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 behaviour or sensitivity analysis are also powerful tools for the diagnosis of biological phenomena.
- Emergence of organogenesis ’rhythms’ in plants [Mathieu et al., 2008],
- Sensitivity analysis to underline key processes and interactions in the NEMA model of Carbon and Nitrogen budget [Bertheloot et al., 2011], [Wu et al., ].
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. Dynamic programming techniques 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).