-> About this Resource
Scope *______
Map *____

-> Preliminary Courses
Contents & Objectives *__________________
Map *____
-> Botany
Contents & Objectives *__________________
Map *____
-> Axis Typology Patterns
Typology basis *___________
Pictograms *_________
Sexuality & development *___________________
Growth *______
Branching rhythms *______________
Branching delays *_____________
Branching positional *________________
Branching arrangement *__________________
Axis orientation *_____________
Architectural models *________________
-> Architectural Unit
About Arc. Models *______________
Models limitations *______________
Architectural Units *______________
Reiteration *_________
Sequence of development *___________________
Morphogenetic gradients *___________________
Physiological age *_____________
-> An Example
Wild Cherry (young) *_______________
Wild Cherry (adult) *______________
Wild Cherry (mature) *________________
Quiz *____
Case study Quiz *_____________
Supplementary resources *____________________

-> Eco-Physiology
Contents & Objectives *__________________
Map *____
-> Growth Factors
Factors affecting Growth *___________________
Endogenous Processes *_________________
Environmental Factors *_________________
Thermal Time *___________
-> Light interaction
P.A.R. *_____
Light absorption *_____________
Photosynthesis *___________
Respiration *_________
Maintenance respiration *__________________
L.U.E. Model *__________
Density effect *___________
Density effect on crop *__________________
-> Biomass
Biomass Pool *__________
Biomass Partitioning *_______________
Crop models *__________
A Crop model example *__________________
Quiz *____
Supplementary resources *___________________

-> Applied Mathematics
Contents & Objectives *__________________
Map *____
-> Probabilities
Section contents *____________
Discrete Random Variable *___________________
Expected value, Variance *___________________
Properties *________
-> Useful Laws
Bernoulli Trials *___________
Binomial Law *__________
Geometric Law *____________
Negative Binomial Law *_________________
-> Dynamic systems
Section contents *_____________
Useful functions *____________
Beta density *__________
Exercises *________
Negative Exponential *________________
Systems functions *______________
Discrete dynamic systems *___________________
Parameter Identification *__________________
Parameter estimation *________________
Supplementary Resources *____________________

-> GreenLab courses
GreenLab presentation *__________________
-> Overview
Presentation & Objectives *____________________
Map *____
Growth and components *___________________
Plant architecture *_______________
Biomass production *________________
Modelling - FSPM *______________
GreenLab principles *________________
Applications *__________
Supplementary resources *_____________________
-> Principles
Presentation & Objectives *____________________
Map *____
-> About modelling
Scientific disciplines *________________
Organs: tree components *___________________
Factors affecting growth *___________________
Model-simulation workflow *____________________
GreenLab inherits from *__________________
GreenLab positioning *_________________
The growth cycle *______________
Inside the growth cycle *___________________
Implementations *______________
Supplementary resources *____________________
-> Development
Presentation & Objectives *____________________
Map *____
Modelling Scheme *______________
Tree traversal modes *________________
-> Stochastic modelling
Principles *_______
-> Development
Growth Rhythm *____________
Damped growth *____________
Viability *______
Rhythmic axis *___________
Branching *________
Stochastic automaton *_________________
-> Organogenesis equations
Principles *_______
Organ cohorts *___________
Organ numbering *_____________
Substructure factorization *____________________
Stochastic case *____________
-> Structure construction
Construction modes *_______________
Construction basis *______________
Axis of development *________________
Stochastic reconstruction *___________________
Implicit construction *________________
Explicit construction *________________
3D construction *____________
Supplementary resources *____________________
-> Production-Expansion
Presentation & Objectives *____________________
Map *____
-> EcoPhysiology reminders
Relevant concepts *______________
Temperature *__________
Light interception *______________
Photosynthesis *___________
Biomass common pool *_________________
Density *______
-> Principals
Growth cycle *__________
Refining PbMs *___________
Organ cohorts *___________
GreenLab vs PbM & FSPM *___________________
-> GreenLab's equations
Summary *_______
Production equation *_______________
Plant demand *__________
Organ dimensions *______________
A dynamic system view *__________________
Equation terms *____________
Full Model *________
Model behaviour *______________
Supplementary resources *____________________
-> Applications
Presentation & Objectives *____________________
Map *____
-> Measurements
Agronomic traits *_____________
Mesurable/hidden param. *___________________
Fitting procedure *______________
-> Fitting structure
Principles *_______
-> Development
Simple development *_______________
Damped growth *____________
Rhythmic growth *_____________
Rhythmic growth samples *___________________
Mortality *_______
Branching *________
-> Crown analysis
Analysis principles *______________
Equations *________
Example / Exercise *_______________
-> Case study
Plant Architecture *______________
Development simulation *__________________
Introducing Biomass *_______________
Biomass partitioning *_______________
Equilibrium state *_____________
Supplementary resources *____________________

-> Tools (software)
Presentation & Objectives *_____________________
Map *____
Fitting, Stats *___________
Simulation *_________
Online tools *__________

GreenLab structural functional plant growth model


GreenLab presentation
    Functional-structural plant models (FSPM) simulate plant development and growth, usually accompanied with visualization of the plant 3D architecture. Aside the classic process-based crop models and individual structural Plant models, GreenLab model (De Reffye and Hu., 2003) displays an original positioning.

    GreenLab is a generic and mechanistic FSPM: various botanical architectures, as defined by (F. Hallé, 1978) can be produced by its organogenesis model, and the plant growth is governed by the competition on biomass among growing organs.

    GreenLab is a mathematical dynamic model aiming to model and simulate plant structure establishment and production. It differs from computational models by the fact that both development and functional processes are described by equations.
    The model therefore quantifies structure (the number of organs, etc.) without requiring exhaustive structural implementation.
    It also differs from classic functional structural plant models by the fact that organ production is quantified by compartments, competing for a common biomass pool.
    It also differs from biomass production based on the Beer Lambert Law, conventionally used in PBM. In a growth cycle, the model sequences organogenesis, biomass production and its partitioning in a dynamic loop.

    A distinguished feature of GreenLab model is that, its organogenesis (in terms of the number of organs) and growth (in terms of organ biomass) are formulated with recurrent equations. It facilitates analytical study of model behaviour, bug-proof of simulation software, and application of efficient optimization algorithm for parameter identification or optimal control problems.

    As a summary, the interest of the GreenLab model relies on its mathematical formulation as a dynamic system (Cournède et al., 2006) which allows efficient simulations, proper statistical identification and evaluation, but also an easy integration of the concepts classically used in crop models to describe plant-environment interactions (Feng et al, 2014). The latest developments also renew flexible structural representations and reconstructions (De Reffye, Jaeger, 2013).

    Currently several levels of GreenLab model exist: (1) the deterministic one (GL1): plants have a fixed pattern for development without feedback from the plant growth; (2) the stochastic level (GL2): pant organogenesis parameters are probabilistic; (3) the feedback model (GL3, still on development): the plant development is dependent on the dynamic relationship between biomass demand and supply (and in turn the environment). It makes it possible to cover the different kinds of behaviour observed in real plants.

    This pedagogic resource describes the deterministic and the stochastic levels (GL1 and GL2 levels).

    The pedagogic resource splits as follows:
    • An overview of GreenLab is presented first
    • Principles of GreenLab are then presented
    • Structural aspects of the GreenLab model follow
    • Functional aspects of the GreenLab model are then explicited
    • Lastly, appications section presents GreenLab model parameter fitting and a case study


    Cournède P.-H., Kang, M. Z., Mathieu, A., Barczi, J. F., Yan, H. P., Hu, B. G., and De Reffye, P. 2006. Structural factorization of plants to compute their functional and architectural growth. Simulation, 82(7), pp. 427-438 (access to paper and pdf)

    Feng, L. , Mailhol, J. C. , Rey, H., Griffon, S., Auclair, D., de Reffye, P. 2014. Comparing an empirical crop model with a functional structural plant model to account for individual variability. European Journal of Agronomy, 53 (1) : pp. 16-27

    Hallé, F., Oldemann, R.A.A., Tomlinson, P.B. 1978. Tropical trees and forests. Berlin: Springer-Verlag.

    De Reffye P., Hu BG, 2003. Relevant qualitative and quantitative choices for building an efficient dynamic plant growth model: GreenLab case. In Hu BG, Jaeger M (Eds), Plant growth modelling and applications (PMA03), Proceedings of the 2003' International Symposium on Plant Growth Modeling, Simulation, Visualization and Their ApplicationsTsinghua University Press, Springer; pp. 87-107. (pdf)

    De Reffye, P., Jaeger, M. 2013. Modèles mathématiques du développement et de la croissance de l'architecture des plantes. Le cas du modèle GreenLab. In Varenne, F., Silberstein, M. (Eds) Modéliser et simuler. Epistémologies et pratiques de la modélisation et de la simulation. Tome 1. Paris : Editions Matériologiques (Sciences et Philosophie, vol. Sciences et Philosophie). pp. 625-658

Requested background

Course Objectives

    The aim of this course is to enable students to:

    • Learn about the GreenLab model assumptions and basis

    • Understand the principles of structural modelling, derived from architectural botany

    • Understand the principles of stochastic structural modelling, derived from statistical analysis

    • Learn about structural parameter estimation from field measurements

    • Understand the principles of fonctional modelling, derived from eco-physiology

    • Understand the principles of fonctional parameter estimation