Law of Maximum
The Law of Maximum also known as Law of the Maximum is a principle developed by Arthur Wallace which states that total growth of a crop or a plant is proportional to about 70 growth factors. Growth will not be greater than the aggregate values of the growth factors. Without the correction of the limiting growth factors, nutrients, waters and other inputs are not fully or judicially used resulting in wasted resources.[1][2][3]
Applications
The factors range from 0 for no growth to 1 for maximum growth. Actual growth is calculated by the total multiplication of each growth factor. For example, if ten factors had a value of 0.5, the actual growth would be:
- 0.5 x 0.5 x 0.5 x 0.5 x 0.5 x 0.5 x 0.5 x 0.5 x 0.5 x 0.5 = 0.001, which is 0.1% of optimum.
If each of ten factors had a value of 0.9 the actual growth would be:
- 0.9 x 0.9 x 0.9 x 0.9 x 0.9 x 0.9 x 0.9 x 0.9 x 0.9 x 0.9 = 0.349, which is 34.9% of optimum.
Hence the need to achieve maximal value for each factor is critical in order to obtain maximal growth.
Demonstrations of "Law of the Maximum"
The following demonstrates the Law of the Maximum. For the various crops listed below, one, two or three factors were limiting while all the other factors were 1. When two or three factors were simultaneously limiting, predicted growth of the two or three factors was similar to the actual growth when the two or three factors were limits individually and then multiplied together.
| Percent of Optimum growth
(Measured growth) |
predicted growth
(calculated growth) | |
|---|---|---|
| Soybeans | ||
| Low phosphorus | 83% | |
| Low nitrogen | 71% | |
| Both low phosphorus | actual result 57% | 59% (83% x 71%) |
| and low nitrogen | ||
| Wheat | ||
| Low moisture | 66% | |
| Low nitrogen | 27% | |
| Both low moisture | actual 18% | 18% (66% x 27%) |
| and low nitrogen | ||
| Bush beans | ||
| Nickel addition | 42% | |
| Copper addition | 71% | |
| Vanadium addition | 39% | |
| All 3 metals | actual 10% | 11% (42% x 70% x 39%) |
| Tomato | ||
| Presence of insects | 37% | |
| Nutrient deficiencies | 78% | |
| Both presence of insects and nutrient deficiencies | actual 29% | 29% (37% x 78%) |
| Tomato – poor physical soil conditions | ||
| Correction with organic matter | 43% | |
| Correction with P.A.M. | 82% | |
| No corrections | 33% | 18% (66% x 27%) |
| Corrections with both organic matter and P.A.M. | 100% |
Growth Factors
A. Adequacy of Nutrients
B. Non-nutrient elements and nutrients excesses that cause toxicities (stresses)
C. Interactions of the nutrients
|
D. Soil Conditioning requirement and physical processes
|
E. Additional biology
|
F. Weather factors
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G. Management
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External links
References
- ^
Wallace, A.; Garn A. Wallace (1993). Limiting Factors, High Yields, and Law of the Maximum. Vol. 15. pp. 409–448. doi:10.1002/9780470650547.ch10. ISBN 9780470650547.
{{cite book}}:|journal=ignored (help) - ^ Arthur Wallace (1994). "Generalized environmentally sound rules for use of fertilizers". Communications in Soil Science and Plant Analysis. 25 (1 & 2): 77–86. doi:10.1080/00103629409369009.
- ^ Arthur Wallace; Richard E. Terry (1998). Handbook of Soil Conditioners: Substances That Enhance the Physical Properties of Soil. CRC Press. pp. 29–39. ISBN 978-0-8247-0117-8.