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
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Discrete Random Variable *___________________
Expected value, Variance *___________________
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-> Useful Laws
Bernoulli Trials *___________
Binomial Law *__________
Geometric Law *____________
Negative Binomial Law *_________________
-> Dynamic systems
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Useful functions *____________
Beta density *__________
Exercises *________
Negative Exponential *________________
Systems functions *______________
Discrete dynamic systems *___________________
Parameter Identification *__________________
Parameter estimation *________________
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-> GreenLab courses
GreenLab presentation *__________________
-> Overview
Presentation & Objectives *____________________
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Growth and components *___________________
Plant architecture *_______________
Biomass production *________________
Modelling - FSPM *______________
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-> Principles
Presentation & Objectives *____________________
Map *____
-> About modelling
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Organs: tree components *___________________
Factors affecting growth *___________________
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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. *___________________
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-> Fitting structure
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-> 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 Course

Development

Structure construction basis


The phytomer builds the elementary unit that the structure is built with.
We have however seen that organogenesis and stochastic modelling apply to a given number of growth cycles, thus considering the axis level.

Axis of Development notion

    In structural and functional structural plant models, plant structure construction is performed individually, plant by plant.

    In the GreenLab model, since an explicit structure is not required to simulate plant development and growth (only the number of organs per cohort needs to be known), structure construction is only partially done.

      More precisely, only simple sequences of structure are computed and stored, one for each physiological age.
      In the case of stochastic simulations, a limited number of stochastic realisations are computed for each physiological age.

      These sequences are in fact defined by the Bernoulli trials applied to each physiological age (and stochastic realization).
      They define the plant's axis of development.

      Axis of development

        The axis of development Axdφ of physiological age φ defines the successive results of the Bernoulli trials applied to the terminal meristem of physiological age φ from the seed stage to plant age.

          Axdφ is thus a state list for instance {0,0,0,1,1,1,0,1,0,1,1....}
          where
          Axdφ(i) = "1" (a Bernoulli trial success) defines therefore a phytomer of physiological age φ, whose ontological age is i.
          This phytomer is thus explicit, and it's properties are explicitly defined; in particular, its bearing organs, defined from the dual scale automaton.
          An efficient way of encoding is to encode the physiological age of its axillary bud instead of "1" (see figure below).

          Axdφ(i) = "0" (a Bernoulli trial failure) defines therefore a rest occurring at growth cycle i.

        Axdφ defines any axis paths of physiological age φ in the plant.

        A simple example

        Axes of development example
        An example of a continuous axis of development (Image P. de Reffye, CIRAD)
          This continuous growth example shows three physiological ages
          Top, the 3 axes of development are shown on 13 growth cycles.
          Physiological age 1 axis has a development ratio of 1, has no rest, and each phytomer bears a physiological age 2 axis.
          Physiological age 2 axis has a development ratio of 0.75, has no rest, and each phytomer bears a physiological age 3 axis.
          Physiological age 3 Axis has a development ratio of 1, has no rest, and each phytomer bears a physiological age 4 axis, but does not branch.
          The corresponding reconstructed structure is shown below. Internodes in grey are virtual ones and indicates rests.

        Another example with rhythmic growth

        Axes of development example
        An example of a crhythmic axis of development (Image P. de Reffye, CIRAD)
          This rhyhtmic growth example shows four physiological ages
          The 4 axes of development are shown on 20 growth cycles.
          All axes show acrotony
          Rest periods on rhythms of the 4 physiological ages are not synchronized.
          The corresponding reconstructed structure is shown below. Internodes in grey are virtual ones and indicates rests.