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Mathematical Modeling of
Glycine max. (Soybean)
Var. Anjasmoro Plant
Growth
Pingkan Aditiawati, Shinta Palupi, Sparisoma Viridi
Abstract - 16
Components of Soybean Plant Cultivation System
N NN
N N N
N
N N
sunlightplant
Water
Nitrogen
fixing
microbe
Soil
nitrogen
Plant
nitrogen
Components Interactions
Parameters
Observed
Plant height
Number of leaves
Non-Destructive
Soil total nitrogen content
Plant tissue total nitrogen
content
Destructive
A1A
A1B
A1C
A2A
A2B
A2C
A3A
A3B
A3C
A4A
A4B
A4C
A5A
A5B
A5C
A6A
A6B
A6C
A7A
A7B
A7C
A8A
A8B
A8C
A9A
A9B
A9C
A10A
A10B
A10C
A11A
A11B
A11C
A12A
A12B
A12C
A13A
A13B
A13C
Data Sampling Process
Why Destructive?
Destructive Sampling Method
Identical Plants
Plant can always
represents each other
Plant Height Observation Result
0.00
50.00
100.00
150.00
200.00
250.00
0 2 4 6 8 10 12 14
soybeanplantheight(cm)
Weeks after planting
PlantHeight
Time Unit
PlantHeight
Time Unit
Sigmoid Growth Curve
𝐻 =
𝐻𝑚𝑎𝑥
𝐻0
𝐻𝑚𝑎𝑥 − 𝐻0
𝑒 𝑟𝑡
1 +
𝐻0
𝐻𝑚𝑎𝑥 − 𝐻0
𝑒 𝑟𝑡
1
2
Plant Height Data Analysis
Whether the destructive sampling method can accomodate a collection of
representative data
3
Hypothesis
The plants are not identical
4
Objectives and Hypothesis
Generating Several Variations of Sigmoid Growth Curves
𝐻 =
𝐻𝑚𝑎𝑥
𝐻0
𝐻𝑚𝑎𝑥 − 𝐻0
𝑒 𝑟𝑡
1 +
𝐻0
𝐻𝑚𝑎𝑥 − 𝐻0
𝑒 𝑟𝑡
0.00
50.00
100.00
150.00
200.00
250.00
0 2 4 6 8 10 12 14
Plantheight(cm)
Weeks after planting
observation data
H1
H2
H3
H4
H5
H6
H7
H8
H9
H10
H11
H12
H13
Difference in Genetic Expressions
Eliminating Several Data
Destructive Sampling Process
Week P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13
0 11,95 11,95 11,95 11,95 11,95 11,95 11,95 11,95 11,95 11,95 11,95 11,95 11,95
1 18,99 18,15 17,34 18,95 19,05 18,20 19,06 20,88 20,84 20,79 18,15 17,34 19,82
2 29,56 27,12 24,85 29,39 29,77 27,32 29,82 35,41 35,23 35,01 27,12 24,85 31,97
3 44,63 39,60 35,01 44,14 45,20 40,14 45,35 57,27 56,73 56,04 39,60 35,01 49,47
4 64,59 56,04 48,23 63,45 65,93 57,27 66,29 86,62 85,29 83,59 56,04 48,23 72,29
5 88,64 76,21 64,59 86,38 91,34 78,68 92,08 120,52 117,85 114,49 76,21 64,59 98,52
6 114,49 98,93 83,59 110,63 119,20 103,31 120,52 153,48 149,08 143,62 98,93 83,59 124,60
7 139,09 122,14 104,12 133,33 146,26 129,07 148,29 180,59 174,45 166,93 122,14 104,12 147,06
8 159,94 143,62 124,64 152,28 169,61 153,48 172,39 199,97 192,43 183,26 143,62 124,64 164,13
9 175,94 161,76 143,62 166,64 187,80 174,52 191,24 212,49 203,96 193,65 161,76 143,62 175,91
10 187,30 175,94 159,94 176,76 200,87 191,24 204,82 220,05 210,90 199,87 175,94 159,94 183,51
11 194,93 186,34 173,13 183,51 209,72 203,67 214,04 224,43 214,91 203,46 186,34 173,13 188,20
12 199,87 193,65 183,26 187,87 215,48 212,49 220,05 226,91 217,18 205,48 193,65 183,26 191,02
13 202,99 198,62 190,74 190,61 219,13 218,52 223,86 228,29 218,44 206,61 198,62 190,74 192,68
Average
11,95
18,98
29,62
45,79
67,73
90,70
113,02
131,76
150,60
167,15
174,98
184,80
196,76
202,99
Interactions Between Plant Height and Number of Leaves
number of leaves variables as the function of plant height generated from one of simulated
data in the previous section, using the following equation:
y = 0,85x + c (1.2)
With y represents the number of leaves and x represents the plant height.
Next we also proposed number of leaves as the function of time, in this case is weeks after
planting, using the following equation:
y = 15,45x + c (1.3)
With y represents the number of leaves and x represents the weeks after planting
The plants involved in the research are not identical,
thus the usage of destructive sampling method for the soybean
plants are not reccomended because it tends to lead into a
collection of less representative data
Number of leaves as a function of plant height in soybean plant is
y=0,85x+c
Conclusion
Thank you
Boote, K.J., Kropff, M.J. and Bindraban, P.S., 2001. Physiology and modelling of traits in crop plants implications
for genetic improvement. Agricultural Systems, 70(2-3), pp.395-420.
Cross, H.Z. and Zuber, M.S., 1973. Interrelationships Among Plant Height, Number of Leaves, and Flowering
Dates in Maize 1. Agronomy Journal, 65(1), pp.71-74.
Grzesiuk, E., Laubitz, D., Wójcik‐Sikora, A., Zabielski, R. and Pierzynowski, S.G., 2001. Influence of intestinal
myoelectrical activity on the growth of Escherichia coli. Bioelectromagnetics: Journal of the
Bioelectromagnetics Society, The Society for Physical Regulation in Biology and Medicine, The European
Bioelectromagnetics Association, 22(6), pp.449-455.
Indonesian Central Bureau of Statistics., 2017. Indonesian Soybean Production Rate Data.
https://www.bps.go.id/subject/6/tenaga-kerja.html#subjekViewTab3. [online]. Accessed on September, 10
2019.
Indonesian Legume and Tuber Crop Research Institute., 2016. Soybean Production Technology, Indonesian
Ministry of Agriculture, pp.1-20.
Jeremy Stangroom. Pearson Correlation Coefficient Calculator. Social Science Statistics.
https://www.socscistatistics.com/tests/chisquare2/default2.aspx [online] Accessed on September, 13 2019
Krisnamurthi, B., 2010. Manfaat Jagung dan Peran Produk Bioteknologi Serealia dalam Menghadapi Krisis
Pangan, Pakan dan Energi di Indonesia. Prosiding Pekan Serealia Nasional, 1(1) pp.1-11.
Lauenroth, W.K. and Bradford, J.B., 2006. Ecohydrology and the partitioning AET between transpiration and
evaporation in a semiarid steppe. Ecosystems, 9(5), pp.756-767.
Madigan, M. T., Martinko, J. M., Bender, K. S., Buckley, D. H., & Stahl, D. A., 2014. Brock Biology of
Microorganisms, pp.1157-1158.
Shimotashiro, T., Inanaga, S., Sugimoto, Y., Matsuura, A. and Ashimori, M., 1998. Non-destructive method for
root elongation measurement in soil using acoustic emission sensors. Plant production science, 1(1), pp.25-
29
Taylor, R., 1990. Interpretation of the correlation coefficient a basic review. Journal of diagnostic medical
sonography, 6(1), pp.35-39.
References
r Value
Plant
Height
Number
of
Leaves
Evaporation Transpiration
Plant
Water
Needs
Total
Nitrogen
of Plant
Tissue
Total
Nitrogen
of Soil
Nitrogen
Fixing
Bacteria
Population
Plant Height 1.00 0.81 -0.31 -0.25 -0.26 -0.37 -0.38 0.12
Number of
Leaves
1.00 -0.05 -0.18 -0.09 -0.25 -0.31 0.01
Evaporation 1.00 0.67 0.46 0.55 0.55 -0.40
Transpiration 1.00 0.58 0.70 0.72 -0.39
Plant Water
Needs
1.00 0.70 0.46 -0.45
Total
Nitrogen of
Plant Tissue
1.00 0.48 -0.37
Total
Nitrogen of
Soil
1.00 -0.42
Nitrogen
Fixing
Bacteria
Population
1.00

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Mathematical modeling of glycine max. (soybean) var. anjasmoro plant growth

  • 1. Mathematical Modeling of Glycine max. (Soybean) Var. Anjasmoro Plant Growth Pingkan Aditiawati, Shinta Palupi, Sparisoma Viridi Abstract - 16
  • 2. Components of Soybean Plant Cultivation System
  • 3. N NN N N N N N N sunlightplant Water Nitrogen fixing microbe Soil nitrogen Plant nitrogen Components Interactions
  • 4. Parameters Observed Plant height Number of leaves Non-Destructive Soil total nitrogen content Plant tissue total nitrogen content Destructive
  • 6. Why Destructive? Destructive Sampling Method Identical Plants Plant can always represents each other
  • 7. Plant Height Observation Result 0.00 50.00 100.00 150.00 200.00 250.00 0 2 4 6 8 10 12 14 soybeanplantheight(cm) Weeks after planting
  • 8. PlantHeight Time Unit PlantHeight Time Unit Sigmoid Growth Curve 𝐻 = 𝐻𝑚𝑎𝑥 𝐻0 𝐻𝑚𝑎𝑥 − 𝐻0 𝑒 𝑟𝑡 1 + 𝐻0 𝐻𝑚𝑎𝑥 − 𝐻0 𝑒 𝑟𝑡
  • 9. 1 2 Plant Height Data Analysis Whether the destructive sampling method can accomodate a collection of representative data 3 Hypothesis The plants are not identical 4 Objectives and Hypothesis
  • 10. Generating Several Variations of Sigmoid Growth Curves 𝐻 = 𝐻𝑚𝑎𝑥 𝐻0 𝐻𝑚𝑎𝑥 − 𝐻0 𝑒 𝑟𝑡 1 + 𝐻0 𝐻𝑚𝑎𝑥 − 𝐻0 𝑒 𝑟𝑡 0.00 50.00 100.00 150.00 200.00 250.00 0 2 4 6 8 10 12 14 Plantheight(cm) Weeks after planting observation data H1 H2 H3 H4 H5 H6 H7 H8 H9 H10 H11 H12 H13 Difference in Genetic Expressions
  • 11. Eliminating Several Data Destructive Sampling Process Week P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13 0 11,95 11,95 11,95 11,95 11,95 11,95 11,95 11,95 11,95 11,95 11,95 11,95 11,95 1 18,99 18,15 17,34 18,95 19,05 18,20 19,06 20,88 20,84 20,79 18,15 17,34 19,82 2 29,56 27,12 24,85 29,39 29,77 27,32 29,82 35,41 35,23 35,01 27,12 24,85 31,97 3 44,63 39,60 35,01 44,14 45,20 40,14 45,35 57,27 56,73 56,04 39,60 35,01 49,47 4 64,59 56,04 48,23 63,45 65,93 57,27 66,29 86,62 85,29 83,59 56,04 48,23 72,29 5 88,64 76,21 64,59 86,38 91,34 78,68 92,08 120,52 117,85 114,49 76,21 64,59 98,52 6 114,49 98,93 83,59 110,63 119,20 103,31 120,52 153,48 149,08 143,62 98,93 83,59 124,60 7 139,09 122,14 104,12 133,33 146,26 129,07 148,29 180,59 174,45 166,93 122,14 104,12 147,06 8 159,94 143,62 124,64 152,28 169,61 153,48 172,39 199,97 192,43 183,26 143,62 124,64 164,13 9 175,94 161,76 143,62 166,64 187,80 174,52 191,24 212,49 203,96 193,65 161,76 143,62 175,91 10 187,30 175,94 159,94 176,76 200,87 191,24 204,82 220,05 210,90 199,87 175,94 159,94 183,51 11 194,93 186,34 173,13 183,51 209,72 203,67 214,04 224,43 214,91 203,46 186,34 173,13 188,20 12 199,87 193,65 183,26 187,87 215,48 212,49 220,05 226,91 217,18 205,48 193,65 183,26 191,02 13 202,99 198,62 190,74 190,61 219,13 218,52 223,86 228,29 218,44 206,61 198,62 190,74 192,68 Average 11,95 18,98 29,62 45,79 67,73 90,70 113,02 131,76 150,60 167,15 174,98 184,80 196,76 202,99
  • 12. Interactions Between Plant Height and Number of Leaves number of leaves variables as the function of plant height generated from one of simulated data in the previous section, using the following equation: y = 0,85x + c (1.2) With y represents the number of leaves and x represents the plant height. Next we also proposed number of leaves as the function of time, in this case is weeks after planting, using the following equation: y = 15,45x + c (1.3) With y represents the number of leaves and x represents the weeks after planting
  • 13.
  • 14. The plants involved in the research are not identical, thus the usage of destructive sampling method for the soybean plants are not reccomended because it tends to lead into a collection of less representative data Number of leaves as a function of plant height in soybean plant is y=0,85x+c Conclusion
  • 16. Boote, K.J., Kropff, M.J. and Bindraban, P.S., 2001. Physiology and modelling of traits in crop plants implications for genetic improvement. Agricultural Systems, 70(2-3), pp.395-420. Cross, H.Z. and Zuber, M.S., 1973. Interrelationships Among Plant Height, Number of Leaves, and Flowering Dates in Maize 1. Agronomy Journal, 65(1), pp.71-74. Grzesiuk, E., Laubitz, D., Wójcik‐Sikora, A., Zabielski, R. and Pierzynowski, S.G., 2001. Influence of intestinal myoelectrical activity on the growth of Escherichia coli. Bioelectromagnetics: Journal of the Bioelectromagnetics Society, The Society for Physical Regulation in Biology and Medicine, The European Bioelectromagnetics Association, 22(6), pp.449-455. Indonesian Central Bureau of Statistics., 2017. Indonesian Soybean Production Rate Data. https://www.bps.go.id/subject/6/tenaga-kerja.html#subjekViewTab3. [online]. Accessed on September, 10 2019. Indonesian Legume and Tuber Crop Research Institute., 2016. Soybean Production Technology, Indonesian Ministry of Agriculture, pp.1-20. Jeremy Stangroom. Pearson Correlation Coefficient Calculator. Social Science Statistics. https://www.socscistatistics.com/tests/chisquare2/default2.aspx [online] Accessed on September, 13 2019 Krisnamurthi, B., 2010. Manfaat Jagung dan Peran Produk Bioteknologi Serealia dalam Menghadapi Krisis Pangan, Pakan dan Energi di Indonesia. Prosiding Pekan Serealia Nasional, 1(1) pp.1-11. Lauenroth, W.K. and Bradford, J.B., 2006. Ecohydrology and the partitioning AET between transpiration and evaporation in a semiarid steppe. Ecosystems, 9(5), pp.756-767. Madigan, M. T., Martinko, J. M., Bender, K. S., Buckley, D. H., & Stahl, D. A., 2014. Brock Biology of Microorganisms, pp.1157-1158. Shimotashiro, T., Inanaga, S., Sugimoto, Y., Matsuura, A. and Ashimori, M., 1998. Non-destructive method for root elongation measurement in soil using acoustic emission sensors. Plant production science, 1(1), pp.25- 29 Taylor, R., 1990. Interpretation of the correlation coefficient a basic review. Journal of diagnostic medical sonography, 6(1), pp.35-39. References
  • 17.
  • 18. r Value Plant Height Number of Leaves Evaporation Transpiration Plant Water Needs Total Nitrogen of Plant Tissue Total Nitrogen of Soil Nitrogen Fixing Bacteria Population Plant Height 1.00 0.81 -0.31 -0.25 -0.26 -0.37 -0.38 0.12 Number of Leaves 1.00 -0.05 -0.18 -0.09 -0.25 -0.31 0.01 Evaporation 1.00 0.67 0.46 0.55 0.55 -0.40 Transpiration 1.00 0.58 0.70 0.72 -0.39 Plant Water Needs 1.00 0.70 0.46 -0.45 Total Nitrogen of Plant Tissue 1.00 0.48 -0.37 Total Nitrogen of Soil 1.00 -0.42 Nitrogen Fixing Bacteria Population 1.00