)

Theoretical biology: study of specific plant systems or phenomena

The study of systems as complex as plants requires the development of powerful methodologies of analysis. Models help biologists to explore some specific phenomena. The most obvious way is through simulation. However, mathematical analysis of model behavior or sensitivity analysis are also powerful tools for the diagnosis of biological phenomena. A good example was given by [Mathieu et al., 2008], proving first theoretically the emergence of organogenesis 'rhythms' in plants, before observing them. An ongoing project concerns the model 'NEMA' [Bertheloot et al., 2011], developed jointly with INRA-Grignon (J. Bertheloot, B. Andrieu). The model describes at organ level budgets of both Carbon and Nitrogen in plants. It involves 5 interacting biological functions, with each around 20 parameters. Specific techniques of global sensitivity analysis are developed (PhD of Qiongli Wu) to explore such type of models, with the objective of underlining key biological processes and interactions.

Risk analysis

Taking into account the uncertainty in model prediction (uncertainty of parameters, climatic uncertainty), the objective is to quantify for farmers the risk associated to yield. The use of data assimilation (of satellite or aerial images for example) is a crucial point to decrease the level of uncertainty. The important application of such study concerns crop-yield insurance.

Optimal control of crop cultivation

How to optimize irrigation or fertilization strategies ? Based on models of plant-soil interactions, we are facing optimal control problems. Our objective is to develop dynamic programming techniques, which seem more adapted to the non-convex situations we are facing. Several questions are of interest: constraints linked to environmental regulations, stochastic control due to climatic uncertainty, control of time-delay systems (due to plant senescence), curse of dimensionality ...

Optimization of parameters for genetic improvement

The first step concerns the link of model parameters to genes (or Quantitative Trait Loci) via quantitative genetics model. Then, we can explore through selection process the attainable space of model parameters, in which we can find optima regarding specific criteria (for specific types of climate for example). A new PhD should start soon in collaboration with J. Lecoeur (Syngenta Seeds).