Applications
Fitting
Plant structure fitting - Crown analysis Example / Exercise
A simple first example
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Fitting cotton tree crowns: a case of continuous growth.
50 cotton tree crowns were analysed. The following table summarizes the number of phytomers found at rank 10 and 11 from the top, respectively.
| Plant | 01 | 02 | 03 | 04 | 05 | 06 | 07 | 08 | 09 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 |
| Rank 10 | 3, | 3, | 4, | 3, | 3, | 3, | 3, | 2, | 3, | 4, | 3, | 3, | 4, | 3, | 3, | 3, | 3, | 2, | 3, | 3, | 2, | 3, | 4, | 4, | 4, |
| Rank 11 | 4, | 4, | 3, | 4, | 3, | 4, | 4, | 4, | 4, | 4, | 3, | 3, | 4, | 3, | 4, | 3, | 3, | 4, | 1, | 3, | 3, | 3, | 4, | 4, | 4, |
| Plant | 26 | 27 | 28 | 29 | 30 | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 | 41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 | 49 | 50 |
| Rank 10 | 3, | 3, | 3, | 3, | 3, | 3, | 4, | 3, | 3, | 3, | 3, | 3, | 4, | 2, | 2, | 4, | 4, | 3, | 3, | 3, | 3, | 4, | 3, | 5, | 4 |
| Rank 11 | 4, | 3, | 3, | 4, | 2, | 3, | 4, | 4, | 3, | 3, | 4, | 3, | 5, | 3, | 3, | 4, | 4, | 4, | 3, | 4, | 3, | 4, | 4, | 5, | 4 |
Table 1. 50 cotton tree crowns. Rank 10 and rank 11 give the number of phytomers found on branches at position 10 and position 11 from crown top, respectively.
Statistics were then computed on the 50 crowns at position K = 10.
The expected value and variance were X10 = 3.2 and V10 = 0.4, respectively.
The development parameters were: (one significant digit)
b1 = 0.9 b2 = 0.9 w = 0.3
Exercices. Cotton tree crowns
Exercice 1. Compute the statistics on the phytomer distributions
1a. Compute the expected value and variance of the cotton tree crowns at rank 10.
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You may use the following online calculators:
- http://easycalculation.com/statistics/standard-deviation.php
- ../../P3_Tools/Tool_stats_001.html
simply drag and drop the Table 1 line contents in the data form.
1b. Compute the intra crown variance from couples defined by ranks 10 and 11
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What is this variance on trees 01, 10, 19 and 30 ?
What is the average variance ?
Exercice 2. Compute the development parameters from phytomer distributions
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Using the crown analysis tool ,
compute the development parameters of the cotton tree, based on the rank 10 and 11 given above.