Root > GreenLab Model > Applications > Fitting > Structure fitting > Crown analysis Principles

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Applications

Fitting

Plant structure fitting- Crown analysis principles


Plant structure can be straitforwardly analysed in order to identify its development parameters, without following its development step by step.
In fact, development parameters describe the functioning of buds as they build the pathways of the plant structure.

Crown definition for analysis

    Let us define a crown as a structure composed of its main stem, bearing branched axes sharing the same physiological age.

    On the main axis, considering the pathway from top to bottom, one can see that the chronological age of the branches increases.
    Hence, for a given axis typology, several development stages can be observed.
    However, development is usually stochastic.
    Each crown results from a randomized model defined from three parameters: w, b1 and b2.
    Parameter w stands for the rhythm ratio (it is understood that the main axis rhythm ratio is the reference, i.e. set to 1).
    Parameter b1 stands for the Bernoulli process related to phytomer appearance on the main axis, while b2 stands for those related to branches.

    At rank K from the tip, the phytomer's chronological age follows a negative binomial law Bn ( K, b1 ) on the main axis.
    Rememeber that the negative binomial law characterizes the number of trials leading to a given number of successes. The rank, K, thus stands for the number of successes (K here, i.e. K formed phytomers from the tip); while pauses, which are hidden, increase the chronological age of the phytomer likely to appear at rank K.

    Let us now suppose that, on the main axis, the chronological age is T (derived from a negative binomial law Bn ( K, b1)). This age also defines the age of the branch arising from the phytomer at rang K. According to the rhythm ratio w, the number of development cycles on the branch arising from rank K will be w . T . On this branch, the number of phytomers also follows a negative binomial law of parameter b2.
    As a result, the phytomer distribution on the branch is a composed law, derived from negative binomials laws of parameters K, b1 and b2.

      Crown definition
      Crown definition (Image P. de Reffye, CIRAD)
        At rank K, on the main axis, in blue, there are K phytomers from the crown top.
        The chronological age of the phytomer at rank K follows a negative binomial Law B(K,b1) of parameter K and b1.
        The branches derived from the main axis, in green, share the same physiological age.
        Their age of development is derived from a negative binomial law B(w.T,b2), where w is the rhythm ratio and T is the chronological age of the phytomer bearing the branch.