-> 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 Course


Implicit and Explicit Structure construction

In computation terms, structure construction is a costly operation, since it requires multiple axes of development copies and instantiations.

If plant 3D structure representation is not required, these rewrittings can be skipped, storing the number of organs in tables (matrices). This fast construction is called the matrix mode.

If not, axis of development state lists are effectively copied. By building a tree graph those nodes stand for a state. This construction is called the list mode.

Structure Matrix mode

    Axes of developments state lists defines the patterns on which the structure is built.
    Building a tree structure thus means defining paths in these axes from state to state within the same axis (axis development) or jumping to another axis (branching).

    In a word, the structure matrix mode stores the number of visits of a given state.

    The structure matrix mode encodes the plant structure as a multidimensional table, indexed by:
    • The organ nature o
      Leaves, roots, internodes, female, male fruits, etc.
      However, since the number of organ types is limited and the typology quite constant, separate tables may be used.
      In the following, index o is omitted

    • The physiological age φ
      as defined from architectural botany, the physiological age φ (in practice limited to 5) is the most representative index

    • The ontogenetical age a
      defined from the bud age since axis appearance (set to 1), expressed in growth cycles

    • A random identifier r
      specifying an identifier r = 1, Nrepφ when stochastic modelling and simulation are chosen.

    Each matrix cell thus stands for an organ cohort and encodes the number of organs of the cohort.

    Given such tables, organ cohort series can easily be retrieved from single additions.
    The complexity of the encoding is linear in growth cycles, making it really efficient.

    Building the structure in matrix mode

    Building the structure means updating the matrix for consecutive growth cycles

      After a new growth cycle, the functional model requires structural changes to be defined:
      - the number of functional source organs at their different ages(the number of fonctional leaves),
      - the number of functional sink organs at their different ages (in order to evaluate the plant demand).

      We assume that the current growth cycle is i.
      Let us consider organs / phytomers / axes of physiological age φ borne at cycle a living at cycle i and write their number M(φ,a,i) (assumed to be known at cycle i)
      At cycle i+1 all cells are initialized to 0 ( M(*,*,i+1) = 0 )

      Let's evaluate the new number of organs / phytomers / axes at the next cycle i+1 in the determinate case (not stochastic).
      We have seen that structure development occurs from the apical bud (leading to new phytomer occurrences on the current axis) and from axillaries (branching process).

      Axis development
        A new phytomer appears on the axis if Axdφ(i+1) > 0.
        Such will be the case of all axes borne at ontological case a and of physiological age φ
        We then have:
        M(φ,a,i+1) = M(φ,a,i+1) + M(φa,i) (M(φ,a,i+1) was initially set to 0)

        Let us now consider the case of a branching (or a transition), with m axillary buds of physiological age φ2
        Note that :
              - with our list encoding φ2 is given by Axd(φ,i)
              - we may have partial or total reiteration with φ = φ2.
        In the branching process a new axis appears, borne at age i+1. We thus have:
        M(φ2,i+1,i+1) = M(φ2,i+1,i+1) + m . M(φ, a, i)

      At this point, a loop must be performed on all ontogenetic ages, since development and branching may occur for each of them.

      This recursive definition is in fact one implementation of the recursive sub-structure construction, as defined previously (see here).

      The stochastic case is derived straightforwardly from the deterministic case, using the stochastic axes of development for each random identifier.

      In more detail, mattrix mode cell filling must be filtered by the corresponding organ properties:
      - the appropriate number of organs per phytomer
      - filter organ occurrence in respect of a minimal ontogenetic age if required
      - filter organ occurrence according to its lifespan (*)
      - limit reiteration development if the maximal order is reached
      (*) Self pruning is not always a good idea to be implemented at this stage:
          it is better to check if the organ is still a biomass producer/consumer when estimating production.
      By doing so, the encoding allows the matrix to be revisited at past growing stage cycles.