« DigiPlante » Modelling, Simulation and Visualization of Plant Growth

1. Mathematical Models of Plant Growth for Applications in Agriculture, Forestry and EcologyPaul-Henry CournèdeApplied Maths and Systems, Ecole Centrale Paris

2. « DigiPlante »Modelling, Simulation and Visualization of Plant Growth a joint team between associated to agronomy research institutes (Institute of Automation, China Academy of Sciences) with very strong links with (China Agricultural University) All these institutions collaborating to develop a joint model:

3. Plant Growth Modelling: a multidisciplinary subject Botany Plant Architecture Agronomy: Ecophysiology Bioclimatology Soil Sciences Applied Mathematics Stochastic Processes Dynamical Systems Optimization, Control Computer sciences Simulation visualization Plant Growth Simulation

4. Outline • Modelling plant growth and development • Model identification from experimental data • Exemples of applications

5. Outline • Modelling plant growth and development • Model identification from experimental data • Exemples of applications

6. CO2 Biomass water Nutriments A model combining two approaches Morphological models => simulation of 3D development Process-based models =>yield prediction as a function of environmental conditions Organogenesis + empirical Geometry = Plant Architecture. Plant development coming from meristem trajectory (organogenesis) Biomass acquisition (Photosynthesis, root nutriment uptake) + biomass partitioning (organ expansion) Compartment level Functional-structural models

7. A familly of Functional-Structural Models of plant growth initiated by P. de Reffye Simulation Mathematical Models Dynamic model Interaction Photosynthesis x organogenesis Functional growth Botany Organogenesis + Geometry Amap Jaeger 1988 Amaphydro Blaise 1998 Sim HP De Reffye 1980 Amapsim I Barczi 1993 GL1 &2 Kang 2003 GL3 Cournède 2004 prototype AMAP GREENLAB France Africa France China

8. A « Growth Cycle » based on plant organogenesis • Development of new architectural units: • continuous : agronomic plants or tropical trees •  rhythmic : trees in temperate regions. • Organogenesis Cycle = Growth Cycle, time discretization for the model • Phytomer = botanical elementary unit, spatial discretization step • For continuous growth, the number of phytomers depends linearly on the sum of daily temperatures. Guo and Ma (2006)

9. fruits Organogenesis + organs expansion Flowchart for plant growth and plant development photosynthesis transpiration leaves CHO Pool of biomass seed H2O GreenLab Plant branches roots

10. A formal grammar for plant development (L-system) Alphabet = {metamers, buds} (according to their physiological ages = morphogenetic characteristics) Production Rules : at each growth cycle, each bud in the structure gives a new architectural growth unit. Factorization of the growth grammar factorization of the plant into « substructures » Computation time proportional to plant chronological age and not to the number of organs !

11. No stress W. stress A generic equation to describe sources-sinks dynamics along plant growth Light Interception Environment Energetic efficiency Development Sinks Function

12. Plant architectural plasticity. L-System production rules for the development depend on plant trophic state = function of the ratio of available biomass to demand (Q / D) • Same set of model parameters • Different light conditions Age 15 15 15

13. Inter-tree competition at stand level Tree on the edge Central tree Method of intersections of projected areas Isolated tree Trees in competition for light

14. Outline • Modelling plant growth and development • Model identification from experimental data • Exemples of applications

15. Estimation of model parameters from experimental data • Plant = Dynamic System • State variables = vector of biomass production • Input Variables = environnement (light, temperature, soil water content) • Parameters • Observations • Trace back organogenesis dynamics from static data collected on plant architecture (numbers of organs produced, modelling of bud functioning) • Trace back source-sink dynamics (biomass production and allocation) from static data on organ masses. • Estimate :

16. Water use efficiency Light interception Sources Fonctions Sinks Fonctions Exemple of parameter estimation on Maize plant Environment Parameters of climatic functions Blades Internodes time Internodes Root mass as a function of time endogenousParameters Blades Cob cob Estimation results source-sink functions Architecture and climate Data Fitting architecture

17. Simulation and visualization of Maize growth Guo et al., 2006

18. Genericity of the growth model Arabidopsis (Christophe et al., 2008) Young pine (Guo et al., 2008)

19. Genericity of the growth model

20. Outline • Modelling plant growth and development • Model identification from experimental data • Exemples of applications

21. Optimal control of irrigation for Sunflower Wu et al., 2005 For (a), sunflower height is 105.9, fruit weight is 623.41, total weight is 1586.72 For (b), sunflower height is 98.3, fruit weight is 656.11, total weight is 1509.78. For (c), sunflower height is 112.1, fruit weight is 881.52, total weight is 1998.97

22. Biomechanics and computation of constraints in trees Tree growth in a constrained environment Mechanical constraints Fourcaud et al., 2003

23. Functional landscapes in ecology • Simulation and visualization of ecological process dynamics at landscape scale (from 100 to 10000 km²). E.g.: water ressource allocation. • prototype : C++ and OpenGL (glut), multi-platform • Visualization of dynamics and image post-treatments Le Chevalier et al., 2007