This document presents a summary of several classical theories on plant growth response to nutrients: 1) Liebig's Law of the Minimum states that plant growth is limited by the scarcest nutrient. 2) Blackman's Law of the Limiting Factor states that the growth rate is determined by the slowest acting growth factor. 3) Willcox's Theory of the Nitrogen Constant found plants absorb about 318 lbs of nitrogen per acre at optimum conditions. 4) Spillman's Equation models the relationship between growth amount, maximum possible yield, growth factor quantity, and a constant. 5) Baule Unit defines the amount of nitrogen, phosphorus, or potassium needed to produce 50% of maximum possible

1. A PRESETATION ON
CROP RESPONSE PRODUCTION FUNCTION

2. Introduction
Plant response to nutrients was one of the earliest subjects of scientific plant
investigation. The classical work of Liebig, Blackman, Mitscherlich and others were the basis
for formulating several theories on growth factor limitation and plant response. Knowledge
of these theories lead to better understanding of plant respond to inputs and other
management practices.
Plant growth is a function of its growth factors, which may be considered as
variables, the magnitude and interactions of which determine the amount of growth. This
may be expressed in the form of an equation.
G = f (x1, x2, x3, ………………, xn )
Where , G is a measure of some growth and x1 to xn are various growth factors. )

3. 1. Law of Minimum (Justus Von Liebig, 1840)
Liebig states that the deficiency or absence of one necessary constituent, all
others being present, the soil is rendered barren for all those crops of the life of which
one constituent is indisepensable. It is sometimes referred to as the barrel concept.
The law postulates that when a nutrient in the soil is in the minimum, it limits
the action of other nutrients which may be present in the optimum. Thus, when P2O5 is in
the minimum, crop yield is determined by the status of the P2O5 in the soil.
Fig.: Limiting factors

4. 2.Law of Limiting Factor (Blackman, 1905)
The law states that when a process is conditioned as to its rapidity by a
number of separate factors, the rate of the process is limited by the pace of the
slowest factor.
Fig.: Diagram to illustrate Blackman’s law of limiting factor

5. 3. Theory Of Nitrogen Constant 318 (Willcox)
The nitrogen constant 318 represent the amount of nitrogen
absorbed per acre by all kinds of plants in a single growth cycle if all
conditions are at optimum.
The constant 318 was used for calculating the maximum possible yield of
crops with the equation
y = k/n
Where,
y = above ground dry matter
n = nitrogen percentage
k = a constant

6. 4. Spillman’s Equation
Spillman exposed the relationship between the amount of growth and
quantity of growth factor as
Y = M(1-Rx )
Where,
Y = amount of growth produced by a given quantity of growth factor X
M = maximum yield possible when all growth factors are present in
optimum amounts
X = quantity of growth factors
R = a constant

7. 5. Baule Unit (Baule, 1918)
Baule suggested that the unit of fertilizer, or any other growth factor, be
taken as that amount necessary to produce a yield that is 50% of the difference
between the maximum possible yield and the yield before that unit was applied.
Plants require different amount of Nitrogen, phosphorus and potassium,
but the amount in pounds of each required to produce a yield that is 50% of the
maximum possible yield is called 1 Baule Unit.
The values of the baule unit in pounds per acre of N, P2O5 and K2O are 223,
45 and 76 respectively. Therefore, 1baule unit of N = 1baule unit of P2O5 = 1unit of
K2O.

8. Reference
Reddy S.R. Growth regulator and growth analysis. Principles of crop production. First
Edition. Ludhiana. Mrs. Usha Raj Kumar for Kalyani Publishers, New Delhi. 2000.
p 20-26.

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