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
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Map *____
-> Probabilities
Section contents *____________
Discrete Random Variable *___________________
Expected value, Variance *___________________
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-> Useful Laws
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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 *______________
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-> 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
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Map *____
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-> Stochastic modelling
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-> Development
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Damped growth *____________
Viability *______
Rhythmic axis *___________
Branching *________
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-> Organogenesis equations
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Organ cohorts *___________
Organ numbering *_____________
Substructure factorization *____________________
Stochastic case *____________
-> Structure construction
Construction modes *_______________
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Axis of development *________________
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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 *__________

Applications

Fitting Model parameters

Fitting functional parameters Procedure


Functional parameter fitting workflow

    Reminder
    As shown earlier, the parameter identification process requires several steps, starting with the structural parameters.

    Functional parameter fitting is performed with measured data corresponding to precise development observation stages.

    The collected data are usually classic agronomic traits as defined previously. They are usually collected on a plant population, at the various observation stages. Follow-up is often impossible since some traits are often easier to collect by destructive collection (such as organ weights and dimensions).

    The hidden functional parameter procedure classically follows this workflow:
      1. The plant structure is simulated at the various observation stages. This simulation (stochastic in general) helps to define a target file showing, for each observation date (i.e. for each observation growth cycle):
      • hopefully the number of organs (distribution of) per cohort
      • organ default properties (for instance their volume set as a constant value in the structural simulation

      2. Functional parameters related to organ phenology and allometry are analysed and modelled.

      These parameters are mainly related to the definition of the functioning durations of the growth cycle.
      • The appearance date. For instance, flowering may appear at a given growth stage only)
      • The expansion duration: the number of cycles the organ takes to reach its mature stage and end of development
      • The functioning duration (specifically for leaves). This duration is greater than the expansion time.
      • Allometry parameters are deduced from the collected organ dimensions. (This means collecting organic series, as defined earlier).
      Those parameters are usually considered as constant and are classically estimated from simple statistics.

      3. Building the target file.
      This file retrieves output from simulations at different growth cycles, corresponding to different observation stages.
      The default agronomic traits generated by the simulation are corrected, and replaced by the data measured at the various observation stages.

      4. Fitting the functional hidden parameters.
      The parameters to be identified are then fitted, usually in several steps, starting from the production equation.
      • The first level estimated is usually the Sp and r values, with the Beer Law extinction factor k set to 1.
      • Organ sinks are then estimated as a single ratio
      • Beta laws are then defined for biomass partitioning (the a parameter first, then the b parameter)
      • Lastly, the secondary growth is estimated (if required)
      At each step, the parameter to be estimated is given a default value (assumed to be close to its final value).
      The fitting iterates on the target file, updating the hidden parameter values until the distance between the simulated traits and the measured ones stays constant (and significantly weak).
      The underlying fitting process is, in our implementations, the generalized least square method or renewal annealing.

      Once a parameter is fitted, the others are added, according to the sequence given thereby