# 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 Maxium"

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 predicted growth Soybeans (Measured growth) (calculated growth) Low phosphorus 83% Low nitrogen 71% Both low phosphorus actual result 57% 59% (83% x 71%) and low nitrogen Low moisture 66% Low nitrogen 27% Both low moisture actual 18% 18% (66% x 27%) and low nitrogen Nickel addition 42% Copper addition 71% Vanadium addition 39% All 3 metals actual 10% 11% (42% x 70% x 39%) Presence of insects 37% Nutrient deficiencies 78% Both presence of insects and nutrient deficiencies actual 29% 29% (37% x 78%) 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

#### 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