🧫 PREDICTING YIELDS

Yield prediction links soil test values, fertilizer doses, and crop response models to support profitable nutrient recommendations.

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Predicting Yields Using Nutrient Functions

Nutrient function Crop yield is a function of 4 major factors:

Yield = f (crop, soil, climate, management).

Nutrient functions are fitted using data obtained in experiments conducted

either in deductive or inductive approach.

Deductive approach

Deductive approach utilizes the natural variation in soil fertility for

calibrating soil test values. Multilocation trials are carried out with same set

of treatments. The responses are then fitted in the fertilizer prescription

models.

Colwell (1967) developed this approach on the basis that some

variables, which affect the response of crop to fertilizers, if omitted from the

correlation between soil test and crop response, led to poor correlations. To

23 (7/16)

prevent this difficulty, a calibration model was suggested based on the

generalization of coefficients of an orthogonal polynomial yield-response

model, which can include all the variables affecting the responses to

fertilizers.

Inductive approach

This approach is by creating fertility gradient artificially in a particular

experimental location by addition of fertilizers. The approach of inducing

fertility gradient (Ramamoorthy, 1970) aims at eliminating influence of the 3

out of 4 factors in the yield function, namely: crop, climate and management

in the experimental location.

A large field having wide variation in fertility is chosen in a location. It

is divided into 4 strips, which are treated with 4 doses of N, P and K

fertilizers, viz., control (N0P0K0), ½ normal dose (N½ P½ K½), normal dose

(N1P1K1) and double dose (N2P2K2). The normal doses are fixed based on

nutrient fixing capacity of the soil. Exhaustive crop like maize is grown.

The calibration crop experiment is then laid out. For the purpose of

correlation, 21 treatments having one untreated check plot are tested.

Quadratic Model:

Percentage of yield maximum concept (sufficiency concept)

This is commonly known as Mitscherlich and Bray approach. An

empirical relationship is developed between percent yield, soil test, and

fertilizer maximum yield (Bray, 1944).

Col1	23 (8/16) Y = A (1-10- Cs b – C x)	Col3	Col4	Col5	Col6	Col7	Col8

0 2 4 6 8 10 12 14

Units of growth factor

(soil and fertilizer)

% of maximum

yield

Presently, this approach is modified and used by the Department of

Agriculture, Tamil Nadu for giving site-specific fertilizer recommendations.

The modified Mitscherlich-Bray equation is:

Log (A-Y) = Log A - Csb – Cx

Where, A = calculated maximum yield

Y = percentage yield

Cs = proportionality factor for soil nutrient

b = soil test value

x = dose of fertilizer added.

The maximum yield (A) is calculated by extrapolation.

Quadratic Model:

Regression model for maximum profit

The amount of fertilizer that produces the greatest profit per hectare is

called the optimum dressing (Cooke, 1972). Ramamoorthy (1974)

established a significant relationship between soil tests, added fertilizers and

crop yields by fitting a multiple regression of the quadratic form ( orthogonal

polynomial yield-response model) :

Y = A + b1SN + b2SP + b3SK + b4SN [2] + b5SP [2] + b6SK [2]

• B7FN + b8FP + b9FK + b10FN [2] + b11FP [2] + b12FK [2]

• b13SNFN + b14SPFP + b15SKFK

Where Y = Crop yield (kg/ ha)

A = Intercept

bi = Regression coefficient

SN, SP, SK = Available contents of soil N, soil P and Soil K

FN, FP, FK = Fertilizer N, Fertilizer P, Fertilizer K

Fertilizer calibrations for varying soil test value for obtaining maximum

profit per hectare could be derived where the response to added nutrient

follows the law of diminishing returns (Ramamoorthy, 1974)

Fertilizer adjustment equation is derived in the form:

FN = a - b SN – c R

FP2O5 = a - b SP – c R

FK20 = a - b SK – c R

Where,

Cost of fertilizer nutrient (Rs./kg) R =

Value of produce (Rs./kg)

Linear model:

Targeted Yield approach

Fertilizer recommendation must aim at providing balanced nutrition to

crops. Balanced nutrition should ensure the nutrients to be present in 23 (10/16)23 (9/16)

available forms in adequate quantities and required proportion for the plant

in order to produce maximum yield. The requirement of nutrient to produce

the expected yield can be worked out based on nutrient uptake .

Nutrient requirement of crops

Crop	Nutrient Requirement (kg) to produce 100 kg of economic produce	Col3	Col4
Crop	N	P2O5	K2O
Rice Wheat Maize Sorghum Finger millet Chick pea Soya bean Ground nut Potato Cotton	2.01 2.45 2.63 2.24 2.98 4.63 6.68 5.81 0.39 4.45	1.12 0.86 1.39 1.33 1.13 0.84 1.77 1.96 0.14 2.83	3.00 3.28 3.58 3.40 3.90 4.96 4.44 3.01 0.49 7.47

Liebig’s law of minimum states that the growth of plants is limited by

the plant nutrient element in the smallest quantity, when all others being

present in adequate amounts. This forms the basis for fertilizer application

for targeted yields, first advocated by Troug (1960) by significant linear

relationship between the yield of grain and uptake of nutrients. Yield target

can be projected within the linear region of the response function.

This approach, popularly known as Soil Test Crop Response

Function ( STCR ), implies that for obtaining a specific yield (grain or any

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other economic produce) a definite quantity of the nutrient must be taken up.

This value can be determined by the magnitude of the expected yield (T in

q/ha) and the nutrient requirement to produce unit quantity of that target (NR

in kg/ha).

Once it is known for a target yield, the fertilizer dose (FD kg/ha) can

be estimated.

It is done by taking into account the efficiency of soil contribution (CS

in percent) from the soil available nutrients (STV in kg/ha), and the efficiency

of fertilizer of fertilizer contribution (CF in percent) from the fertilizer nutrients

(FD in kg/ha) towards the total uptake.

NR CS FD = X 100 T

CF

CF

X 100 T

X STV

Where F and S stand for fertilizer and soil nutrient in Kg/ha and T is

yield target in q/ha.

23 (11/16)

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Summary Cheat Sheet

Key Recall Points

• PREDICTING YIELDS is exam-relevant for SSAC122 and objective questions in soil science.
• Use soil-test based interpretation with focus on pH, CEC, and nutrient availability.
• Apply the 4R principle: right source, right rate, right time, and right method.

Exam Traps

• Do not mix up soil fertility concepts with fertilizer quantity alone.
• Numerical and term-based questions often test definitions, units, and threshold values.
• In problem-solving, interpretation must follow soil reaction, crop stage, and management context.

References

3 sources • [1] [2] [3]

[1]

ICAR e-Course: Soil Chemistry, Soil Fertility and Nutrient Management

Official

[2]

Brady and Weil, The Nature and Properties of Soils

Book

[3]

Indian Council of Agricultural Research

Official