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GreenLab Course

Development

Stochastic axis of development


Axes of development lists define the basis of structure construction in the GreenLab model.
In stochastic simulations, a limited number of axes allows numerous structure reconstructions.

Stochastic reconstruction

    In the stochastic case, structure reconstruction using the axes of development remains similar to the determinist case.

    Generation of stochastic axes of development
      Principles: for each physiological age, Nrepφ stochastic axes of development are created, on the basis of stochastic modelling:
      - random generators are initialized for each axis (defining a new seed for random sequences)
      - in the development simulations, the Bernoulli trial test each phytomer occurrence
      - viability is estimated at each growth cycle, if mortality occurs, the axis is filled to the dead state ("-1") until the end
      - on awakened phytomers, branching occurrence and delay are estimated then stored with the phytomer attributes
      - a random number is attributed for each axillary, defining the appropriate "random" axis of development to be considered in structure reconstruction.

    In practice, Nrepφ is set at 10 to 20 simulations per physiological age.
    At high physiological ages, some stochastic axes of development creations may be identical (such is also the case when event probabilities are high).

    Structure construction remains virtually the same as the deterministic case.

    Axis development
      The successive states describing a specific axis in the plant structure can be retrieved from one of its corresponding axes of development (same physiological age). Defining a seed number, the axis description is still a simple copy, with an offset corresponding to the ontogenetic age.
      This copy ends at the shorter term derived from:
      - plant age,
      - a transition to a higher physiological age,
      - a termination specified in the selected axis of development (determinate growth, or death)

    Axis branching
      The branching process is a similar operation, except that the corresponding axis of development is defined by the physiological age of the axillary and the seed number computed during axis construction.

    Using this procedure, the number of potential structure reconstruction increases considerably.
    At each branching, there are Nrepφ possibilities of using a different axis of development.
    That is to say that, on a simple plant with 2 physiological ages branching at each phytomer, with a stochastic axis on physiological age 2, the number of combinations at N growth cycles is Nrep2N-1.


    Example

      In the following example, Nrep is set to 25 for all physiological ages.
      Leaf insertions are also presented

    Stochastic Axis of development
    Stochastic axes of development (Drawings M. Jaeger, CIRAD)
      SImulations of stochastic axes of development (Nrep = 25, three physiological ages)
      Left and top left: Six axes of development out of the 25 for each physiological age are shown
      Right and bottom right: Three stochastic reconstructions derived from the 75 stochastic axes