Liebig's law of the minimum

The law has also been applied to biological populations and ecosystem models for factors such as sunlight or mineral nutrients.

Only by increasing the amount of the limiting nutrient (the one most scarce in relation to "need") was the growth of a plant or crop improved.

For example, the growth of an organism such as a plant may be dependent on a number of different factors, such as sunlight or mineral nutrients (e.g., nitrate or phosphate).

μI,μN,μP are the specific growth rates in response to the concentrations of three different limiting nutrients, represented by I,N,P respectively.

The use of the equation is limited to a situation where there are steady state ceteris paribus conditions, and factor interactions are tightly controlled.

In human nutrition, the law of the minimum was used by William Cumming Rose to determine the essential amino acids.

In 1931 he published his study "Feeding experiments with mixtures of highly refined amino acids".

Frances Moore Lappé published Diet for a Small Planet in 1971 which popularized protein combining using grains, legumes, and dairy products.

When he wrote his autobiography he recounted in 1993 the finding: More recently Liebig's law is starting to find an application in natural resource management where it surmises that growth in markets dependent upon natural resource inputs is restricted by the most limited input.

Neoclassical economic theory has sought to refute the issue of resource scarcity by application of the law of substitutability and technological innovation.

[10] This would be either the point where the increment to be advanced is so small it cannot be justified economically or where technology meets an invulnerable natural barrier.

It may be worth adding that biotechnology itself is totally dependent on external sources of natural capital.