COURSES

-> 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 *__________

Discovering a functional structural plant model. Overview


Plant modelling: a challenge

With over 300 000 species on Earth, the world of flowering plants is incredibly diverse. But, despite this diversity, plant structure is built from the same basic botanical elements, leaves, stems, fruits, roots, etc., whose functions are unchanged as sources and sinks for biomass production and partitioning.

However, to understand such a complex system as plant growth and development, knowledge about botany (plant structure organization) and physiology (action of environmental parameters, water transport, respiration, and photosynthesis) is not sufficient. Moreover, statistical correlations and empirical functions between measured variables such as temperature, light, plant height or weight are also not sufficient mathematically speaking, since these measures are themselves resulting of a complex functioning that involves the hidden parameters of an underlying mathematical model that is to be built.

Identifying the relevant parameters that bridge together the various disciplines results in translating the reality into a mathematical model, that will allow plant behavior study. The complexity of the real world must be dropped down in order to build efficient models. This can be achieved by a dialog between biologists, who have the qualitative knowledge, and mathematicians, who handle quantitative relationships through equations.

Computing the numerical values of the hidden parameters from measurements on real plant architecture is what is called an inverse problem. Engineering applications for agriculture can be worked out only if this problem is solved.
Plant architecture results from both meristem functioning (organogenesis) and photosynthesis (biomass production and partitioning) and it may be assumed that plant architectural development concerns the growth process trajectory keeping at any time in its memory the underlying structure. Thus the hope is to trace back the growth process from measurements on plant architecture in given environmental conditions, and furthermore to control the plant behavior from acting on the environmental parameters.

Finally, the research work may be considered as fulfilled if it is possible to simulate the growth process with a minimum number of parameters and to build step by step the plant architecture with all the organs in the right place inside the plant structure and with the correct biomass content. This is the goal of a computerized implementation. Such important problems as optimizing the use of resources (water, fertilizers in fields, temperature and light in glasshouses) and cultivation systems (planting density, pruning) can then be successfully solved.

This resource presents an efficient dynamical plant growth and architecture model built on the basic knowledge coming from botany, ecophysiology, agronomy, applied mathematics, and computer science.