Team Digiplante

Members
Overall Objectives
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Bibliography

## Section: New Results

### Applied mathematics

#### Optimization and Control

A new joint Phd (Liama- ECP) Qi Rui has undertaken a study on miscellaneous issues about plant growth optimization for applications in Agriculture. The topics concern both the strategy to choose to optimize the source-sink relationship versus different kinds of yields and the decision support systems for optimizing farming methods. GreenScilab mainly developed in Liama by Kang MZ, is used for this purpose.

Corresponding to the kind of yield: fruits (cotton plant, sunflower, etc.), wood (logs, boards in trees), leaves (lettuce, tea plant), roots (beet-root), optimizing the sources and sinks relationships during the plant growth requires quite different strategies, that have a direct link with Genetics. For the farming systems concerning the optimization of densities, irrigation, fertilizers, new models have to be tested on virtual plantations. We think that simulating growth of virtual plantations under different environmental conditions is a new tool quite interesting for Agriculture. Heuristic methods are tested for this purpose (ex P.S.O.).

#### Multiscale formalism for the analysis of plants

V. Letort continues her Phd work on the generalization of the sources and sinks concepts in a plant. The ``Rattle'' model, which transforms a branch in a meta-organ made of a set of compartment (leaves, wood, and fruits), is operational. It allows simplifying dramatically the measurements on plants. It has been successfully tested on such different plants for scale as Arabidopsis and Pine tree. V. Letort works on the geometrical construction of the rings (secondary growth) of the wood inside the branches that gives their diameters. Allocation of the biomass to the rings is given by a simple equation. The amount of biomass to build the ring in a local place is proportional to the above leaf surface seen from this place anywhere into the tree architecture. This is provided by a simple operation on substructures (Kang 2002 Liama). Secondary growth using biomass diffusion through the topological structure is a bottleneck of the tree construction for the classical FSM using parallel growth. DigiPlante team improves the method to assess the ascent and the descent of the biomass produced by the leaves into the tree rings at the branch connection. In 2007, this work will be applied on Beech trees (INRA Forêt Ð Nancy) and on Pine trees (Chinese Academy of Forestry).

#### Parametric Identification : functional parameters

A generalization of the estimation procedure initially developed by Zhang et al. (2003) has been implemented in the DigiPlante software (PH Cournède). Branching plants with interactions between growth and development can be analyzed. Moreover, several plants with different topological structures or different ages can be fitted by the same set of functional source and sink parameters.

Besides, some theoretical work is done to improve the statistical method of parameter estimation, especially to determine the covariance matrix of the noise entailed by model errors, measurement errors and control errors.

#### Parametric Identification : Stochastic Model of Development

Studies on the calibration of the stochastic development of plants have begun in 2006. A procedure based on the plant production analysis at the compartment level to fit the number of organs and the biomass production, both in means and variances, has been worked out. The analysis uses different growth stages with several repetitions of the same plant. For each compartment means and variances are provided and the information is sufficient to compute the state probabilities of bud functioning and the parameters of sink and source relatioship using generalized least square method.

It is not necessary to study the detailed topological structure of each plant, which is tedious, but only the distribution of the cumulative production for both organs and biomass for each kind of compartment. Studies on the expression of the generating function have been carried out with the collaboration of Kang, Cournède and Quadrat (Metalau project). Two publications have been submitted. Development of software for GL2 level is in progress. A prototype exists in GreenScilab developed by Kang and Letort) and the first plant to be analysed for its stochastic behaviour is the wheat (for tillering). Data are coming from the Wageningen University.

#### Interaction between plant growth and architectural development

A. Mathieu got her Phd degree at the ECP in April 2006. The document contains the first studies of the behaviour of the model of interactions between organogenesis and photosynthesis. It gives a good explanation to the major events that occurs in the plant architecture during the Growth process (young stages, apparition of reiterations, fruits, tree aging, etc.) One of the interesting properties of the model is the possible apparition of a rhythmic mode of functioning as a result of the balance between the sources and sinks. Studies of such behaviours on cultivated plants like sweet-pepper or cucumber, will be undertaken in 2007 in collaboration with agronomic centers (Wageningen, CAU). First steps on the calibration of the thresholds that trigger the retroactions have been tried on such plant as young beech trees, coffee tree, rice tillers. There are still a lot of works to do for applications. Several papers have been submitted to journals.

#### Functional Landscape

Marc Jaeger join DigiPlante at november 2006, as well as Vincent Le Chevalier (ECP) starting a PhD. In early spring, at LIAMA (Beijing), both started to work on landscape functioning aiming to simulate crop plantations and small landscape with a ``reactive'' environment. The goal is to simulation water exchanges (rain, runoff on terrain and absorption, diffusion in soil, plant water uptake and evapotranspiration) in interaction with DigiPlante growth model. A first prototype was build end of this year, including run-off, absorption in interaction with a simple plant model implementation, and basic visualisation tool. Results were submitted and accepted to PMA06, submission to JCST is on the way.

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