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III. Concepts of Fertilizer Evaluation

III. Concepts of Fertilizer Evaluation

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BIOLOGICAL EVALUATION OF FERTILIZERS



281



reliable predictions as to how different fertilizers will influence economic

yields of plants. Consequently, fertilizer evaluation at the present time

is based in part on fundamental considerations and in part on more

empirical studies in which plant response to several sources of a given

nutrient is measured with little consideration of why the plants respond

differently to different fertilizers. The succeeding sections will be

concerned primarily with (1)the techniques of evaluating fertilizers on

the basis of plant response data, and (2) the relationships between the

observed response data and the nature of the plant-soil-fertilizer system

where such relationships have been established.



A. NATURJZ

OF RESPONSECURVES

Numerous examples of response of crops to varying quantities of

fertilizers supplying a deficient nutrient are available in the literature.

The data Iisted in Table V illustrate a typical example. These data show

TABLE V

Average Yields of Irrigated Corn on 9 Sites in Eastern Oregon, as Influenced by

Additions of Nitrogen as Ammonium Sulfatea



a



Nitrogen

(Ib./acre)



Yield

(bu./acre)



0

50

100

150



75.6

99.7

109.6

110.3



From Hunter and Yungen (1955).



that the corn responded to each successive increment of nitrogen supplied

as ammonium sulfate, but the response to each successive increment

decreased and, in fact, the response to the last increment was very

small. Apparently, the yields were approaching some limiting value

which depended upon factors other than the quantity of ammonium

sulfate applied. The data indicate that further additions of ammonium

sulfate fertilizer would not have increased yields appreciably, but

changing other factors in the environment might have changed the

value of the limiting yield appreciably.

Evidence from other experiments indicates that decreases in yields

may occur if fertilizer additions are increased appreciably beyond the

quantities required for the limiting yields. An example of this behavior

is listed in Table VI of Munson and Doll ( 1959), where both excessive

nitrogen and phosphate additions reduced predicted yields below those

predicted for lower rates of nitrogen and phosphate.

Presumably, in the example listed in Table V the corn was responding



282



G . L. TERMAN, D. R. BOULDIN, AND J.



R. WEBB



to the nitrogen component of the ammonium sulfate. In terms of fertilizer

evaluation, the experimenter is interested in determining how some other

source of nitrogen (for example, ammonium nitrate or sodium nitrate)

would have influenced plant response. When two or more fertilizer

sources of the same nutrient are compared under otherwise similar

conditions, two different situations may arise when the results are

analyzed. These two situations are discussed as Case I and Case I1

below.

Case I. Same limiting yield for all sources: fertilizers differ only in

m i e n c y . In this situation the yield with two sources under test approach

the same limiting value and the responses obtained with the two sources

at lower rates of addition are more or less different, depending upon the

relative value of the two sources.

Almost invariably the response function fitted to the data for one

source will become identical to the response function obtained with

the other source if a simple transformation of the nutrient axis is made.

For example, if

'y.4 = f ( X A )

(1)

where Y.%is the yield obtained with quantity

f (X, ) is some arbitrary function, then



XA



of fertilizer A and



Y,=f(bXB)

(2)

where b is a constant and Ys is the yield obtained when quantity X B

of fertilizer B is added.

An example of this situation follows. In a greenhouse experiment

conducted by TVA at Wilson Dam, Alabama, -6+14 mesh granules

of anhydrous dicalcium phosphate ( DCPA ) and concentrated superphosphate (CSP) were compared as sources of phosphorus for oat

forage. Amounts of the two fertilizers supplying 30, 60, 120, and 240 mg.

of phosphorus were mixed with 3 kg. of Hartsells fine sandy loam ( p H

TABLE VI

Dry hlatter Yields of Oats as Influenced by Quantities of Phosphorus Supplied as

4 + 1 4 Mesh Anhydrous Dicalcium Phosphate (DCPA) and 4 + 1 4 Mesh

Concentrated Superphosphate (CSP)

Quantity of P

added (mg. P. per

3 kg. soil)

0

30

60

120

240



Yield of dry matter (g. per culture)

DCPA



CSP



2.2

7.8

12.5

19.1

25.6



2.2

11.9

18.9

23.8

26.6



283



BIOLOGICAL EVALUATION OF FERTILIZERS



5.2), and oats were grown for 84 days. The above-ground portions of the

plants were harvested and were weighed after drying. The results listed

in Table VI show that the yields of dry matter were different when the

smaller quantities of phosphate were added, but the differences between

the yields with the two sources were very small when 240 mg. of phosphorus was added. The data suggest that differences in limiting yields

obtained with the two sources would be very small. The hypothesis

stated in Eqs. ( 1) and ( 2 ) is illustrated by Fig. 2, where the yields are

plotted against the quantity of phosphorus added as concentrated superw



30r



I



I



I



a



a

'

W



I



.*o'



I



I



I



I

-0



Be'-----



20

/



I-



/



LEG END:

0 CSP

P DCPA

LL



0



n



I



w

0



30



60



SO



120 150



180 210 240



X C S P OR ~ . ~ ~ X D C P A

P

QUANTtTY OF (NUTRIENT) ADDED,

MG./ 3 KO. OF SOIL

FIG.2. Yields of dry matter by oats plotted against quantity of phosphorus added

as concentrated superphosphate (XcBp) or 0.50 times that added as anhydrous

dicalcium phosphate ( O.56XD,,,),



phosphate and against the quantity of phosphorus supplied as anhydrous

dicalcium phosphate multiplied by 0.56 (the procedure used to determine the parameter 0.56 will be discussed below). The results in Fig. 2

indicate that the behavior of the two fertilizers conforms to the situation

described by Eqs. (1) and ( 2 ) . This result implies that, if



= 0.56XDCP*



(3)

the same yield of dry matter would have been obtained in the experiment

described above. Thus, the quantities of phosphorus required to produce

any given yield were different for the two fertilizers, but the behavior

of the fertilizers was similar in other respects. In essence, they differed

XCSP



284



G . L. TERMAN, D. R. BOULDIN, AND J. R. WEBB



only by a factor which will be defined later as an availability coefficient

or as an efficiency factor. Extending the above principles to several

sources, the situation denoted by Case I may be described by Eq. (4)

Yi



= f ( b,X,)



(4)



where Y, is the yield obtained with quantity X of fertilizer i; br is a

parameter characterizing fertilizer i; f ( b&) is an arbitrary function

selected to describe the results. It is possible that the same limiting yields

would be obtained and yet Eq. ( 4 ) would not apply to all sources. This

situation will be discussed below.

30 I



L



r



I



I



I



.a.

.

-...

Y



Ar



F'



I



I



i

l



L E G END:

0 AS

0



CN



Case 11. Limiting yields differ among sources. In this situation the

yields with two or more sources do not approach the same limiting value.

An example of this behavior is illustrated in Fig. 3 with data Mulder

( 1956) obtained in a field experiment with spring wheat using ammonium

sulfate and calcium nitrate as sources of nitrogen.

It is obvious that in this case the limiting yields with the two sources

of nitrogen are entirely different and presumably some factor other than

nitrogen per se needs to be studied. In this case, Mulder (1956) found

that when magnesium was added, the yields with the two sources

approached the same limiting value for all practical purposes.

Further examples of Case Z and Case 11. Lorenz and Johnson (1953)

studied the response of potatoes to ammonium sulfate and calcium



285



BIOLOGICAL EVALUATION OF FERTILIZERS



nitrate on Hesperia fine sandy loam (pH 7.5) in greenhouse experiments.

They found that the limiting yields obtained with ammonium sulfate

were much higher than with calcium nitrate. From subsequent laboratory

and greenhouse experiments they concluded the phosphate level in the

soil was rather low and the pH decrease associated with microbiological

transformation of NH4+ to NO3- had increased the ability of the

cultures treated with ammonium sulfate to supply phosphorus to the

plants. When adequate phosphate fertilizer was applied, limiting yields



cn”

v)



a

w

a



0



0



A



o a

w w

~ - n

: 5 l0um

aA

a

a



5

X



5 -



0



A



A

0

0

0

LEGEND:

0 1953

0 1954



a

5



A 1955

0

0

25

50

75

P E R CENT OF A O A C - A V A I L A B L E PZO,

W AT E R-SOLUBL E F O R M



100

IN



FIG.4. hlaximum predicted yield increases of corn to P,O, in several fertilizers

plotted against the percentage of AOAC-available P,O, in water-soluble form. (From

Pesek and Webb, 1957.)



with the two nitrogen sources were very nearly the same, although

perhaps somewhat higher with calcium nitrate than with ammonium

sulfate.

Webb and Pesek (1958) reported a series of experiments performed

in Iowa over a number of years in which several phosphate fertilizers

were compared when hill-placed with corn. In further analysis of the

data (Pesek and Webb, 1957) it was found that the predicted maximum

yield responses to P205varied widely among sources of phosphorus.

Results of their analysis of the data are presented in Fig. 4, where the



286



G . L. TERMAN, D. R. BOULDIN, AND J. R. WEBB



maximum predicted yield response to P205 (predicted limiting yield

with a given source of PzO, minus the yield with no added phosphorus)

is plotted against the percentage of the AOAC-available P205 in watersoluble form. The results listed in this figure demonstrate that indeed

the limiting yields may vary among different sources of the same

nutrient, and in this case it is obvious that the limiting yields are

correlated with the percentage of the AOAC-available P205 in watersoluble form. However, this behavior is not a property of the fertilizer

per se, but depends upon the method of placement, as shown in a

second series of experiments. Webb and Pesek (1959) compared many

of these same fertilizers by broadcasting and plowing under for corn.

The results of the experiments indicate very little if any difference among

fertilizers in which the AOAC-available P205in water-soluble form varied

from 0 to 100 per cent. There was no evidence that limiting yields varied

among sources.

Prummel (1957) summarized a series of field experiments in the

Netherlands in which broadcast and row placements of superphosphate,

potassium sulfate, and nitro chalk were compared. He concluded that

broadcast and row placements gave the same limiting yields, but with

row placement the limiting yields were attained at lower levels of applied

nutrient.

Hagin ( 1957) compared powdered and granular superphosphate in

greenhouse experiments with red clover on several soils. On one soil,

powered superphosphate gave much higher limiting yields than granular

superphosphate.

Presumably, a more careful search of the literature would reveal

additional examples of both Case I and Case 11. When Case I prevails,

fertilizer evaluation is reduced to a problem of determining relative

efficiencies; different quantities of a nutrient supplied in either of two

fertilizers will be required to produce a given yield, but if enough of

either source is added the same yield can always be produced. If Case I1

prevails, both relative efficiency and yield potentials must be considered

and both considerations may be very important economically. Within the

range of yields less than the lower of the two limiting yields, relative

efficiency is the important consideration; however, the range of yields

included between the two limiting yields can be obtained only with the

source giving the higher maximum yield.

No fundamental explanation for the observed differences in limiting

yields is evident in all the examples cited above. Perhaps the really

important point to consider is that the phenomena described by Case I1

are worthy of further research work. In many areas of the world, limited

arable crop land together with large populations demand that crops be



BIOLOGICAL EVALUATION OF FERTILIZERS



287



fertilized to essentially the limiting yield level. Perhaps the underlying

causes of different limiting yields with different sources of nutrients

will provide additional clues on how to raise the limiting yields to

higher values. At any rate, it is surely unsatisfactory to leave any of these

observations unexplained.

In some cases, differences in limiting yields between two fertilizers

may be the result of differences in accessory nutrients in the two

fertilizers. Ordinary superphosphate usually contains about 5 per cent

sulfur ( S ) in the form of CaS0,.2H20, whereas fertilizers prepared from

electric furnace phosphoric acid usually contain very small amounts of

sulfur. Under conditions of sulfur deficiency, differences between ordinary superphosphate and fertilizers prepared from furnace acid may be

the result of differences in sulfur supplied. Perhaps equally noteworthy

are differences in micronutrient contents. Bingham ( 1959) determined

the micronutrient contents of several phosphorus sources in the United

States and found that the eastern phosphates usually contained less zinc

than western phosphates. Clark and Hill (1958) analyzed several samples

of rock phosphate. They found considerable variation in the micronutrient content of phosphates from different deposits and among samples

from the same deposit. Phosphates and phosphoric acid prepared from

electric furnace phosphorus contain much lower quantities of micronutrient elements than corresponding products prepared from “wet

process a c i d (phosphoric acid produced from rock phosphate and

sulfuric acid).

As illustrated by the data of Lorenz and Johnson (1953), which

were quoted above, the fertilizer reactions with the soil may influence

the ability of the soil to supply nutrients to plants, particularly when

band placements are used. Lindsay and Stephenson (1959a) demonstrated that the solution formed when superphosphate is placed in soil

may dissolve considerable amounts of iron, aluminum, and manganese.

Presumably, other elements are also influenced by these solutions. Other

fertilizer solutions may behave in a similar fashion, although the ability

to dissolve the various elements may vary widely among fertilizers.

Hence, the fertilizer may change the ability of the soil to supply

nutrients to the plant, even though the fertilizer itself does not contain

any of the nutrients in question.

One other aspect of the situation may be noteworthy. When comparing band placements of phosphates, rather high concentrations of

phosphate in the soil solution adjacent to the band may be produced

with AOAC water-soluble phosphates ( Bouldin and Sample, 1959b).

With AOAC water-insoluble phosphates, the concentration of phosphate

in the soil solution may be somewhat lower. Because the seedling plant



288



G. L. TERMAN, D. R. BOULDIN, A h 9 J. R. WEBB



has a rather restricted root system, the higher concentrations of phosphate in the soil solution produced by the water-soluble phosphate may

result in a plant much better supplied with phosphorus than one adjacent

to a band of AOAC water-insoluble phosphate. This in turn may lead

to a generally more vigorous plant in the succeeding growth period.

Perhaps a mechanism such as this would explain the different limiting

yields observed by Pesek and Webb (1957). A research project to test

this hypothesis may be worth while.

In the preceding discussion the general occurrence of two situations

has been noted, namely, under situations denoted by Case I, the same

limiting yields are obtained with different sources of the same nutrient;

whereas under the situations denoted by Case 11, different limiting yields

are obtained. In the succeeding two sections the techniques of fertilizer

evaluation in these two situations will be discussed.



B.



TECHNIQUES



FOR



EVALUATING

FERTILIZERS

WITH

LIMITING

YIELDS



THE



SAME



For the most part, the principles of biologicaI assay may be applied

to the results in Case I. Black and Scott (1956) and White et al. (1956)

have discussed the application of these principles to fertilizer evaluation

in a very concise manner. In terms of fertilizer nutrient added



a=yX

where a is the availability, y is the availability coefficient, and X is the

quantity of nutrient added.

Using this definition of availability, fertilizer evaluation is reduced to

the problem of determining the availability coefficients for each of

several sources of the same nutrient. In general, this procedure is useful

only when the quantity of one nutrient is varied, while all others are

kept at a constant level. For example, several sources of phosphate may

be compared in an experiment with levels of added nitrogen and

potassium kept constant. Usually, if levels of other nutrients are vaned,

either intentionally or otherwise, different limiting yields will be obtained

and the results should be analyzed according to procedures described

under Case 11.

As pointed out by Black and Scott (1956), absolute values for a

cannot be measured. The usual method of analysis is to use some

procedure which enables the investigator to derive numbers which are

presumed to be related to a through an unknown proportionality

constant. Some investigators proceed one step further and express the

results relative to some arbitrary standard fertilizer or treatment.



BIOLOGICAL EVALUATION OF FERTILIZERS



289



The theory of this method is illustrated-by the following equations.

The function defined by Eq. (5) expresses the yield as a function of a



Y =f(a)

(5)

where Y is the yield, and f ( a ) is some function of the availability of

the nutrient under study. Since no independent, absolute method of

measuring a is available, the assumption is usually made that numbers

protional to a can be measured. Thus, for practical use Eq. ( 5 ) needs to

be rewritten as Eq. ( 6 )

Y=f(ka)

(6)

Substituting the expression yX for a, Eq. ( 6 ) becomes



Y = f(kyX)



(7)



By proper treatment of data in a well-designed experiment, values of

parameters in Eq. ( 7 ) and values of kyX for a variety of fertilizers may

be determined. The term “availability coefficient index” will be used

to refer to ky. Usually the assumption is that y is independent of X.

Black and Scott (1956) suggest that this is not always true. In a practical

sense, the data will usually be consistent with any hypothesis designed

to test this assumption because experimental errors and the arbitrary

nature of function ( 7 ) makes any valid statistical test difficult. Likewise,

it is difficult to test the hypothesis that f ( k y X ) is different for any of

the fertilizers included in a particular experiment. Thus, for the sake of

convenience, the assumption is usually made that y is independent of

X and that function ( 7 ) will describe the responses to all fertilizers in

a particular experiment, since deviations from this model are usually

within experimental error.

The usefulness of the availability coefficients is illustrated in the

following discussion. Suppose the farmer wishes to know which of

several sources of a nutrient to apply under a given situation. According

to the above discussion, when ylXl = y2X2 = y3X3, etc., the same plant

yields will be obtained. That is,



Y = f ( k y i x i ) = f ( ky,&) = f ( kysX3)

If C1, C2, and C3 are the prices of the nutrient per unit of X ,

respectively, the cost of the yield Cyl, C1’2, Cy3, etc., is

cy1= XlCl



= x2c2

= x3c3



c1.2



c

p

3



Hence, the farmer would probably pick the fertilizer which would be

cheapest. In the example illustrated in Fig. 1, ky for concentrated super-



390



G . L. TERMAN, D. R. BOULDIN, AND J. R. WEBB



phosphate and anhydrous dicalcium phosphate (per unit of P208) is

equal to 1.0 and 0.56, respectively. If concentrated superphosphate could

be purchased for 10 cents per pound, it would be more profitable to use

anhydrous dicalcium phosphate only if the price was less than 5.6 cents

per pound of Pz05. If 10 pounds of P20, were applied as concentrated

superphosphate, fertilizer costs would be one dollar. However, 18 pounds

of P,O, as anhydrous dicalcium phosphate would have to be applied to

obtain the same yield. This 18 pounds of P205 would cost more than a

dollar unless the price were less than 5.6 cents per pound of PZO;. The

same conclusion would be reached regardless of the yield selected. This

example illustrates the usefulness of availability coefficients in decisionmaking processes. The economists usually maximize profits; they might

perhaps arrive at a slightly different conclusion in the above situation

(Munson and Doll, 1959; Pesek and Webb, 1957).

Several types of functions have been used to define the response to

added nutrients [ Eq. ( 7 ) ] in fertilizer evaluation experiments. The

simplest to use is the concurrent straight-line model of White et al.

( 1956 ) . In this model the response to each fertilizer is represented by a

straight line, with the added restriction that all lines pass through a

common point when X = 0 (that is, the yield in the absence of added

nutrient is the same for all sources).

Usually, response is not a linear function of added nutrient except in

cases where the level of the native soil nutrient and the availability of

fertilizer nutrient are low. Furthermore, unless there is other evidence

to the contrary, differences in limiting yields may exist. Hence, this model

is convenient for its simplicity but is questionable unless data on limiting

yields are also available.

Several functions which express yield as a nonlinear function of

added nutrient have been used in analyses of experiments. One of the

most used is Eq. ( 8 ) , commonly called the Mitscherlich equation:

y = A[1 - 1 O - ( b 1 9 + 8 ) ]

(8)

where T is the yield when quantity X of nutrient is applied; A is the

limiting yield, that is, the yield approached as X increases indefinitely; k

is a parameter defined by Eq. ( 6 ) ; y is the availability coefficient of

the fertilizer; and s is the level of nutrient native to the soil. A transformation of this equation, called the Spillman equation, may also be

used :

Y=A-BCX

(9)

where B = A ( lo-"), C = lo-".

For economic interpretation of yield data, polynomial functions of

various forms are commonly used. Munson and Doll ( 1959) have discussed



BIOLOGICAL EVALUATION OF FERTILIZERS



291



these and other equations. Steenbjerg and Jakobsen (1959) and Hagin

(19SO) suggest that a sigmoid-type curve may represent the data better

when available nutrients are very low.

Perhaps the simplest procedure of all is to draw freehand the

response curve for a standard fertilizer, and then use graphical interpolation to compare the other fertilizers. Cooke and Widdowson (1959)

used this procedure. Cooke (1956) plotted response curves for superphosphate and estimated the efficiency of other phosphorus sources in

terms of “superphosphate equivalents.” This method gives results comparable to those obtained by calculation of availability coefficients and

is simple to apply.

Determining the parameters in the Mitscherlich or Spillman equations

by statistical methods for no phosphorus and for each source applied at

more than two levels is laborious. White et al. (1956) calculated the

sum of squares of deviations from the concurrent Spillman model (same

A and B for all sources) for various values of A and B and then picked

the values of A and B that resulted in the smallest sum of squares.

Values of C [Eq. ( 9 ) ] are also obtained by this procedure. By definition,

log C = -kyX. Relative availabilities of the several fertilizers are then

calculated from these values of k y X . Electronic computers materially

reduce the time required for this procedure. Although laborious, this

procedure is a very satisfactory means of analyzing data from experiments in which several sources are applied at two or more quantities.

A common experimental design includes two or more quantities of a

“standard source, and only one quantity of several “test” sources. With

this design, the response data obtained with the “standard” source are used

to calculate A in Eqs. ( 8 ) or ( 9 ) . The value of the parameter A may be

calculated using a least squares procedure described by Eid et al. (1954)

or a graphical procedure used by Bouldin and Sample ( 1959a).

The graphical procedure is applied as follows: Rearranging Eq. ( 8 )

and taking logarithms of both sides

log ( A -Y ) = log AlO-’



-k y X .



(10)

Thus, a plot of the logarithm of ( A -Y ) against X will give a straight

line with slope -ky. Several values of A are picked by inspection and the

logarithms of ( A - Y ) are plotted against X . The value of A is then

selected which gives the best straight line. When X is zero, log ( A -Yo)

= log A10-8 where Yo is the check yield. Substituting this value for

log A10-6 in Eq. ( l o ) , and rearranging:



ky=-



1



X



log



A-Y

A - Yo



___



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