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
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 *___________________
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Biomass production *________________
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-> Principles
Presentation & Objectives *____________________
Map *____
-> About modelling
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The growth cycle *______________
Inside the growth cycle *___________________
Implementations *______________
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-> Development
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Map *____
Modelling Scheme *______________
Tree traversal modes *________________
-> Stochastic modelling
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-> 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 *____________
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-> 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 *________
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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 *_____________
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-> Tools (software)
Presentation & Objectives *_____________________
Map *____
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Simulation *_________
Online tools *__________

Tools (software)

Fitting Plant structure


Crown analysis

    Crown analysis Simple estimator.

    From phytomers distribution at ranks K and K+L, it computes inter crown expected value, variance, and the (K,L) average intra crown variances.
    Those statistical are used to estimate the development parameters:
    • The rhythm ratio w between the main axis and the braches.
    • The probability b1, characterizing the development on the main axis (Bernouilli)
    • The probability b2, characterizing the development on the branches (Bernouilli)

    Enter first the reference rank K and the coupling rank K+L.
    Enter then phytomers distribution numbers separated by the delimiter (comma ',' is default). Example : 3,12,14, 6, 5, 5
    Both lists are suppossed to be complete and aligned.

    Rank Distribution
    Reference (K):
    Coupling (K+L):
    Delimiter       

      Results:
      Number of crowns N :
      Rank position K :
      Rank offset L :
      Expected value (inter crown mean) XK:
      Variance (inter crown) VK:
      Variance (intra crown) vK:
      Structural parameters
      Negative binomial b1:
      Negative binomial b2:
      Rhythm ratio w:


Crown analysis equations
    In this implementation all main axis phytomers are supposed to branch, and branches are alive (no mortality occurs).

    On a significant number N of crowns, the phytomer distribution (on branches) at rank K from the tip is supposed to be known, as well as the distribution at rank K+L. XK (respectively VK) stand for the expected value number (respectively the variance) of phytomers on branch axis at rank K. vK stands for the expectation of the couple (K,L) variances (intra-crown variance).

    Those statistical values lead to identify numerical solutions for the development parameters w, b1 and b2 values at rank K.



    In practice, small values for L are better in order to minimize variances.
    Chose L = 0 for plants showing multiple axillaries per nodes (such as Coffea), and L = 1 for plants bearing a single axillary per node (such as Cotton tree).