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Fitting Plant structure


Crown analysis

    Crown analysis Simple estimator.

    From phytomers distribution at ranks K and K+L, it computes inter crown expected value, variance, and the (K,L) average intra crown variances.
    Those statistical are used to estimate the development parameters:
    • The rhythm ratio w between the main axis and the braches.
    • The probability b1, characterizing the development on the main axis (Bernouilli)
    • The probability b2, characterizing the development on the branches (Bernouilli)

    Enter first the reference rank K and the coupling rank K+L.
    Enter then phytomers distribution numbers separated by the delimiter (comma ',' is default). Example : 3,12,14, 6, 5, 5
    Both lists are suppossed to be complete and aligned.

    Rank Distribution
    Reference (K):
    Coupling (K+L):
    Delimiter       

      Results:
      Number of crowns N :
      Rank position K :
      Rank offset L :
      Expected value (inter crown mean) XK:
      Variance (inter crown) VK:
      Variance (intra crown) vK:
      Structural parameters
      Negative binomial b1:
      Negative binomial b2:
      Rhythm ratio w:


Crown analysis equations
    In this implementation all main axis phytomers are supposed to branch, and branches are alive (no mortality occurs).

    On a significant number N of crowns, the phytomer distribution (on branches) at rank K from the tip is supposed to be known, as well as the distribution at rank K+L. XK (respectively VK) stand for the expected value number (respectively the variance) of phytomers on branch axis at rank K. vK stands for the expectation of the couple (K,L) variances (intra-crown variance).

    Those statistical values lead to identify numerical solutions for the development parameters w, b1 and b2 values at rank K.



    In practice, small values for L are better in order to minimize variances.
    Chose L = 0 for plants showing multiple axillaries per nodes (such as Coffea), and L = 1 for plants bearing a single axillary per node (such as Cotton tree).