-> 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



GreenLab Organ cohorts
      Metamers of the same physiological age and the same chronological age are considered as identical, whatever their positions in the plant structure.

        The set defined by all metamers of the same physiological age p and the same chronological age t defines organ cohorts Co(p,t), where o stands for the various organs borne by the metamer.

        Hence, in a given organ cohort, all organs are of the same type (leaf, internode, flower, etc.) and show the same properties and evolution.
        The GreenLab models uses this assumption, evaluating biomass demand and biomass consumption from a single representative of each cohort, multiplied by the number of organs No(p,t) of each cohort Co(p,t).

        Compared to process-based models, GreenLab can thus be seen as an extension, defining several cohorts for each organ type instead of a single compartment.
        The set of cohorts reflects the establishment of minimized architectural dynamics, restricted to the physiological age and the organ age.

        In practice, the cohort chronological age has to be expressed from two dates: the cohort appearance date da and the current date dc. The appearance date must be expressed relatively to the full plant appearance date, while the current date can be expressed relatively to the appearance of the set of organs (i.e. the cohort age).


      Two cohorts Co(p,da, dc) and Co(p,da+i, dc+i) of the same organ, with the same number of organs, the same physiological age, the same age, but two different appearance dates show different evolutions, since the biomass availability level is not stable during plant development and growth.

    Organic series
      The evolutions of cohorts are called organic series, a term coined by R. Buis in 1983.

      Ageing evolution
        Ageing evolution of a given cohort Co(p,da,dc+n), is simply the chronological evolution; the current date is incremented (by a number n of growing cycles). .
        In such a case, usually:
          - the number of elements in the cohort is assumed to be constant
          - the corresponding organ sizes (corresponding to the biomass allocated so far) increase
          - the corresponding organ gets older, and may reach its term of functioning.
        For the given Organ o, the organic series Co(p,da,da+l), born on date da, built for the full organ life span l, defines the chronological organic series of o, born on date da, of physiological age p.

      Position along an axis
        Evolution can also be considered on the basis of structural elements. We will show further, that field observations of series built from organs on the same axis, from tip to insertion, allow structural statistical properties to be expressed.
        In this case, the series is built from representatives of cohorts on successive appearance dates, corresponding to successive ranks of organ insertion along the axis.
        In fact, along the axis, the organic series can be considered from the list of successive cohorts related to the appearance dates dai -> daf (= dc) of the organs.
        From top to bottom, each organ position defines a rank in the different cohort sets.
        These ranks will be consecutive if the organ appearance was effective for each growth cycle (no rests).

        Both organic series are independent from structure architectural considerations as shown below.

          Organic series
          Organic Series in plant structures (Image P. de Reffye, CIRAD)
            These examples of series are shown in red, on three structures of the same unique physiological age and the same chronological age.
            a) A single axis with different phytomers. Two organic series respectively related to the leaves and the internodes describe the organ successions from upper tip to bottom.
            b) A monopodial structure showing two similar organic series paths. From apex to seed, all organic series are identical; the successive organ ranks are related to the same cohorts.
            c) A sympodial structure. Here also, from apex to seed, all organic series are identical. On this example, they are also identical to those of the monopodial structure, since cohorts from both monopodial and sympodial structures share the same number of organs and organ sizes.


Buis, R., Barthou, H. 1983. Relations Dimensionnelles dans une série organique en croissance chez une plante supérieure. IXème Congrès international de Biologie Mathématique, Paris, 8-10 septembre 1983. Bio-Mathematics revue, Les éditions européennes - France., pp. 1-19 (pdf)