Ideal and saturated soil fertility as bench marks in
nutrient management
II. Interpretation of chemical soil tests in relation
to ideal and saturated soil fertility
Bert H. Janssen a,*, Peter de Willigen b
a Wageningen University, Department of Soil Quality, The Netherlandsb Alterra, Green World Research, Soil Science Centre, P.O. Box 47, 6700 AA Wageningen, The Netherlands
Available online 18 April 2006
Abstract
In a previous paper (Part I), the ideal soil fertility and the saturated soil fertility were expressed on a relative scale, called soil fertility
grade (SFG). In the current paper (Part II), the relation between SFG and soil test values is discussed. The required uptake of nutrients
from the soil is translated into soil organic carbon, P-Olsen, exchangeable K, and pH (H2O) using relationships developed for a model on
Quantitative Evaluation of the Fertility of Tropical Soils (QUEFTS). Target soil test values were calculated for target yields between 2
and 10 Mg ha�1 season�1. The required uptake of soil nitrogen is a function of target yield, and it is linearly related to soil organic carbon.
Results of the calculations indicate that when target yields are less than 7–8 Mg ha�1, stover must be incorporated to maintain soil organic
carbon above the critical level of 6 g kg�1. When yields are below 2 Mg ha�1, also organic sources from outside the field have to be
brought in.
The interpretation of chemical soil test values according to the ISF-SSF framework may be rather difficult in practice, as is demonstrated
with eight African soils. The major reason is that the soil supplies of N, P and K seldom are in the same proportions as in ISF-SSF. For none of
the used African soils replacement input or a neutral nutrient budget would be the best management option. Replacement input will often lead
to inefficient use and even waste of nutrients. Optimum soil test values depend on target yield, but the ratios of soil test values do not depend on
target yield. Therefore key values were established for the ratio of soil organic carbon to P-Olsen and for the ratio of soil organic carbon to the
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Agriculture, Ecosystems and Environment 116 (2006) 147–155
Abbreviations: CEC, cation exchange capacity (mmolc kg�1); Ex-K, soil exchangeable K (mmol kg�1); HSUgsK, maximum K uptake from soil
(kg ha�1 season�1); HSUgsN, maximum N uptake from soil (kg ha�1 season�1); HSUgsP, maximum P uptake from soil (kg ha�1 season�1); IK, input of
K (kg ha�1); IN, input of N (kg ha�1); IP, input of P (kg ha�1); IUgsK, K derived from input, present in grain and stover (kg ha�1); IUgsN, N derived from input,
present in grain and stover (kg ha�1); IUgsP, P derived from input, present in grain and stover (kg ha�1); ISF, ideal soil fertility, fertility at which the soil in
combination with replacement nutrient input does exactly satisfy the nutrient demand of a maximally producing crop, provided no nutrients get lost; PhE,
physiological efficiency (or internal utilization efficiency), ratio of grain yield (Y) to uptake in grain and stover (Ugs) (kg kg�1); PhEN, physiological efficiency
of nitrogen, ratio of grain yield (Y) to uptake of nitrogen in grain and stover (UgsN) (kg kg�1); PhEP, physiological efficiency of phosphorus, ratio of grain yield
(Y) to uptake of phosphorus in grain and stover (UgsK) (kg kg�1); pH (H2O), soil pH measured in a 1:2.5 extract of soil: water; P-Olsen, soil P extracted with
0.5 M NaHCO3 (mg kg�1); QUEFTS, Quantitative Evaluation of the Fertility of Tropical Soils; RAS, required amount of stover (Mg ha�1); RF, recovery
fraction, fraction of applied nutrients that is absorbed by the crop in grain and stover (IUgs (I)�1, kg kg�1, subscripts c, a, refer to crop, accumulation; RFK,
recovery fraction of applied K (kg kg�1); RFN, recovery fraction of applied N (kg kg�1); RFP, recovery fraction of applied P (kg kg�1); Sav, soil available
nutrients (kg kg�1); SFG, soil fertility grade, fraction of SSF; SSF, saturated soil fertility, fertility at which the soil by itself does exactly satisfy the nutrient
demand of a maximally producing crop; SOC, soil organic carbon (g kg�1); SOM, soil organic matter (g kg�1); SUgs, nutrients, derived from soil, present in
grain and stover (kg kg�1); SUgsK, potassium, derived from soil, present in grain and stover (kg kg�1); SUgsN, nitrogen, derived from soil, present in grain and
stover (kg kg�1); SUgsP, phosphorus, derived from soil, present in grain and stover (kg kg�1); TEx-K, target soil exchangeable K (mmol kg�1); TP-Olsen, target
soil P extracted with 0.5 M NaHCO3 (mg kg�1); TSOC, target soil organic carbon (g kg�1); TUgs, nutrients present in grains and stover at target yield (kg ha�1);
TY, target yield (Mg ha�1); UgsN, nitrogen present in grains and stover (kg ha�1); UgsP, phosphorus present in grains and stover (kg ha�1)
* Corresponding author at: Department of Plant Sciences, Wageningen University, P.O. Box 430, 6700 AK, Wageningen, The Netherlands.
Tel.: +31 317 482141; fax: +31 317 484892.
E-mail address: [email protected] (B.H. Janssen).
0167-8809/$ – see front matter # 2006 Elsevier B.V. All rights reserved.
doi:10.1016/j.agee.2006.03.015
B.H. Janssen, P. de Willigen / Agriculture, Ecosystems and Environment 116 (2006) 147–155148
square root of exchangeable K. Based on these key values, a new classification scheme with recommended input ratios is presented. The
scheme has six classes for N and P ratios, and seven classes for N and K ratios.
# 2006 Elsevier B.V. All rights reserved.
Keywords: Nutrient input; Nutrient ratios; Nutrient use efficiency; Recovery fraction; Replacement input; Soil tests; Soil fertility; Stover incorporation;
Target yield
1. Introduction
In a previous paper (Janssen and de Willigen, 2006),
concepts from plant physiology, soil chemistry and
agronomy were integrated into the framework of ideal soil
fertility (ISF) and saturated soil fertility (SSF). Fertility itself
was considered in a restricted sense as the capacity of the
soil to supply nutrients to the crop. We alleged that the
resulting coherent and transparent framework would enable
the setup of nutrient management advisory frameworks, on
the basis of chemical soil test values, for any crop at any
place. In routine soil testing, chemical soil characteristics are
assessed with the objective of ‘obtaining a value that will
help to predict the amount of nutrients needed to supplement
the supply in the soil’ (Tisdale et al., 1985). The required
nutrient supplement depends on the economics of fertilizer
use. The ISF-SSF framework, however, takes sustainability,
environmental protection and balanced plant nutrition as
starting points.
ISF and SSF were expressed in a relative scale, called
soil fertility grade (SFG). The value of SFG was set at 1
for saturated soil fertility (SSF). At the ideal soil fertility
(ISF), SFG is a fraction (1 � RF) of SSF, where RF stands
for the recovery fraction of input nutrients. ISF is
precisely the steady-state soil fertility level that is
obtained when nutrient input is equal to nutrient output
in harvested products and no nutrients get lost. In the
present paper, the relation of ISF and SSF with soil test
values is discussed. Although a soil test is seen as a
chemical method for estimating the nutrient-supplying
power of a soil (Tisdale et al., 1985), direct relations
between data from chemical soil analysis and nutrient
supply by the soil are seldom presented. We apply
equations developed for that purpose by Janssen et al.
(1990) in the model on Quantitative Evaluation of the
Fertility of Tropical Soils (QUEFTS).
In this paper, Section 2 describes the QUEFTS
relationships between nutrient uptake and chemical soil
data and their use in the ISF-SSF framework. Section 3
deals with maintenance of organic matter, required
chemical soil test values and nutrient inputs in relation
to target yield. Section 3 also discusses the interpretation of
soil test values for N, P and K in practice. Section 4
discusses the applicability of the framework of ideal and
saturated soil fertility in practice, the implications of N:P:K
proportions and the validity of neutral nutrient budgets and
replacement input.
2. Relations between soil fertility indices and
nutrient uptake from soil
2.1. Relations developed for the model QUEFTS
The model QUEFTS (Janssen et al., 1990) uses relations
between data from chemical soil analysis and nutrient
uptake by maize. They are based on experimentally
established regression equations derived from fertilizer
field trials in Suriname and Kenya, described in earlier
reports (Janssen, 1973, 1975; Guiking et al., 1983; Smaling
and Janssen, 1987; Boxman and Janssen, 1990) and in
unpublished student theses and reports of the Centre of
Agricultural Research in Suriname (CELOS). For the sake
of simplicity, we apply here the equations of the original
QUEFTS paper (Janssen et al., 1990). Somewhat different
equations proved more appropriate in specific areas
(Smaling and Janssen, 1993; Samake, 2003), but they
require more input data than those of the original version. In
fertilizer trials designed to find relations between chemical
soil analysis and nutrient uptake, it is essential that the crop
grows under excellent conditions and that the nutrient under
study is the major growth limiting factor. Only if soil fertility
is less than saturated soil fertility (SFG < 1) for the
particular nutrient, and the other nutrients, water and
sunshine are amply available, the uptake of the particular
nutrient can be the highest possible uptake from soil.
Between 10 and 20 soil properties have been investigated
for the development of the original QUEFTS model, of
which four proved best serving the purposes: soil organic
carbon (SOC), ‘available’ P according to the method of
Olsen, exchangeable K (Ex-K), and pH (H2O) (Janssen
et al., 1990). The relationships of the uptake of N, P and K
with SOC, P-Olsen and Ex-K are affected by pH (H2O), for
which different pH correction factors are applied in
QUEFTS. Using one fixed value of pH, the pH correction
factors can be left out provided the coefficients in the
equations have been adopted to that pH. At ideal soil fertility
pH must be optimum. A value of 6 for pH (H2O) is
considered as optimum. For soils with pH (H2O) of 6, the
following equations are used to calculate the highest
possible uptake (in grain and stover) from soil (HSUgsN,
HSUgsP, HSUgsK, in kg ha�1 season�1):
HSUgsN ¼ 5SOC ðg kg�1Þ (1)
HSUgsP ¼ 0:35SOC ðg kg�1Þ þ 0:5P-Olsen ðmg kg�1Þ (2)
cosystems and Environment 116 (2006) 147–155 149
�1
HSUgsK ¼ 250Ex-K ðmmol kg Þ� ð2þ 0:9SOC ðg kg�1ÞÞ�1: (3)
In this paper a modified version of Eq. (3) is used to
facilitate the calculation of the ratio of soil nutrients in
Section 3.4:
HSUgsK ¼ 250Ex-K ðmmol kg�1ÞðSOC ðg kg�1ÞÞ�1: (4)
At a value of 20 g kg�1 for SOC, Eqs. (3) and (4) are
identical.
Although the equations were found by regression
analysis they be interpreted in terms of soil chemistry. It is
assumed that the mass of the topsoil (0–20 cm) is
2500 Mg ha�1, and that C:N is 10; so, 1 g kg�1 of SOC
represents 2500 and 250 kg ha�1 of organic carbon and N,
respectively. Eq. (1) calculates that HSUgsN is 5 kg ha�1
per growing season per g kg�1 of SOC, which corresponds
to 2% of organic N in the topsoil. Because the ratio Ugs
(Ugsri)�1 is 0.8 for N (Table 2 in Part I), the total turnover
of N (Ugsri) is 1/0.8 or 1.25 as high as Ugs, and
corresponds to 2.5% of topsoil organic N per season.
Eq. (2) indicates that HSUgsP is related to inorganic P and
to organic carbon and hence to organic P. Exchangeable K
regulates HSUgsK. The inverse relationship between
HSUgsK and SOC in Eqs. (3) and (4) takes into account
that with increasing SOC the cation exchange capacity
(CEC) increases, and hence the relative K saturation
decreases for a given value of exchangeable K. Flaig et al.
(1963) found that CEC of organic matter varies from 2.5
to 4 mmolc per gram organic matter, which comes down to
4–7 mmolc, say 5.5 mmolc per gram SOC. Neglecting the
contribution of clay to CEC, CEC is estimated at 44 and
220 mmolc per kg soil with 8 and 40 g kg�1 SOC, the
values of SOC found for ISF and SSF, respectively, at a
target yield of 10 Mg ha�1 (Table 1). Relative K saturation
is then 5 and 11% at ISF and SSF, respectively. So, K
saturation at ISF is 0.47 times K saturation at SSF, while
Ex-K at ISF is around 0.1 times Ex-K at SSF. In reality, K
saturation will be a little lower, depending on the
contribution of clay to CEC. These are realistic values
for K saturation.
2.2. Calculation of soil fertility indices at ISF and SSF
For the calculation of soil fertility indices as a function of
SUgs, the QUEFTS equations are applied in the opposite
way, again assuming an optimum pH (H2O) of 6. Using T for
target, TSOC, TP-Olsen, and TEx-K are calculated with
Eqs. (5)–(7):
TSOC ¼ 0:2SUgsN (5)
TP-Olsen ¼ 2SUgsP� 0:7TSOC (6)
TEx-K ¼ 0:004� SUgsK� TSOC: (7)
B.H. Janssen, P. de Willigen / Agriculture, E
The values of SUgs are in kg ha�1, those of TSOC in
g kg�1, while TP-Olsen is in mg kg�1, and TEx-K in
mmol kg�1. TP-Olsen and TEx-K in Eqs. (6) and (7) can
only be found after TSOC has been calculated with Eq. (5).
In Table 4 of Part I (Janssen and de Willigen, 2006), an
example was given of the procedure for the calculation of
SUgs. The objective was to calculate the minimally required
values of SUgs at ISF, and therefore maximum values of RF
were applied, being 0.8, 0.4 and 0.6 for N, P and K,
respectively (Part I). For a target yield of 10 Mg ha�1, the
required SUgs values of N, P and K were 40, 17.1 and
62 kg ha�1, respectively. With Eq. (5) was calculated that
TSOC is 8 g kg�1. The values for TP-Olsen and TEx-K
were found with Eqs. (6) and (7), and with TSOC is
8 g kg�1.
3. Some complications and implications
3.1. Maintenance of critical SOM levels
From Eq. (5) it follows that target soil organic carbon
(TSOC) is linearly related to the uptake of soil N (SUgs) and
hence, as shown in Section 2.2 of Part 1, to target uptake
(TUgs) and target yield (TY). At low TY, the calculated
TSOC may be below values considered as critical from a soil
physical point of view. According to Pieri (1989), soils are
physically degraded if the ratio of SOM to (clay + silt) is
below 0.05. Janssen (1993) considered SOM contents of 15
and 35 g kg�1 desired for sandy loams and clay soils,
respectively. For sandy loams containing 100 g kg�1 of clay
and 200 g kg�1 of silt, and for clayey soils containing
400 g kg�1 of clay and 300 g kg�1 of silt, the SOM
requirements set by Pieri and Janssen coincide. In the
present paper we consider a SOM content of 10 g kg�1 or
25,000 kg ha�1 (in a topsoil of 2.5 million kg ha�1) as the
absolute minimum, which comes down to a SOC content of
6 g kg�1 or 15,000 kg carbon per ha. Following Pieri (1989),
this 10 g kg�1 is the critical SOM content of soils with
200 g kg�1 of (clay + silt), i.e. loamy sands to sandy loams.
Given a turnover rate of 2.5% per season (Section 2.1),
375 kg C is converted into CO2 per ha per season, and hence
a same amount of 375 kg C has to be applied with effective
organic matter. Assuming the humification coefficient
(Annex 2 in Part I) is 0.3, the required production of root
C is 375/0.3 or 1250 kg C per ha, and the required
production of root biomass is 1250/0.45 or 2778 kg ha�1.
The corresponding grain yield is 7.5 Mg ha�1, because root
biomass is 0.37 times grain biomass, as follows from Table 2
in Part 1. At lower yields, roots and stubble alone cannot
maintain SOC at the critical level of 6 g kg�1. Other carbon
sources are required. The source easiest at hand is stover.
Assuming that stover has the same values as roots for
humification coefficient (0.3) and C mass fraction
(450 g kg�1), the sum of roots and stover dry matter that
must be worked into the soil is 2778 kg. The required
B.H. Janssen, P. de Willigen / Agriculture, Ecosystems and Environment 116 (2006) 147–155150
Table 1
Soil data at SSF and ISF and inputs at ISF in relation to target maize yield
Unit Target grain yield (Mg ha�1)
10 8 6 4 2
Soil data at saturated soil fertility (SSF)
SOC g kg�1 40.0 32.0 24.0 16.0 8.0
P-Olsen mg kg�1 29.0 23.2 17.4 11.6 5.8
Ex-K mmol kg�1 24.8 15.9 8.9 4.0 1.0
Soil data at ideal soil fertility (ISF)
SOC g kg�1 8.0 6.4 6.0 6.0 6.0
P-Olsen mg kg�1 28.6 22.9 16.5 9.9 3.4
Ex-K mmol kg�1 2.0 1.3 1.0 0.8 0.7
Inputsa at ideal soil fertility (ISF)
Incorporated stoverb kg ha�1 0 0 555 1296 2000
Fractionc 0.09 0.32 1.00
N kg ha�1 200 160 117 74 30
P kg ha�1 28.5 22.8 16.9 10.8 4.8
K kg ha�1 155 124 86 46 6
a Required input of N, P and K to reach target yield on soils with the given characteristics for ideal soil fertility.b Required incorporation of stover to maintain SOC at 6 g kg�1.c Incorporated stover as fraction of total stover production.
amount of stover (RAS in Mg ha�1) is related to grain yield
via:
RAS ¼ 2:778� 0:37TY: (8)
The minimum required TY following from Eq. (8) is
2.027 Mg ha�1, rounded to 2 Mg ha�1. If yields are lower,
organic sources from outside the field or from agroforestry
trees have to be brought in. The required stover incorpora-
tion to maintain SOC at the critical level is given in Table 1.
The incorporation of stover has consequences for the
quantity of nutrients leaving the field, and hence for the
required nutrient inputs and the demanded levels of P-Olsen
and Ex-K. Per ton of stover incorporated, the external input
can be reduced by 5 kg N, 0.45 kg P and 12.5 kg K (see
Table 2 in Part I). Because of the higher SOC content, P-
Olsen can be lower than when no stover is incorporated
Eq. (6), but Ex-K has to be higher Eq. (7).
3.2. Nutrient management in relation to soil fertility
Table 1 lists target soil fertility indices at SSF and ISF,
nutrient applications at ISF, and rate of stover incorporation,
all in relation to target yield. The minimum target yield is set
at 2 Mg ha�1, because at lower yields roots plus stover are
not sufficient to maintain SOC at 6 g kg�1. It is assumed that
no losses occur. SOC and P-Olsen at SSF and ISF are
linearly related to target yield. Exchangeable K decreases
more than proportionally with decreasing target yields. The
effect of stover incorporation on required nutrient input is
stronger for K than for N and P, because straw is relatively
high in K.
In Table 1 SOC and Ex-K are much greater at SSF than at
ISF. In contrast, P-Olsen is hardly higher at SSF than at ISF,
especially when stover is incorporated. Because the recovery
fraction (RF) of N is set at 0.8, it follows from Eq. (9a) in Part I
that soil fertility grade (SFG) for N is only 0.2 at ISF, and
hence SOC at ISF is only 0.2 times SOC at SSF. For P and K,
RF is set at 0.4 and 0.6, and hence SFG at ISF is 0.6 and 0.4 for
P and K, respectively. However, P-Olsen at ISF must be much
greater than 0.6 times P-Olsen at SSF, because SOC
contributes to P supply (Eq. (2)) and SOC at ISF is only
0.2 times SOC at SSF. On the other hand, TEx-K is at ISF
much smaller than 0.4 times Ex-K at SSF, because TEx-K is
linearly related to SOC (Eq. (7)). The data in Table 1
underscore that P-Olsen alone and Ex-K alone are insufficient
to characterize soil P and soil K, respectively, as their
interpretation is greatly affected by soil organic carbon.
At ISF, nutrients are used in the most efficient way, but
when soil fertility is between ISF and SSF, nutrients can still
be used efficiently, provided nutrients are applied according
to I = (1 � SFG)TUgs(RF)�1 (Eq. (6) in Part 1). Above SSF,
the potential loss of nutrients is at least the quantity that
forms the difference between available soil nutrients (Sav)
and the total turnover (TUgsri) of nutrients of the crop:
Sav � TUgsri. The ratio SUgsri (Sav)�1, an indicator for
nutrient uptake efficiency, is then less than 1. Such soils
should not receive any input but must be mined.
High fertility usually is found in soils of volcanic, marine
and fluvial origin, in areas with high livestock density and
around villages. The SSF values of SOC 40 g kg�1, P-Olsen
29 mg kg�1, and Ex-K 24 mmol kg�1 for yields of
10 Mg ha�1 (Table 1) are close to those found near
homesteads on loamy to clayey soils in Tanzania (Baijukya
and De Steenhuijsen Piters, 1998), and to the data of Kenya,
Field 11 in Table 2 referring to soils derived from volcanic
ash in Kenya (Van der Eijk, 1997).
On low fertility soils, mass fractions of N and P in roots
and stover may be very low, resulting in immobilization of N
B.H. Janssen, P. de Willigen / Agriculture, Ecosystems and Environment 116 (2006) 147–155 151
Table 2
Soil data, uptake of soil nutrients, soil fertility grade, required nutrient input, and proportions of soil N, P and K
Referencesa 1 2 3 4 5 6
Country Kenya Tanzania Malawi Malawi Ivory Coast Tanzania Kenya Kenya
Codeb Kwale Tumbi MZ 18 MZ 21 Site VII S2 Field 13 Field 11
Soil test values
pH (H2O)c 6 6 5.8 5.6 6.1 5.8 5.8 6.2
SOC (g kg�1) 6.5 6 4.2 9.3 12.9 18 20 30
P-Olsen (mg kg�1) 0.5 7.5 12.5 10.3 3 6 3.4 59.6
Ex-K (mmol kg�1) 1.6 2 2.6 3.7 2.5 5 10 20
Calculated uptake of soil nutrients (HSUgs), kg ha�1d
N 33 30 21 47 65 90 100 150
P 2.5 5.9 7.7 8.4 6.0 9.3 8.7 40.3
K 62 83 155 99 48 69 125 167
Soil fertility grade (SFG)d
N 0.16 0.15 0.11 0.23 0.32 0.45 0.50 0.75
P 0.09 0.21 0.27 0.29 0.21 0.33 0.31 1.41
K 0.40 0.54 1.00 0.64 0.31 0.45 0.81 1.08
Required inpute
N 209 213 224 192 169 138 125 63
P 64.9 56.6 52.0 50.2 56.2 48.0 49.5 �29.5
K 156 119 0 93 178 143 50 �19
Proportions of uptake of soil N, P and Kf
N 12.9 5.1 2.7 5.5 10.7 9.7 11.5 3.7
P 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0
K 24.4 14.2 20.0 11.8 8.1 7.5 14.4 4.1
a References: 1, Smaling and Janssen (1993); 2, Nyadzi (2004); 3, Makumba (2003); 4, Van Reuler and Janssen (1996); 5, Mowo (2000); 6, Van der Eijk
(1997).b Code refers to the code of the particular field in the cited publication.c Some African soils were selected with pH (H2O) around 6.d Calculated uptake of soil nutrients (HSUgs) and corresponding soil fertility grade (SFG) are explained in the text.e Required nutrient input for a target yield of 10 Mg ha�1.f For the calculation of the proportions of uptake of soil N, P and K, HSUgsP was set at 1.
and P and reducing the uptake fraction of both applied and
native soil N and P. If not sufficient N or P is available for
immobilization, the formed SOM is of poor quality with
high C:N and C:P ratios and low N and P mineralization.
Because of the low nutrient supply, crops are forced to invest
in roots at the expense of grain and straw, resulting in low
physiological nutrient use efficiency (PhE). Sandy and
loamy soils with lower SOC levels than the set minimum
level of 6 g kg�1 have low water-holding and nutrient
retention capacities, so that nutrients are leached easily,
further lowering the nutrient uptake efficiency. Such soils
have a poor physical stability and are prone to slaking, run-
off and erosion. The often resulting low plant density
increases erosion risks and give weeds the opportunity to
germinate. Under such conditions QUEFTS equations
should not be applied. It would be better not to use these
low-fertility soils for production of annual food crops.
3.3. Interpretation of soil test values
In principle, soil test values can be interpreted by
interpolation or extrapolation of the data in Table 1. In
practice, however, interpolation may prove quite difficult,
because the proportions among soil test values often differ
from those at ISF and SSF as given in Table 1. Another
difficulty in practice is that many soils have higher or lower
pH (H2O) than the optimum of 6, for which Table 1 has been
set up. An example of the difficulties encountered during soil
fertility evaluation is given in Table 2. The table presents soil
test values of a number of African soils. These soils were
selected as their pH was close to 6. Soils with other pH could
have been used as well, but it would make the procedure
more complicated because then pH correction factors
(Janssen et al., 1990) must be incorporated in the equations
relating soil test values to uptake of soil nutrients.
The interpretation of the soil test data in Table 2 started
with the calculation of the uptake of soil N, P and K (HSUgs),
applying Eqs. (1), (2) and (4). The further evaluation was
done for target maize yields of 10 Mg ha�1.
The target uptakes (TUgs) and replacement inputs for a
target yield of 10 Mg ha�1 are 200, 28.5 and 155 kg ha�1 of
N, P and K, respectively (Table 1). Soil fertility grade (SFG)
was calculated as the ratio of HSUgs to TUgs. In Part 1 of this
paper, it is shown that at ISF, SFG for N, P, and K is 0.2, 0.6
and 0.4, respectively. Only one of the calculated SFGs,
namely for K in Kenya, Kwale, corresponded to ISF. The
actual SFG was less than SFG at ISF (Table 3) in three of the
eight soils for N, in seven soils for P, and only in one soil for
B.H. Janssen, P. de Willigen / Agriculture, Ecosystems and Environment 116 (2006) 147–155152
Table 3
Key valuesa of SOC (P-Olsen)�1 and SOC (ffiffiffiffiffiffiffiffiffiffiffiEx-Kp
)�1
SOC (P-Olsen)�1b SUgsN (SUgsP)�1c IN (IP)�1d State of soil N and Pe
<0.16 1.43 Only N Extreme N deficiency
0.16–0.28 1.43–2.33 >7 Severe N deficiency
0.28 2.33 7 N deficiency, as at ISF
0.28–1.37 2.33–7 3.5–7 Moderate N deficiency
1.37 7 3.5 Balanced soil N/P, as at SSF
>1.37 >7 <3.5 P deficiency
SOC (ffiffiffiffiffiffiffiffiffiffiffiEx-Kp
)�1 SUgsN (SUgsK)�1 IN (IK)�1 State of soil N and Ke
<4.6 <0.43 Only N Extreme N deficiency
4.6–5.7 0.43–0.65 <1.3 Severe N deficiency
5.7 0.65 1.3 N deficiency, as at ISF
5.7–8.0 0.65–1.3 1.0–1.3 Moderate N deficiency
8.0 1.3 1.0 Balanced soil N/K, as at SSF
8.0–12.9 1.3–3.33 0–1.0 K deficiency
>12.9 >3.33 Only K Extreme K deficiency
a For explanation see text.b SOC, P-Olsen and Ex-K are expressed in g kg�1, mg kg�1 and mmol kg�1, respectively.c SUgs stands for uptake (in maize grain and stover) of soil nutrients. Uptake ratio is expressed in kg kg�1.d Recommended ratios of inputs (I) of N, P and K, expressed in kg kg�1. Recovery fractions of N, P and K were set at 0.8, 0.4, and 0.6, respectively.e State of soil nutrients in relation to the given key valuesa of SOC (P-Olsen)�1 and SOC (
ffiffiffiffiffiffiffiffiffiffiffiEx-Kp
)�1.
K. The required input was calculated as (TUgs � HSUgs)
(RF)�1, where the recovery fractions (RF) were set at the
values derived in Part 1: 0.8, 0.4 and 0.6 for N, P and K,
respectively. The required inputs were of course higher than
replacement input where actual SFG was less than SFG at
ISF. Field 11 from Kenya was so rich in P-Olsen and
exchangeable K, that the calculated required inputs were
negative.
In none of these soils the soil supplies of N, P and K were
in the proportions 2.3:1:3.7 which are found at ISF (Table 4
in Part I). As a consequence for none of these soils
replacement input, or more general a neutral nutrient budget,
would be the best management option. It is concluded that in
practice the simple recommendation to keep nutrient inputs
equal to nutrient outputs seldom is correct and often will
result in inefficient use and even waste of nutrients. Nutrient
management cannot do without chemical analysis of at least
soil N, P, K and pH, and should be tailored to target yields.
3.4. Ratios of soil test values as a tool in nutrient
management
From Table 2 it was inferred that soils usually do not
supply nutrients in appropriate ratios. Which ratios are
appropriate depends on soil fertility level. At SSF, N, P and
K are taken up from the soil in the optimum proportions for
maize (7:1:5.5, Table 4 in Part I). As shown in Section 3.1 in
Part I, neither soil nutrients nor input nutrients are taken up
in optimum proportions at ISF, but the sums of N, P and K
taken up from both soil and input are in the optimum
proportions of 7:1:5.5. Although the required soil test values
depend on target yield level, the ratios of soil test values do
not change with target yield. Hence, these ratios may be used
for the interpretation of soil nutrient states and for advice on
the relative amounts of N, P and K to be added.
In Table 3, four key values of the ratios of the uptakes of
soil N, P and K are presented. One value concerns ISF.
Another one is the balanced situation, where the proportions
of uptake of soil N, P and K are 7:1:5.5. The other two key
values refer to nutrient ratios extremely out of balance with
one nutrient maximally diluted (maximum (PhE)), and the
other maximally accumulated in the crop (minimum (PhE)).
When N is maximally diluted in the crop, PhEN = 70 (Table
2 in Part 1), and when P is maximally accumulated,
PhEP = 100, and hence the lowest value of the ratio of the
uptakes of N and P (UgsN (UgsP)�1) is 1.43 (=100/70). On
the other hand, when N is maximally accumulated in the
crop, PhEN = 30 (Table 2 in Part 1), and when P is
maximally diluted, PhEP = 600, and hence the highest value
of the ratio UgsN (UgsP)�1 = 600/30 = 20. Similarly, the
lowest and highest values of UgsN (UgsK)�1 are 0.43 (=30/
70) and 3.33 (=100/30).
The highest possible uptake of soil nutrients, HSUgs, is
related to SOC for each of the three nutrients N, P and K
(Eqs. (1), (2) and (4)). The ratios SOC (P-Olsen)�1 and SOC
(Ex-K)�1 required for the key values of uptake of soil
nutrients in Table 3 are found by combining Eqs. (1) and (2),
and (1) and (4), respectively. At balanced proportions, the
uptake of N is 7 times the uptake of P, and 1.29 times the
uptake of K. So, for balanced uptake of soil nutrients,
HSUgsN (HSUgsP)�1 must be 7, and HSUgsN (HSUgsK)�1
must be 1.29, and hence
5SOC ¼ 7 ð0:35SOCþ 0:5P-OlsenÞ; or
SOC ðP-OlsenÞ�1is 1:37
B.H. Janssen, P. de Willigen / Agriculture, Ecosystems and Environment 116 (2006) 147–155 153
and
5SOC ¼ 1:29� 250 ðEx-K SOCÞ�1; or
SOC2 ðEx-KÞ�1is 64:5:
It is more convenient to use SOCffiffiffiffiffiffiffiffiffiffiffiEx-Kp� ��1
instead of
SOC2 (Ex-K)�1.
At balanced N/K, SOCffiffiffiffiffiffiffiffiffiffiffiEx-Kp� ��1
isffiffiffiffiffiffiffiffiffi64:5p
which is
8.03. At lower values of SOC (P-Olsen)�1 and
SOCffiffiffiffiffiffiffiffiffiffiffiEx-Kp� ��1
, N is limiting, and at higher values P
and K are limiting. Once more it is stressed that these
relationships are valid for soils with a pH (H2O) around 6.
When the uptakes of soil nutrients are balanced, also the
uptakes of input nutrients must be balanced. The appropriate
ratios of the inputs (IN, IP, IK) can be calculated with the
help the recovery fractions of N, P and K (RFN, RFP and
RFK), which have been set at 0.8, 0.4 and 0.6, respectively:
IN : IP ¼ IUgsN ðRFNÞ�1 : IUgsP ðRFPÞ�1
¼ 7=0:8 : 1=0:4 ¼ 3:5 : 1
IN : IK ¼ IUgsN ðRFNÞ�1 : IUgsK ðRFKÞ�1
¼ 1:29=0:8 : 1=0:6 ¼ 0:97 : 1; rounded 1 : 1:
The values of 3.5 and 1.0 are found in Column 3 in
Table 3 for balanced soil N/P and balanced soil N/K,
respectively, in Column 4.
At ISF, the ratios of the inputs are by definition equal to
the ratios of target uptakes. So the ratio of the inputs of N and
P (IN/IP) is 7, and the ratio of the inputs of N and K (IN/IK)
is 1.29. The uptake of soil nutrients (HSUgs) at ISF is also a
function of the recovery fraction: (HSUgs) = (1 � RF) TUgs
(see Part 1). It follows (see also Table 3):
HSUgsN ðHSUgsPÞ�1 ¼ 7 ð1� RFNÞ ð1� RFPÞ�1
¼ 7ð0:2=0:6Þ ¼ 2:33;
and
HSUgsN ðHSUgsKÞ�1 ¼ 1:29 ð1� RFNÞð1� RFKÞ�1
¼ 1:29ð0:2=0:4Þ ¼ 0:65:
The values of 2.33 and 0.65 are found in Column 2 of
Table 3 for N deficiency, as at ISF in Column 4. The
corresponding SOC (P-Olsen)�1 and SOCffiffiffiffiffiffiffiffiffiffiffiEx-Kp� ��1
(Column 1) were again derived from Eqs. (1), (2) and (4).
In a similar way, the values of SOC (P-Olsen)�1 and
SOCffiffiffiffiffiffiffiffiffiffiffiEx-Kp� ��1
, and the corresponding IN/IP and IN/IK
for the other key uptake ratios of soil nutrients in Table 3
were calculated. At ISF, the ratios SOC (P-Olsen)�1 and
SOCffiffiffiffiffiffiffiffiffiffiffiEx-Kp� ��1
are considerably lower than for soils with
balanced nutrient supplies. At lower ratios than at ISF, more
N, and at higher ratios more P and K must be applied than
corresponds with ‘‘replacement input’’. At the extreme
ratios, only the deficient nutrient should be applied. At
extreme P deficiency, SUgsN (SUgsP)�1 must be 20. When P-
Olsen is 0, the ratio SOC (P-Olsen)�1 is 14.3 (=5/0.35).
Therefore SOC (P-Olsen)�1 for extreme P deficiency could
not be assessed.
4. Discussion
4.1. Application of the ISF-SSF framework
The second part of this paper mainly deals with the
relation between the uptake (in grains and stover) nutrients
derived from the soil (SUgs) and chemical soil test values.
This relation is the most vulnerable component of the ISF-
SSF framework, because not many field trials have been
designed especially for the establishment of the relation
between soil test values and uptake of soil nutrients. We have
used the relationships as applied in the model QUEFTS. Soil
pH (H2O) was set at the optimum value of 6. Studies are on
the way to establish similar soil–crop relationships as used in
QUEFTS, for a wide range of soils and ecological zones,
also for other crops than maize.
Given the fact that additions of nutrients are practically
always needed, farmers ask for advice about application
rates. Recommendations are sometimes presented in
models, but mostly in booklets with tables, and usually
based on soil analytical data. In many tropical environments,
such tables are not available, and extension officers and even
agronomy researchers may feel uncertain about the
interpretation of the soil data (e.g. Drechsel et al., 1996;
Struif Bontkes and Wopereis, 2003; Bruulsema, 2004).
Moreover, recommendations should take environmental
risks of nutrient emissions into account.
As said in Part I (Janssen and de Willigen, 2006), a major
advantage of the proposed framework with ideal and
saturated soil fertility as bench marks is that it can be used as
an building set and be applied to all practical situations, even
if no local experimental results are known. Moreover, the
reasoning and line of thinking underlying the ISF-SSF
framework are helpful in designing effective field trials. It is
possible to calculate the required soil test values for SSF and
ISF, and the corresponding optimum inputs for each nutrient.
In principle, recommendations for soils with other chemical
data can be formulated by interpolation of the ISF-SSF
framework. Five soil fertility classes can be distinguished:
(i) over-saturated, above SSF; (ii) SSF; (iii) satisfactory soil
fertility, between SSF and ISF; (iv) ISF; (v) low soil fertility,
below ISF. The corresponding recommendations for nutrient
inputs are: no input for soil fertility classes (i) and (ii), less
than replacement input for (iii), replacement input for (iv),
and more than replacement input for (v). Eq. (6) in Part I
forms the guideline for input (I) recommendations:
I = (1 � SFG)TUgs(RF)�1.
4.2. Nutrient proportions
The proportions of soil nutrients often differ from the
proportions in replacement input. As a consequence, the
B.H. Janssen, P. de Willigen / Agriculture, Ecosystems and Environment 116 (2006) 147–155154
input of one nutrient must be relatively high and that of
another nutrient relatively low. Replacement input may be
advised without knowledge of soil analytical data. It will,
however, be an exception rather than a rule that replacement
input is the best thing to do. ISF is the only soil fertility level
for which replacement input is recommendable. Never-
theless, it is obvious that also at ISF nutrient input must be
higher than the nutrient output in the crop if nutrient losses
occur. It was also shown in Part I that when nutrient input is
equal to the output in crops and losses, ISF is still the only
level of soil fertility that is in steady-state, at least for
nutrients that do not accumulate in the soil.
Recommendations on nutrient inputs should be based on
soil analysis, and be tailored to target yields. At soil fertility
levels lower or higher than ISF, nutrient input must be higher
or lower than replacement input. Inappropriate ratios among
soil nutrients are a major reason why replacement input is
seldom recommendable. Because nutrient ratios have a
strong impact on nutrient use efficiency, it was tried to
establish key ratios of chemical soil test values. They were
derived from the ratios of nutrients in crops, recovery
fractions of input nutrients and the equations used for the
translation of uptake of soil nutrients into chemical soil test
values. Three key ratios were presented for ratios SOC (P-
Olsen)�1 and four for SOCffiffiffiffiffiffiffiffiffiffiffiEx-Kp� ��1
, resulting in six
classes of recommended input ratios of N and P, and seven
classes of recommended input ratios of N and K.
4.3. Soil organic matter
If target yields are low, the minimum requirement for soil
organic matter is not related to soil N supply, but to soil
structure stability. In sandy loams, minimum soil organic
carbon (SOC) to prevent collapse of soil structure was set at
6 g kg�1 (as derived from literature). It was shown that SOC
cannot be maintained at this critical level by roots and
stubble alone when maize grain yield is below 7–8 Mg ha�1,
and not by roots plus incorporated stover when grain yield is
below 2 Mg ha�1. Soils should better not be planted to
annual food crops, when yields of maize receiving
replacement nutrient input are below 2 Mg ha�1. They
should be left to nature, or used for grazing or for perennials
(tree crops). Sometimes it is worthwhile to grow highly
valuable horticultural crops on these soils, because they pay
the investments of fertilizers, irrigation and biocides.
On the other hand, there is little wisdom in trying to get
SOC contents far above the minimum requirement,
because that demands huge applications of stover and
organic manure and locks up large quantities of N and P in
the soil. Moreover, unnecessarily high SOC contents may
cause low availability of K, and stimulate leaching of N
and P. The latter happens especially in ecological zones,
such as in Western Europe, where during the winter period
nutrient uptake by crops mostly is absent while miner-
alization may continue but slowly, and rainfall exceeds
evapotranspiration.
4.4. Is the ISF-SSF framework different?
The question has been raised what new is about the ISF-
SSF framework. It is not a new methodology of soil analysis
or field research. It may be seen as a new methodology of
interpretation of soil test values.
The next question is then: does ISF-SSF framework
arrive at other nutrient management recommendations than
the existing systems. The answer is that the application rates
of fertilizers in general will be somewhat lower for
recommendations according to the ISF-SSF than for
recommendations according to systems where profit
maximization is strived at. Does this mean that yields are
lower when the ISF-SSF framework is followed? Not
necessarily. By taking balanced nutrient proportions as a
leading guideline, the part of yield response curves
representing diminishing returns to a single nutrient is
shortened. As has been stated by De Wit (1992), inputs lose
their variable character when other growing conditions are
optimized. Balanced nutrient proportions are part of those
optimized growing conditions. Important is that the overall
use efficiency increases when all resources are considered at
the same time.
Another question is in what way the ISF-SSF framework
differs from the model QUEFTS. First of all, the ISF-SSF
framework explicitly takes sustainability, environmental
protection and balanced plant nutrition as starting points and
not the economics of fertilizer use. Further the ISF-SSF
framework is simpler than QUEFTS, mainly because the
physiological efficiency (PhE) is set at a default optimum
value while QUEFTS takes into account that PhE can vary
between the minimum and maximum values that are shown
in Table 3 of Part I (Janssen and de Willigen, 2006). There
is also a great resemblance in that both systems make use of
the same equations for quantitative interpretation of soil
data.
The ISF-SSF framework deals in the first place with
tropical agroecosystems, but applies equally well to affluent
countries coping with nutrient surpluses, eutrophication of
the environment and degradation of natural ecosystems.
Finally, did we learn something from the development of
ISF-SSF framework? Yes, a lot, or better we were reminded
to many simple facts in soil–crop–environment relations. To
mention some items:
� i
deal soil fertility is different for N, P and K; soil N may below while soil P must be high,
� f
rom an environmental as well as from an agronomicpoint of view it is the question whether neutral nutrient
budgets or replacement input of nutrients form a well
thought-out concept,
� s
oil organic matter is the most important soil fertilitycharacteristic, but this does not imply that it should be
maintained at very high levels,
� s
oil test values should be considered in mutual connec-tion.
cosystems and Environment 116 (2006) 147–155 155
It is our hope that the ISF-SSF framework can find its way
as a building set, especially in those areas where soil testing
still has to take off.
B.H. Janssen, P. de Willigen / Agriculture, E
5. Conclusions
Given a certain target grain yield of maize, it is possible to
calculate the required soil test values for saturated soil
fertility (SSF) and ideal soil fertility (ISF), and the
corresponding optimum inputs for each nutrient.
In practice, the proportions of soil nutrients often differ
from the proportions required for ISF. Because replacement
input is only advisable at the ratios of soil test values found
at ISF, it is questioned whether neutral nutrient budgets or
replacement input of nutrients form a well thought-out
concept.
The ratios of chemical soil test values at ISF depend on
the optimum ratios of the nutrients in the crop and the
recovery fractions of input nutrients. For replacement input,
the appropriate ratio of SOC (in g kg�1) to P-Olsen (in
mg kg�1) was calculated to be 0.28, and the appropriate ratio
of SOC to the square root of Ex-K (in mmol kg�1) was found
to be 5.7, in soils with a pH (H2O) of 6.
It was calculated that SOC cannot be maintained at the
critical level of 6 g kg�1 by roots and stubble alone when
maize grain yield is below 7–8 Mg ha�1, and not by roots
plus incorporated stover when grain yield is below
2 Mg ha�1. Hence, soils should better not be planted to
annual food crops, when yields of maize receiving
replacement nutrient input are below 2 Mg ha�1.
Although soil organic matter is the most important soil
fertility characteristic, it is not efficient to try to keep it at
very high levels.
Acknowledgement
The authors gratefully acknowledge the critical com-
ments by Dr. Ellis Hoffland and Prof. Oene Oenema on a
previous version of the manuscript.
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