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 growth factors are arithmetically additive. 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 x0.5 0.5 x 0.5 x 0.5 or 0.001 of optimum (0.1%).

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 x0.9 0.9 x 0.9 x 0.9 or 0.349 of optimum (34.9%).

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

Nitrogen Phosphorus Potassium Calcium Magnesium Sulfur Iron Zinc Manganese Copper Boron Chlorine Cobalt Sodium Nickel

B. Non-nutrient elements and nutrients excesses that cause toxicities (stresses)

Nickel Cadmium Nickel Copper Boron Sodium chloride Aluminium Bicarbonate others

C. Interactions of the nutrients

Cation ratios (metals) Carbon:Nitrogen ratio recycling available soil ratios of heavy metals ratios of all the nutrients Nitrate vs ammoniacal nitrogen

D. Soil Conditioning requirement and physical processes

Low pH (soluble Al) high pH salinity, EC (electrical conductivity) either too low or too high, ratios of sand vs. silt vs. clay presence of rocks soil organic matter soil aeration limestone soil moisture conditions (frequency of rain or irrigation) depth to water table other subsoil conditions earthworms cation exchange capacity soil erosion (dust and water) redox, soil crusting structures of soil that give aeration and water penetration fixation of nutrients by soil hydrophobic conditions other aspects of soil quality, slope and topography of lands

E. Additional biology

Favorable and unfavorable microorganisms Mycorrhizae Diseases Insects Weeds other macro organisms and anaerobic decomposition products

F. Weather factors

Intensity, amount, frequency of rain events Wind Hail Snow day and night temperature times of freezing, humidity light hours and percent of light saturation (cloud cover) photoperiods air pollution

G. Management

Crop rotations timing of operations choice of tillage use of appropriate cultivars and varieties irrigation fertilizer distribution use of soil conditioners to correct problems

External links

• Law of the Maximum, in Handbook of soil science by Malcolm E. Sumner

References

1. Wallace, A., and Garn A. Wallace (1993). "Limiting Factors, High Yields, and Law of the Maximum". Horticultural Reviews 15. doi:10.1002/9780470650547.ch10.
2. 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.
3. Arthur Wallace & Richard E. Terry (1998). "Handbook of Soil Conditioners: Substances That Enhance the Physical Properties of Soil": 29–39. ISBN 0-8247-0117-8.