Internal nutrient efficiencies of irrigated lowland rice in tropical and subtropical Asia

Internal nutrient ef®ciencies of irrigated lowland

rice in tropical and subtropical Asia

C. Witta, A. Dobermanna,*, S. Abdulrachmanb, H.C. Ginesc,Wang Guanghuod, R. Nagarajanef, S. Satawatananontg,

Tran Thuc Sonh, Pham Sy Tani, Le Van Tiemk,G.C. Simbahana, D.C. Olka

aInternational Rice Research Institute (IRRI), Soil and Water Sciences Division,

MCPO Box 3127, 1271, Makati City, PhilippinesbResearch Institute for Rice (RIR), Sukamandi, Subang, West Java, Indonesia

cPhilippine Rice Research Institute (PhilRice), Maligaya, Nueva Ecija, PhilippinesdZhejiang University (ZU), Hangzhou, Zhejiang, PR China

eSoil and Water Management Research Institute (SWMRI), Thanjavur, Tamil Nadu, IndiafTamil Nadu Rice Research Institute (TNRRI), Aduthurai, Tamil Nadu, India

gPathum Thani Rice Research Center (PTRRC), Thanyaburi, Pathum Thani, ThailandhNational Institute for Soils and Fertilizers (NISF), Chem, Tu liem, Hanoi, Viet Nam

iCuu Long Delta Rice Research Institute (CLRRI), Omon, Cantho, Viet NamkVietnam Agricultural Science Institute (VASI), Van dien-Thanh tri, Hanoi, Viet Nam

Received 5 November 1998; received in revised form 10 May 1999; accepted 12 May 1999

Abstract

This study estimates the nitrogen (N), phosphorus (P) and potassium (K) requirements of irrigated rice (Oryza sativa L.) in

South- and Southeast Asia. Grain yield and plant nutrient accumulation in above-ground plant dry matter (DM) were measured

at physiological maturity of rice (n � 2000) in on-station and on-farm experiments in six Asian countries between 1995 and

1997. These data were used to model the nutrient requirements for yields up to 11 t haÿ1 using the QUEFTS (Quantitative

Evaluation of the Fertility of Tropical Soils) approach. The model required the estimation of two borderlines describing the

minimum and maximum internal ef®ciencies (IE, kg grain per kg nutrient in plant DM), which were estimated at 42 and 96 kg

grain kgÿ1 N, 206 and 622 kg grain kgÿ1 P and 36 and 115 kg grain kgÿ1 K, respectively. The model predicted a linear

increase in grain yield if nutrients are taken up in balanced amounts of 14.7 kg N, 2.6 kg P and 14.5 kg K per 1000 kg of grain

until yield targets reached ca. 70±80% of the climate-adjusted potential yield (Ymax). The corresponding IEs were 68 kg

grain kgÿ1 N, 385 kg grain kgÿ1 P and 69 kg grain kgÿ1 K for a balanced nutrition. The model predicted a decrease in IEs

when yield targets approached Ymax. The derived borderlines are valid for current modern, high-yielding indica cultivars with a

harvest index of 0.50 kg kgÿ1 and can be used for all methods of crop establishment. Only Ymax is required as site- or season-

speci®c information when estimating nutrient requirements for a yield target making the model applicable for all irrigated

lowlands in South- and Southeast Asia. Predicted IEs were greater than actual IEs measured in more than 200 farmers' ®elds

Field Crops Research 63 (1999) 113±138

*Corresponding author. Tel.: +63-2-845-0563; fax: +63-2-891-1292

E-mail address: [email protected] (A. Dobermann)

0378-4290/99/$ ± see front matter # 1999 Elsevier Science B.V. All rights reserved.

PII: S 0 3 7 8 - 4 2 9 0 ( 9 9 ) 0 0 0 3 1 - 3

(n � 700), the latter averaging 59 kg grain kgÿ1 N (27±100 kg kgÿ1), 354 kg grain kgÿ1 P (158±1069 kg kgÿ1), and 64 kg

grain kgÿ1 K (27±179 kg kgÿ1) with grain yields ranging from 1.5 to 9.9 t haÿ1 (mean 5.2 t haÿ1). Low and varying IEs in the

farmers' practice were caused by nutritional imbalances, inadequate irrigation, or problems with pests and weeds. # 1999

Elsevier Science B.V. All rights reserved.

Keywords: Internal ef®ciency; Nutrient ef®ciency; Nutrient accumulation; Nutritional balance; Rice; QUEFTS; Crop nutrient requirements;

Nitrogen; Phosphorus; Potassium

1. Introduction

Biomass production of irrigated rice (Oryza sativa

L.) is mainly driven by the supply of nitrogen, the most

limiting nutrient in irrigated rice, in a situation where

crop growth is not limited by water supply, weed

problems or pest infestation (De Datta et al., 1988b;

Kropff et al., 1993). Thus, the demand of the rice plant

for other macro-nutrients mainly depends on the N

supply (Dobermann et al., 1998). There are consider-

able uncertainties about crop N, P and K requirements

because the internal ef®ciencies (IE, kg grain per kg

nutrient in above-ground plant dry matter) vary greatly

depending on variety, nutrient supply, crop manage-

ment and climatic conditions. Estimates of total nutri-

ent removal per ton of rice grain ranged from 15 to

24 kg N, from 2 to 11 kg P and from 16 to 50 kg K

(Goswami and Banerjee, 1978; Yoshida, 1981; van

Duivenbooden et al., 1996; Dobermann et al., 1996a,

b; Cassman et al., 1997). At issue is whether these

values represent the current range of nutrient require-

ments of modern, high-yielding cultivars. Further-

more, literature data were often summarized despite

known or unknown differences in sampling, quality of

the measurement, and other important experimental

details in order to derive average, generic nutrient

uptake requirements of a crop as `rules of thumb'.

However, nutrient requirements especially for ele-

vated yield targets remained uncertain because inter-

nal nutrient ef®ciencies are not linearly related to

grain yield.

Another problem is that estimates of nutrient

requirements mostly derived from ®eld experiments

conducted at a relatively small number of research

stations in Asia in the last decades. Although these

experiments supply valuable information for a given

site, results can only partly be extrapolated to estimate

nutrient requirements in farmers' ®elds because of the

much broader range of soil, climatic, agronomic and

socioeconomic conditions at the farm level. One

potential extrapolation error is caused by the fact that

soils in research stations often have a different crop-

ping history than farmers' ®elds, including greater

fertilizer use and often increased soil nutrient

levels. In such a situation, `general estimates' of crop

nutrient requirement derived from an on-station

experiment may overestimate the actual nutrient

requirement because luxurious supply of one or more

nutrients would result in low IEs measured in the

experiment.

Therefore, we argue that estimates of crop nutrient

uptake requirements should be based on more generic

approaches such as the model QUEFTS (Quantitative

Evaluation of the Fertility of Tropical Soils) (Janssen

et al., 1990) which accounts for interactions among

macro-nutrients affecting the IE of N, P and K and

allows differentiation according to different yield

levels targeted. Farm- or ®eld-speci®c management

strategies that include site- or season-speci®c knowl-

edge of crop nutrient requirements and indigenous

nutrient supply will probably be required in order to

achieve average rice yields of 8.0 t haÿ1 in the future

(Hossain and Fischer, 1995; Dobermann and White,

1999). Thus, more information-intensive fertilization

strategies are needed to better ®t fertilizer inputs to the

seasonal pattern of crop nutrient demand and soil

nutrient supply. In a ®rst step towards such site-

speci®c nutrient management (SSNM) in irrigated

rice (Dobermann and White, 1999), this paper aims

at (i) characterizing the current situation in farmers'

®elds by reporting data on straw yield, grain yield,

components of yield and plant nutrient concentrations

from a large database mainly consisting of on-farm

experiments in the irrigated lowlands of tropical and

subtropical Asia, and at (ii) quantifying the crop

requirements for N, P and K based on nutrient inter-

actions for (economic) yield targets taking the climate

adjusted potential yield into account.

114 C. Witt et al. / Field Crops Research 63 (1999) 113±138

Exploiting above-mentioned data base on grain

yield and nutrient accumulation in above-ground plant

dry-matter (DM), the speci®c objectives of our study

were

1. to generate an empirical model describing the

internal nutrient ef®ciencies for targeted yields of

modern rice cultivars as a function of climate

adjusted potential yield, and the maximum

possible accumulation and dilution of N, P, and

K in the plant in relation to grain yield,

2. to assess whether a generic, empirical relationship

between grain yield and accumulation of plant N, P,

and K in the QUEFTS model is valid in different

rice-growing environments, and

3. to specify improved general estimates of the aver-

age N, P, and K requirements of rice.

2. Theoretical considerations

2.1. The QUEFTS model

The QUEFTS model divides the relationship

between grain yield and nutrient supply into four

separate steps by taking into account limitations in

supply, acquisition and utilization of N, P and K. The

model was originally developed to calculate the yield

of tropical maize as a function of N, P and K avail-

ability from soil and fertilizer sources (Janssen et al.,

1990). However, the model is also applicable to other

crops once the basic relations between grain yield and

nutrient supply of a crop are known. Further, QUEFTS

can also be used to evaluate the crop response to

fertilizers or to estimate the fertilizer input require-

ments to achieve a certain yield target (Janssen and

Guiking, 1990; Smaling and Janssen, 1993). De®ni-

tions and origin of variables needed for calculating the

N, P and K requirements of rice are given in Appen-

dix A and full details of the model are given by

(Janssen et al., 1990, 1992).

The ®rst step of the QUEFTS model requires the

estimation of the soil-supplying capacity or potential

indigenous supplies of N, P and K for a given site or

®eld. This can be done in various ways among which

the estimation from soil tests or from nutrient uptake

or grain yield measured in on-farm nutrient omission

plots (i.e., a plot without fertilizer application of the

respective macro-nutrient) appear to be most promis-

ing (Dobermann and White, 1999). In step 2, the

actual uptake of a nutrient (UN, UP, UK) is calculated

as a function of the potential supply of that nutrient

(SN, SP, SK), i.e., the indigenous supply of a nutrient

plus the effective supply of a nutrient applied as

fertilizer taking the fertilizer recovery ef®ciency into

account. The relation between potential supply and

actual uptake of a nutrient is assumed to be parabolic

between a situation I, where the actual uptake equals

the (low) potential supply, and a situation II, where

increasing the potential supply of a nutrient does not

result in any additional nutrient uptake. The latter

situation may occur if other nutrients are limiting or

if the maximum yield level is reached. Step 2, there-

fore, provides two uptake estimates of each nutrient as

a function of the potential supply of the two other

nutrients (e.g., UN(P) and UN(K)). The minimum

uptake of each pair results in one ®nal estimate of

nutrient uptake (UN, UP, UK).

The relationship between grain yield and nutrient

accumulation in total above-ground plant DM is

de®ned in steps 3 and 4 of the model. In step 3,

two yield estimates are obtained for each nutrient

(YND, YNA, YPD, YPA, YKD, YKA, see Appen-

dix A) from the UN, UP and UK estimated in step 2

(Fig. 1(a)). These are the possible minimum and

maximum yield levels that can be achieved with the

respective ®nal nutrient uptake estimate taking into

account the climate adjusted, cultivar-speci®c poten-

tial yield at a given site (Ymax). For this step, a

representative data set on grain yield and nutrient

uptake is required in order to derive borderlines

describing the maximum possible accumulation and

dilution of N, P and K in the plant in relation to grain

yield. A ®nal nutrient uptake estimate of, for example,

50 kg N haÿ1 would result in two yield estimates, one

estimate for the situation where N is maximally

accumulated (YNA, Fig. 1(a)) and one for the situa-

tion where N is maximally diluted (YND, Fig. 1(a)).

In step 4, possible yield ranges are combined into

one ®nal yield estimate by accounting for the inter-

actions between N, P and K. Using the yield ranges

de®ned in step 3, yield estimates are calculated for

each possible pair of nutrients. This is demonstrated in

Fig. 1(b), where an estimate of the N-limited yield as

affected by the P supply (YNP) is obtained from a

mathematical overlay of the possible yield ranges

C. Witt et al. / Field Crops Research 63 (1999) 113±138 115

identi®ed in step 3 (Fig. 1(a)). A certain P uptake

resulted in two yield estimates depending on whether

P is maximally accumulated (YPA) or diluted in the

plant (YPD). Within the yield range that is possible

based on the P uptake (YPA-YPD), a parabolic equa-

tion is then used to estimate YNP from the predicted N

uptake (UN). In situation III depicted in Fig. 1(b),

grain yield would be N limited while P is available in

surplus. With increasing N supply and uptake, how-

ever, P supply would increasingly become a constraint

for plant growth so that grain yield would be P limited

in situation IV. Like this, yield estimates are generated

for each possible pair of nutrients (YNP, YNK, YPN,

YPK, YKN, YKP). The combined ®nal yield estimate

for all three nutrients is then obtained as the mean of

these six estimates.

Following Janssen et al. (1992), optimal (balanced)

nutrition can then be obtained by maximizing the total

yield-producing uptake ef®ciency (TYPUE, Appen-

dix A). The uptake of a particular nutrient is assumed

to be most ef®cient in a situation of low supply of that

nutrient as long as other nutrients are not limiting plant

growth. Theoretically, the ratio between uptake and

supply of a nutrient (uptake ef®ciency) will equal 1 if

the nutrient is limiting while the uptake ef®ciency of

other nutrients is much lower. Since it is impossible to

maximize the uptake ef®ciencies of all nutrients

simultaneously, Janssen et al. (1992) suggested to

maximize the mean of the N, P and K uptake ef®-

ciencies after correcting for the minimum nutrient

uptake required to produce any measurable grain yield

(r-values). Thus, yield-producing uptakes (UNy, UPy,

UKy) were de®ned as nutrient uptake minus the

respective r-value (Appendix A). Analogously, r-

values were used to derive yield-producing supplies

from indigenous sources and applied fertilizer nutri-

ents (SNy, SPy, SKy). The ratios of UNy/SNy, UPy/

SPy and UKy/SKy were called yield-producing uptake

ef®ciencies and the mean of these ratios formed the

TYPUE. Optimization routines can be used to ®nd the

best combination of fertilizer input (NPK) for a given

soil supply of these nutrients resulting in the optimal

UN, UP and UK (�nutritional optimum) at maximum

TYPUE.

2.2. Critical model assumptions

In the following, we will elaborate on some assump-

tions made in Step 3 of the QUEFTS model dealing

with the relationship between grain yield and plant

nutrient accumulation, i.e., the internal ef®ciency (IE)

of a nutrient. A general assumption is that grain yield

only depends on the availability of N, P and K and that

other nutrients, water supply and pests are not limiting

Fig. 1. The schematic relationship between grain yield and plant N accumulation in total above-ground plant dry-matter (DM) as calculated

by the QUEFTS model (after Janssen et al., 1990). In Fig. 1(a), boundary lines represent the maximum dilution (YND) and accumulation of N

(YNA) in the above-ground DM. Constants aN and dN determine the slope of the respective boundary line while constant rN is the minimum

N uptake requirement to produce any measurable grain yield. Ymax is the climate adjusted yield potential. QUEFTS calculates the possible

internal efficiency of a nutrient (i.e., kg grain produced per kg plant nutrient) depending on nutrient interactions for situations where other

nutrients (e.g., P in Fig. 1(b)) or Ymax (Fig. 1(c)) are limiting yield. In Fig. 1(b), the yield range that can be achieved with a certain, fixed P

uptake is indicated by two horizontal lines representing situations of maximum dilution (YPD) and accumulation of P (YPA), while YNP is the

combined yield for N and P uptake. In Fig. 1(c), YN represents the optimum nitrogen uptake requirement to achieve a certain grain yield target

without that other nutrients are limiting. For definition of variables, see also Appendix A.


yield. In this situation, grain yield is a function of

nutrient supply and Ymax, which is determined by the

cultivar and the climatic conditions. The relation

between grain yield and nutrient uptake is assumed

to be linear at lower uptake levels since the nutrient

uptake would be at its maximum under conditions of

limited nutrient supply (van Duivenbooden et al.,

1996). Theoretically, the actual plant nutrient accu-

mulation under such conditions should be close to the

line of maximum dilution of the respective nutrient in

the plant (e.g., YND, Fig. 1(c)) but it is not likely that

all major nutrients can be maximally diluted. Instead,

IEs of all three nutrients would be between their

maximum and minimum values in an ideal situation

of balanced N, P and K nutrition so that neither

nutrient is maximally diluted or accumulated. In this

situation of nutritional balance, the relationship

between grain yield and nutrient uptake as predicted

by QUEFTS follows a linear-parabolic-plateau model

(e.g., YN, Fig. 1(c)), primarily depending on the

envelope functions and the site- and season-speci®c

yield potential. These balanced nutrient requirements

can be generated by running the model for various

yield targets at a given yield potential.

The linear part of the relation between grain yield

and nutrient accumulation as predicted by the

QUEFTS model solely depends on the de®nition of

the border lines describing the envelope of maximum

and minimum accumulation in a situation of nutri-

tional balance (Fig. 1(c)). Border lines can be derived

from data sets covering a wide range of situations

where nutrients are limiting (nutrient omission plots)

or available in surplus (fertilized plots). At elevated

yield levels, however, internal nutrient ef®ciencies

decrease in a non-linear fashion when actual yields

approach the potential yield (Fig. 1(c)).

A critical assumption of this approach is that the IEs

of short-to-medium duration, modern high-yielding

rice varieties are similar for a wide range of yield

levels which appears to contradict studies on genoty-

pic variation in IE ef®ciencies (Broadbent et al., 1987;

Tirol-Padre et al., 1996; Singh et al., 1998). However,

our main hypothesis was that standard border lines of

maximum and minimum nutrient accumulation are

applicable for all tropical and subtropical sites with

irrigated lowland rice in Asia. This had the advantage

that the potential yield would be the only variable

in QUEFTS that needed to be adjusted to estimate

crop nutrient requirements for a particular season and

site.

There is also some concern that the true nutrient

requirements of a crop would be underestimated when

relating grain yield to nutrient uptake in above-ground

DM since the storage of nutrients in the root system is

neglected (Appel, 1994). However, fertilizer require-

ments of rice as calculated by QUEFTS would prob-

ably not change tremendously if the model was based

on the relationship between grain yield and total plant

nutrient accumulation in above- and below-ground

plant DM as explained in the following for nitrogen.

In our approach using QUEFTS, the potential indi-

genous N supply (INS) is estimated from the nutrient

accumulation in above-ground plant DM either

directly from plant analysis or indirectly from a soil

test in a N omission plot receiving only fertilizer-P and

-K (Dobermann and White, 1999). With this approach,

the N requirement of the root system can be taken out

of the equation under the assumption that the differ-

ence in root N accumulation between unfertilized and

fertilized plots is negligible. This is legitimate for

irrigated rice because (i) root N accumulation at

physiological maturity of rice accounts for only 6%

(ranging from 2% to 15%) of the total above- and

below-ground plant N (ten Berge et al., 1999); and (ii)

the root biomass tends to be relatively insensitive to

increases in above-ground biomass caused by fertili-

zer-N application (Bronson et al., 1997; Witt et al.,

1999). Thus, the gain in precision is probably not

worth the effort that would be required to measure

nutrient accumulation in both above- and below-

ground biomass at maturity.

3. Materials and methods

The data on straw yield, grain yield, components of

yield and nutrient concentrations reported here repre-

sent the largest on-farm database for irrigated lowland

rice in South and Southeast Asia. It is important to

highlight that all data were gathered using the same

standardized procedures for sampling and sample

processing.

3.1. Origin of the data set

The data originated from 15 sites including tropical

and subtropical environments in six Asian countries


(Table 1). Most data derived from IRRIs Mega Project

on `Reversing Trends of Declining Productivity in

Intensive, Irrigated Rice Systems'. In this project,

measurements were taken during several dry and

wet seasons (DS, WS) in more than 200 farmer's

®elds (n � 2460) and seven long-term fertility experi-

ments (LTFE, n � 348) at experimental stations in

Vietnam (Omon and Hanoi), the Philippines (Malig-

aya), Indonesia (Sukamandi), Thailand (Suphan Buri),

India (Aduthurai) and China (Jinhua) between 1994

and 1997. At each site, on-farm experiments with

different fertilizer treatments were conducted in 20±

45 farms within a radius of ca. 15±20 km around a

local research station, thus covering a range of soils,

agronomic practices and socioeconomic production

characteristics (IRRI, 1997a).

Further data originated from a survey conducted in

farmers' ®elds in Nueva Ecija province, Philippines,

during the 1994 DS and WS (n � 155) (Dobermann

and OberthuÈr, 1997), and from the International Net-

work on Soil Fertility and Sustainable Rice Farming

(INSURF). The latter data (n � 72) were collected

from LTFEs at 12 agricultural Research Stations in

China (Shipai, Jinxian and Qingpu), India (Coimba-

tore and Pantnagar), Indonesia (Maros, Lanrang and

Sukamandi), Philippines (Laguna, Maligaya and

Camarines Sur) and Vietnam (Cuu Long) in the

1993 DS (IRRI, 1995; Dobermann et al., 1996a).

Few selected data from two on-station experiments

with high fertilizer-N rates at IRRI and PhilRice were

obtained from the literature (Peng et al., 1996a).

3.2. Cropping systems and management

The cropping systems at experimental stations were

comparable to those in farmers' ®elds at all sites and

always included two annually grown rice crops. Col-

laborating institutions and the crop calendar at IRRIs

Mega Project sites are given in Table 2.

The method of rice crop establishment in farmers'

®elds was mostly transplanting except for the Mega

Project sites in Suphan Buri, Thailand, and Omon,

Vietnam, where wet seeding was practiced in both

farmers' ®elds and LTFEs. At all other sites, rice was

transplanted in LTFEs. In the Philippines, farmers

mostly transplanted rice in the WS but rarely in the

DS (wet seeding). About 66% of all data derived from

®elds with transplanted rice.

The only sites with subtropical environments were

the Mega Project sites in Hanoi and Jinhua, as well as

three of the INSURF LTFEs conducted at different

sites in China, but climatic conditions during rice

growing periods were similar to those of tropical

environments. Semi-dwarf, modern high-yielding

indica cultivars with a short-to-medium growth period

(100±125 days), were grown at all sites. Rice crops

Table 1

Origin of data

Country Type of experiment Treatments n Source

China, India, Indonesia,

Philippines, Thailand,

Vietnam

Farmer's field (>200) ÿF (621), �NP (201),

�NK (201), �PK

(616), FFP (718),

SSM (103)

2460 IRRIs Mega Project on `Reversing Trends of

Declining Productivity in Intensive, Irrigated

Rice Systems', unpublished data


Philippines, Thailand,

Vietnam

Long-term fertility

experiments (7)

ÿF (58), �N (50),

�NP (58), �NK (58),

�PK (58), �NPK (66)

348 IRRIs Mega Project on Reversing Trends in

Declining Productivity, unpublished data


Philippines, Vietnam

Long-term fertility

experiments (12)

ÿF (12), �NP (12),

�NK (12), �PK

(12), �NPK (12)

72 International Network on Soil Fertility

(INSURF), Dobermann et al., 1996a; IRRI, 1995

Philippines Farmer's field (155) FFP (155) 155 Dobermann and OberthuÈr, 1997

Philippines On-station experiments

(2)

�NPK (19), �PK

(2)

21 Peng et al., 1996a

Note: Treatments included control plots without N, P and K fertilization (ÿF), plots with one (�NP, �NK, �PK) or two omitted nutrients

(�N), full N, P and K fertilization (�NPK), farmer's fertilizer practice (FFP), and a researcher's NPK split following the site-specific nutrient

management (SSNM) as described by Dobermann and White (1999). In addition to the total numbers of observations (n), numbers in

parenthesis refer to the number of experiments or observations of the respective treatment.


were fully irrigated during the DS and also during the

WS to supplement seasonal rainfall so that water

supply was rarely limiting plant growth. Weeds,

insects and pests were controlled as required to avoid

yield losses in LTFEs. Pest damage differed with

season and site in on-farm trials, and could not fully

be avoided as low yields or low harvest indices

indicated in some cases.

Apart from plots receiving full N, P and K fertiliza-

tion, treatments in LTFEs always included control

plots without N, P and K fertilization (ÿF) and

single-nutrient omission plots such as �PK, �NK

and �NP plots, i.e., treatments where only one nutri-

ent was limiting yield (Table 1). Where required,

blanket doses of micronutrients (Zn) were applied

to all treatments to prevent interference by Zn de®-

ciency. In addition to these four treatments, on-farm

trials at the Mega Project sites also included a farmer's

fertilizer practice (FFP, pure monitoring plot) and a

site-speci®c nutrient management plot (SSNM) (Olk

et al., 1999). The SSNM treatment is a researchers'

practice aiming at a balanced nutrition of N, P and K

using the QUEFTS model developed by Janssen et al.

(1990), and dynamic, plant-based adjustment of N

application (Dobermann and White, 1999). Given the

diversity of experimental conditions, speci®c details

of fertilizer treatments are not reported here because

this paper exclusively aimed at evaluating the relation-

ship between grain yield and plant nutrient accumula-

tion for a wide range of possible nutrient supplies and

environmental conditions.

3.3. Plant measurements

In the Mega Project, every LTFE had four replicates

while the on-farm experiments had three replicates

until 1996 and two since 1997. Plot sizes were 30±

40 m2 in the LTFEs and 300±1000 m2 in on-farm

experiments each containing two sampling plots of

36 m2. While plot sizes in the other studies differed

from plot sizes at the Mega Project sites (Peng et al.,

1996b; Dobermann et al., 1996a, Dobermann and

OberthuÈr, 1997), the following standard procedure

for determining straw yield, grain yield, components

of yield (un®lled spikelets, 1000-grain weight, number

of panicles per m2, spikelets per m2) and plant nutrient

concentrations was applied at all sites.

Table 2

Collaborating institutions, sites and crop calendar of the IRRI Mega Project on `Reversing Trends of Declining Productivity in Intensive,

Irrigated Rice Systems' between 1994 and 1997


Plant samples were taken at physiological maturity

(PM)1 and harvestable maturity (HM)2. For direct-

seeded rice, plants were collected from two 0.25 m2

sampling areas at PM and pooled for the determination

of components of yield. A 12-hill sample was col-

lected in transplanted rice. All plant samples including

un®lled spikelets, ®lled spikelets and straw were oven-

dried to constant weight at 708C, weighed and ground.

Tissue-N was measured by micro-Kjeldahl digestion,

distillation, and titration procedures (Bremner and

Mulvaney, 1982), tissue-P by the molybdenum-blue

colorimetric method after dry-ashing (2 h at 2008Cplus 4 h at 4908C) (Yoshida et al., 1972), and tissue-K

by using an atomic adsorption spectrophotometer after

soaking dried plant material in 1 N HCl for 24 h

(Yoshida et al., 1972). Quality control measures

included the chemical analysis of standard plant sam-

ples with known N, P and K concentrations.

Grain yields were obtained from a central 4±5 m2

harvest area at HM and yields (kg haÿ1) are reported at

a standard moisture content of 0.14 g H2O gÿ1 fresh

weight. The 1000-grain weight was determined using

a sub-sample of the oven-dry grain yield of the 5 m2

harvest area. Straw yields (kg haÿ1) were estimated

from the oven-dry grain yield of the 5 m2 harvest area,

and the grain to straw ratio of the 12-hill or 0.25 m2

area plant sample taken at PM. Likewise, un®lled

spikelets (kg haÿ1) were estimated using the ratio of

®lled to un®lled spikelets of the 12-hill or 0.25 m2 area

sample. The total above-ground plant DM was calcu-

lated as the sum of grain yield, straw yield and un®lled

spikelets in kg haÿ1. Plant N, P, and K accumulation in

kg haÿ1 were then estimated using the concentrations

of the respective nutrient as determined on a sub-

sample of the 12-hill or 0.25 m2 area sample taken at

PM. All directly measured plant parameters are based

on oven-dried plant material with a residual moisture

content of ca. 3% except for grain yield (adjusted to

14% moisture content).

The harvest index, i.e., grain yield as a proportion of

above-ground plant DM, was obtained from the oven-

dry 12-hill or 0.25 m2 area sample. The nutrient

harvest index is the nutrient accumulation in grain

as a proportion of total nutrient accumulation in

above-ground plant DM. The internal ef®ciency (IE,

kg kgÿ1) of a nutrient is de®ned as the amount of grain

yield in kg haÿ1 (adjusted to 14% moisture content)

produced per kg plant N, P or K accumulation in

above-ground plant DM (oven-dry weight). The reci-

procal internal ef®ciency (RIE, kg kgÿ1) was calcu-

lated from the average IE of all data and is the amount

of a nutrient in the plant DM needed to produce

1000 kg grain.

3.4. Model development

In order to adapt and test the QUEFTS model for

irrigated rice, we modi®ed steps 3 and 4 of the model

dealing with the relationship between grain yield and

nutrient accumulation in total above-ground plant DM

by

(a) selecting suitable data that fulfill the boundary

conditions of the model,

(b) defining borderlines that describe the max-

imum and minimum accumulation of N, P and K,

and assessing their sensitivity to different criteria

of data selection,

(c) assessing whether intercepts that describe the

minimum nutrient uptake required to produce any

measurable grain yield were needed,

(d) simulating curves of optimum uptake require-

ments of N, P and K at different Ymax (YN, YP,

YK),

(e) assessing whether the same borderline models

are suitable for all modern, short-to-medium

duration rice varieties and whether these borderline

models can be used for different climatic seasons,

i.e., sites and seasons with different Ymax, and

(f) comparing model-simulated optimal IEs with

measured IEs of N, P and K in farmers' fields.

We used a Microsoft Excel spreadsheet version of

QUEFTS in combination with a solver module for the

simulation of generic nutrient uptake curves (YN, YP,

YK) representing optimal internal efficiencies of N, P

and K at different yield levels. In order to derive YN,

YP and YK even for very low yields, potential indi-

genous nutrient supplies (INS, IPS, IKS, Appendix A)

in the model were set to the lowest values observed in

the data set (8 kg N, 2 kg P and 14 kg K haÿ1).

1Physiological maturity (PM) is the point at which grain filling

ends which typically occurs several days before harvestable

maturity.2Harvestable maturity is reached after grain moisture has

decreased to ca. 18±23%.


Recovery fractions of applied fertilizer-N, -P and -K

were irrelevant and all set to 0.50 kg kgÿ1. Maximiz-

ing TYPUE under the constraint that UNy/SNy �UPy/SPy � UKy/SKy � 0.95 (see Appendix A), the

QUEFTS model was run several times each time

slightly increasing the yield target from initially

1 t haÿ1 to a yield target close to Ymax. Each model

run generated recommendations for fertilizer applica-

tion rates, which were irrelevant for this exercise, and

the balanced nutrient requirements for the respective

yield target which were recorded and plotted as line

graph (e.g., YN, Fig. 1(c)). This procedure was done

for different Ymax, ranging from 6 to 11 t haÿ1.

4. Results and discussion

Descriptive statistics of the data set from ®elds with

farmer's fertilizer practice are given in Tables 3±5.

Selected parameters of the entire data set which were

necessary for the calibration of the QUEFTS model

are presented in Table 6. It should be noted that

parameters were calculated independently so that

inconsistencies may occur due to different numbers

of observation.

4.1. Yields and yield component in farmer's fields

We assume that our data from ®elds with farmer's

fertilizer practice are a representative sample of the

whole irrigated lowland rice area in tropical and

subtropical Asia. Average grain yields of 5.2 t haÿ1

in farmers' ®elds (Table 3) were similar to the

4.9 t haÿ1 presently achieved in all Asia (IRRI,

1997b). The diversity in the origin of the data (i.e.,

various management practices, sites and seasons)

provided a solid overview of the potential variation

of each plant parameter. Straw yields averaged

5.0 t haÿ1 and ranged from 1.7 to 10.1 t haÿ1 while

grain yields ranged from 1.5 to 9.9 t haÿ1. The latter

corresponds well with the climate-adjusted yield

potential of ca. 10 t haÿ1 estimated for currently

grown modern rice cultivars in most tropical environ-

ments (Kush, 1993; Kropff et al., 1994a; Matthews et

al., 1995).

The average grain to straw ratio was 0.95 and the

harvest index was 0.47 (Table 3). The HI ranged from

0.25 to 0.63 and was little greater for the DS (0.48)

than for the WS crops (0.45) (data not shown). This

may be related to greater pest damage and yield losses

due to lodging as observed during wet seasons. Also,

differences in growth duration until maturity between

DS and WS crops are known to affect the grain to

straw ratio (Hay, 1995). The observed harvest indices

were slightly lower than the anticipated HI of 0.50 or

more that can be achieved with good crop manage-

ment using modern high-yielding indica cultivars with

a growth duration between 100 and 130 days (IRRI,

1978; Peng et al., 1994; Hay, 1995). However, recent

studies indicated that grain yields of >9 t haÿ1 can be

achieved in the tropics even with a HI < 0.50 as long as

the sink size (spikelets per m2) is suf®ciently large

(Ying et al., 1998a). Related to this, lower grain yields

in tropical than subtropical environments were mainly

attributed to differences in biomass production. In our

data set, ca. 87% of the variation in grain yield was

explained by total above-ground biomass (data not

shown).

Spikelet numbers averaged 28 700 per m2 but ran-

ged from ca. 11 500 to 65 000 spikelets per m2

(Table 3). The average number of panicles per m2

was 490 ranging from 146 to 1573. For plants yielding

>6 t haÿ1 (average 6.8 t haÿ1, n � 208), the average

HI was 0.50 and number of spikelets was �35 000 per

m2 with 16% un®lled spikelets (data not shown). At

these yield levels, ca. 68% in the variation of spikelet

number per panicle was explained by the panicle

number per m2. The two parameters were negatively

correlated so that a lower number of panicles was

partly compensated by an increase in the number of

spikelets per panicle. The correlation between panicle

number per m2 and spikelet number per panicle was

similarly strong for grain yields between 4 and

6 t haÿ1 (r2 � 0.63, data not shown). This yield range

appears to be typical for the present situation in

farmers' ®elds (see lower and upper quartiles,

Table 3). The HI of plants yielding between 4 and

6 t haÿ1 was 0.47%, and 19% of the spikelets were

un®lled while plants with grain yields of <4 t haÿ1 had

an average HI of 0.43% and 25% un®lled spikelets

(data not shown). This clearly indicates that nutrient

supply was not the only factor limiting yield at lower

yield levels. Lodging, insuf®cient solar radiation dur-

ing grain ®lling, inadequate water supply (less criti-

cal), as well as pests (insects, diseases, weeds) were

probable causes of yield reduction in many farms,

especially during the WS.


The great variation in both panicle density (panicles

per m2) and number of spikelets per panicle, as shown

in Table 3, was largely in¯uenced by the method of

crop establishment. It is well established that trans-

planting restricts vegetative growth so that the number

of tillers is reduced in comparison to wet-seeded rice

(De Datta et al., 1988a, b; Schnier et al., 1990).

Despite differences in components of yield between

crop establishment methods, however, parameters

such as grain yield, HI, internal N ef®ciency and

partial factor productivity (grain yield per unit N

applied) tend to be similar in N-fertilized farmers'

®elds due to compensation among yield components

(Peng et al., 1996b). We therefore concluded, that it

Table 3

Grain and straw yield, total above-ground plant dry-matter (DM), harvest index, yield components, concentrations of N [N], P [P], and K [K]

in grain and straw, plant N, P and K accumulation in grain, straw and above-ground plant DM, and nutrient harvest index (kg nutrient in grain

per kg nutrient in above-ground plant DM) at maturity of irrigated lowland rice grown in fields with farmer's fertilizer practice (FFP

monitoring plots) across six tropical Asian countries, 1995±1997

Parameter Unit na Mean SDb Minimum Lower

quartile

Median Upper

quartile

Maximum

Grain yield t haÿ1 712 5.2 1.4 1.5 4.2 5.2 6.1 9.9

Straw yield t haÿ1 707 5.0 1.2 1.7 4.1 4.9 5.8 10.1

Total dry-matter t haÿ1 707 9.9 2.3 3.2 8.4 10.0 11.4 17.1

Grain to straw ratio g gÿ1 707 0.95 0.20 0.36 0.81 0.95 1.09 1.97

Harvest index g gÿ1 707 0.47 0.05 0.25 0.44 0.47 0.51 0.63

1000-grain weight g 617 22.9 3.1 14.6 20.5 23.0 25.2 31.1

Panicles (PAN) PAN mÿ2 713 490 206 146 330 488 617 1573

Spikelets (SP) SP mÿ2 708 28666 8793 11486 22464 27469 33529 65036

SP/PAN 708 66.7 25.7 19.4 46.4 60.4 86.5 151.7

Filled SP/PAN 708 54.2 23.3 14.3 35.6 47.6 72.0 134.8

Filled SP/SP 708 80.4 8.4 51.4 75.7 81.5 86.8 96.5

[N] in grain g kgÿ1 712 11.6 2.1 6.5 10.2 11.1 12.5 21.6

[P] in grain g kgÿ1 668 2.2 0.6 0.6 1.8 2.2 2.6 4.6

[K] in grain g kgÿ1 701 3.0 1.5 1.0 2.3 2.7 3.3 11.9

[N] in straw g kgÿ1 707 7.1 1.9 3.1 5.7 6.8 8.2 12.1

[P] in straw g kgÿ1 663 1.0 0.4 0.2 0.7 1.0 1.3 2.3

[K] in straw g kgÿ1 697 14.5 5.0 1.8 11.7 14.4 17.3 30.8

N in grain kg haÿ1 710 53.3 16.5 15.7 41.9 52.5 62.9 141.1

P in grain kg haÿ1 666 10.5 3.6 2.9 7.8 10.1 12.5 21.3

K in grain kg haÿ1 699 14.4 9.4 3.1 9.1 12.0 16.7 72.7

N in straw kg haÿ1 705 35.1 12.9 7.5 25.7 33.2 43.0 76.8

P in straw kg haÿ1 661 5.1 2.4 1.0 3.2 5.0 6.5 16.2

K in straw kg haÿ1 694 70.7 28.5 9.4 50.3 68.0 89.4 192.0

N in total DM kg haÿ1 703 91.2 26.6 26.5 72.3 88.9 107.3 213.9

P in total DM kg haÿ1 659 16.0 5.4 5.2 12.1 15.6 19.1 35.8

K in total DM kg haÿ1 692 88.1 30.6 20.4 65.6 84.5 106.6 218.5

N Harvest index g gÿ1 703 0.59 0.07 0.30 0.54 0.59 0.65 0.77

P harvest index g gÿ1 659 0.66 0.09 0.36 0.61 0.66 0.71 0.89

K harvest index g gÿ1 692 0.17 0.10 0.04 0.12 0.15 0.19 0.74

a Number of observations.b Standard deviation.


was legitimate not to discriminate between methods of

crop establishment when investigating the relationship

between grain yield and plant nutrient accumulation.

4.2. Nutrient concentrations, uptake and internal

efficiencies in farmers' fields

Nutrient concentrations in g kgÿ1 and the accumu-

lation of N, P and K in kg haÿ1 for ®elds with farmer's

fertilizer practice are presented in Table 3. The aver-

age nutrient concentrations in grain were 11.6 g

N kgÿ1, 2.2 g P kgÿ1 and 3.0 g K kgÿ1, while con-

centrations in straw were 7.1 g N kgÿ1, 1.0 g P kgÿ1

and 14.5 g K kgÿ1. Re¯ecting the wide range of

environmental conditions and nutrient supplies, how-

ever, nutrient concentrations varied tremendously in

both grain (6.5±21.6 g N kgÿ1, 0.6±4.6 g P kgÿ1 and

1.0±11.9 g K kgÿ1) and straw (3.1±12.1 g N kgÿ1,

0.2±2.3 g P kgÿ1 and 1.8±30.8 g K kgÿ1). Lowest

nutrient concentrations were mainly observed in nutri-

ent omission plots during growing seasons with opti-

mal climatic conditions. In contrast, observed

Table 4

Internal efficiency (IE, kg grain per kg nutrient in above-ground dry-matter (DM)), and reciprocal IE (RIE, kg nutrient in above-ground plant

DM per 1000 kg grain) for N, P and K at maturity of irrigated lowland rice grown in fields with farmers' fertilizer practice (FFP) and nutrient

omission plots across six tropical Asian countries, 1995±1997

Parameter Unit na Mean SDb Min. Lower

quartile

Median Upper

quartile

Max.

Nitrogen (N)

IE, -N plots kg kgÿ1 597 69 15 37 59 69 79 116

IE, FFP kg kgÿ1 703 59 11 27 51 58 65 100

RIE, -N plots kg tÿ1 597 14.4 Ð 8.6 12.7 14.4 16.9 27.0

RIE, FFP kg tÿ1 703 17.1 Ð 10.0 15.3 17.4 19.6 37.1

Phosphorus (P)

IE, -P plots kg kgÿ1 138 345 95 214 287 333 379 793

IE, FFP kg kgÿ1 660 354 105 158 277 342 424 1069

RIE, -P plots kg tÿ1 138 2.9 Ð 1.3 2.6 3.0 3.5 4.7

RIE, FFP kg tÿ1 660 2.8 Ð 0.9 2.4 2.9 3.6 6.3

Potassium (K)

IE, -K plots kg kgÿ1 181 71 24 25 52 69 83 148

IE, FFP kg kgÿ1 692 64 21 27 51 60 71 179

RIE, -K plots kg tÿ1 181 14.1 Ð 6.8 12.1 14.5 19.4 40.3

RIE, FFP kg tÿ1 692 15.7 Ð 5.6 14.0 16.6 19.8 37.2

Note: The average grain yield was 4.1 t haÿ1 in �PK (ÿN) plots, 5.5 t haÿ1 in �NK (ÿP) plots and 4.2 t haÿ1 in �NP (ÿK) plots. For other

plant parameters referring to FFP plots, see Tables 2 and 3.a Number of observations.b Standard deviation.

Table 5

Amount of fertilizer-N, -P and -K applied per cropping season to irrigated lowland rice grown in fields with farmer's fertilizer practice across

six tropical Asian countries, 1995±1997


quartile

Median Upper

quartile

Maximum

Fertilizer-N kg haÿ1 687 118 40 29 89 114 142 270

Fertilizer-P kg haÿ1 687 18 11 0 11 18 25 64

Fertilizer-K kg haÿ1 687 24 27 0 0 14 43 184



maximum nutrient concentrations occurred in situa-

tions of excessive supply while simultaneously other

nutrients or environmental conditions strongly limited

plant growth. On average, nutrient accumulation in the

above-ground plant DM was 91 kg N haÿ1, 16 kg

P haÿ1 and 88 kg K haÿ1 producing a yield of

5.2 t haÿ1 (Table 3). The nutrient harvest index, i.e.,

nutrient accumulation in grain as a proportion of

nutrient accumulation in above-ground plant DM,

was similar for N (0.59 g gÿ1) and P (0.66 g gÿ1)

but much lower in case of K (0.17 g gÿ1).

In the following, we restrict our discussion mainly

to the internal nutrient ef®ciencies given in Table 4

because we argue that the commonly used estimates

for irrigated rice needed revision. Across all farms and

seasons, the average IEs were 59 kg grain per kg plant

N, 354 kg grain per kg plant P and 64 kg grain per kg

plant K, equivalent to 17.1 kg N, 2.8 kg P and 15.7 kg

K per 1000 kg grain (Table 4) or a N : P : K ratio of

6.1 : 1 : 5.6 in plant DM. Our estimates of IEs in

farmers' ®elds were higher for N and K but lower

for P than those usually found in the literature

(Yoshida, 1981; van Duivenbooden et al., 1996).

For example, summarizing results of >50 older on-

station experiments, IEs of 53 kg grain per kg plant N,

400 kg grain per kg plant P and 41 kg grain per kg

plant K were proposed for irrigated lowland rice (van

Duivenbooden et al., 1996). This is equivalent to

average nutrient requirements of 18.7 kg N, 2.5 kg

P and 24.7 kg K per produced ton of grain yield with

an average N : P : K ratio in the plant DM of ca.

7.5 : 1 : 9.9. The average harvest index, however,

was only 0.44 in these experiments and it is likely

that differences in sampling techniques and methods

of plant analysis introduced substantial errors.

Our data are more representative for farmers' ®elds

as they are based on a very large database covering a

wide range of environmental and crop management

conditions and a uniform sampling methodology. It is

likely that previously used estimates mainly represent

the nonlinear part of the relationship between grain

yield and nutrient uptake, whereas farmers mostly

operate in the linear part (Fig. 1(c)). A decrease in

internal nutrient ef®ciencies can generally be expected

when target yields are close to the yield potential

(Cassman et al., 1995; Dobermann et al., 1996a, b).

For example, internal N ef®ciencies measured

for yields close to Ymax (9.1±9.9 t grain haÿ1) were

Table 6

Descriptive statistics of the data sets used for developing empirical models describing the relationship between grain yield and nutrient uptake

in rice. Grain and straw yield, total above-ground plant dry-matter (DM), harvest index, accumulation of N, P and K in above-ground plant

DM, and internal efficiencies (IE, kg grain per kg nutrient in above-ground plant DM) and reciprocal IE (RIE, kg nutrient in above-ground

plant DM per 1000 kg grain) of N, P and K at maturity of irrigated lowland rice grown in farmers' fields and at experimental stations across six

tropical Asian countries, 1992±1997. Data with a harvest index of <0.40 kg kgÿ1 were excluded


quartile

Median Upper

quartile

Maximum

Grain yield kg haÿ1 2627 4776 1542 946 3630 4723 5798 9933

Straw yield kg haÿ1 2627 4283 1336 875 3379 4238 5121 9738

Total dry-matter kg haÿ1 2513 8654 2610 1832 6785 8630 10439 17904

Harvest index g gÿ1 2627 0.49 0.05 0.40 0.45 0.49 0.52 0.66

N in total DM kg haÿ1 2306 75 31 8 52 70 93 214

P in total DM kg haÿ1 2118 14 6 2 10 13 17 34

K in total DM kg haÿ1 2276 77 32 14 54 72 94 245

IE, Nitrogen kg kgÿ1 2306 66 14 23 55 64 75 121

IE, Phosphorus kg kgÿ1 2120 371 117 101 291 358 433 1210

IE, Potassium kg kgÿ1 2276 66 20 27 52 63 74 196

RIE, Nitrogen kg tÿ1 2306 16.0 3.5 8.3 13.3 15.6 18.2 43.4

RIE, Phosphorus kg tÿ1 2118 2.9 0.9 0.8 2.3 2.8 3.4 9.9

RIE, Potassium kg tÿ1 2276 16.6 4.8 5.1 13.5 15.9 19.1 37.1



48± 58 kg grain per kg plant N in research station

experiments in the Philippines (Cassman et al., 1997;

Ying et al., 1998b). The greater IE of K in the farmers'

®elds (64 kg kgÿ1) as compared to commonly pro-

posed literature values of 40±50 kg kgÿ1 appears to be

an indication of greater, sometimes even luxury K

supply of the research-station soils, illustrating the

limited extrapolation value of such data.

Internal ef®ciencies of N and K were greatly

affected by nutrient management. Due to nutrient

limitation, N and K were more diluted in plants of

the respective nutrient omission treatments than in

FFP plots receiving fertilizer-nutrients (Table 4).

Thus, IEs were greater in treatments without applica-

tion of the respective nutrient (-N, -P or -K plots) than

in plots with farmer's fertilizer practice (FFP). The

internal nitrogen ef®ciency averaged 69 kg grain per

kg of plant N in -N treatments and 59 kg kgÿ1 in FFP

plots. Likewise, 71 vs. 64 kg grain were produced per

kg plant K in -K and FFP plots (Table 4). In contrast,

there was little difference in IEs of P among -P and

FFP plots (345 vs. 354 kg grain per kg plant P).

Although the estimates of internal ef®ciencies in

farmers' ®elds are probably valid for the linear part of

the relationship between grain yield and plant nutrient

accumulation, values refer to current crop and ferti-

lizer management practices and may not re¯ect the

optimum nutritional balance where the three macro-

nutrients are neither limiting nor available in surplus.

In our data set, fertilizer rates of N, P and K varied

greatly in farmers' ®elds (Table 5) which is consistent

with the observation that farmers often do not adjust

fertilizer rates to the indigenous nutrient supplies in

their ®elds (Cassman et al., 1996; Dobermann et al.,

1998). Thus, the observed large variation in internal

nutrient ef®ciencies does not only re¯ect site- and

season-speci®c differences in temperature and solar

radiation but also nutritional imbalances and problems

related to irrigation, pest and weed control. This calls

for a modeling approach to estimate the `true' opti-

mum nutrient uptake requirements.

4.3. Selection of data for adjusting QUEFTS to rice

A major component of the calibration of the

QUEFTS model for rice was to determine the border-

lines of maximum dilution and accumulation of nutri-

ents in the plants (Fig. 1(a)). This required a data set

where plant growth was not limited by factors other

than N, P or K supply. It is likely, however, that these

conditions were not met in all farmers' ®elds or plots

at experimental stations of our data set. Data points

representing plants with suf®cient nutrient uptake to

sustain higher yields but less grain formation due to

drought, lodging, pests, diseases or low solar radiation

during grain ®lling had to be excluded prior to the

calibration of QUEFTS. A low harvest index (HI) can

be expected under such conditions of restricted growth

(Hay, 1995), which makes the HI a potential tool for

selecting an appropriate data set for the calibration. In

our data set, grain yields did not exceed 6 t haÿ1 when

the HI was 0.40 or lower (Fig. 2). Furthermore, yields

were >6 t grain haÿ1 in ca. 20% (n � 600) of all cases

but only 1% of the plant samples had a HI < 0.45 and

yielded >6 t haÿ1. Thus, a HI of >0.45 can be expected

when grain yields of modern high yielding varieties

reach >6 t haÿ1. Only few plant sample had a

HI < 0.45 and yielded >7 t haÿ1 (Fig. 2). However,

we chose the more conservative HI of 0.40 as a

threshold value for excluding data from the calibration

of QUEFTS since a large number of plants with a HI

between 0.40 and 0.45 came from N, P or K omission

plots. These samples were useful for the calibration

since the nutrient that was not applied was most likely

limiting plant growth and therefore maximally diluted

in the plants. About 15% of all data had a HI < 0.40 but

the mean of most plant parameters was not affected by

the data elimination and standard deviations decreased

only slightly due to the large number of observations.

There was little change in average IEs of N, P and K due

to the data elimination (data not shown) but a number of

extreme IE values were eliminated.

4.4. Empirical models describing the envelope of the

relationship between grain yield and uptake of

N, P and K in rice

We used the reduced data set with a HI >

0.40 kg kgÿ1 (Table 6) to de®ne the two linear func-

tions describing the maximum accumulation and dilu-

tion of N, P and K in above-ground plant DM. The

slope of the boundary line representing the maximum

accumulation (a) of a nutrient in the plant (e.g.,

constant aN, Fig. 1(a)) would be equivalent to the

minimum internal nutrient ef®ciency observed in the

data set if all data would be included in the envelope.


Likewise, the slope of the boundary line representing

the maximum dilution (d) of a nutrient (e.g., constant

dN, Fig. 1(a)) would be equivalent to the maximum IE

value. Hypothetically, these straight boundary lines

could also be drawn `by hand' simply including all

data points in the envelope formed by the two bound-

ary lines. This would only be legitimate if a data set

met the prerequisite that (i) plant growth was only

limited by nutrient uptake and (ii) that any variation in

plant parameters was genuine and not caused by

experimental errors. It is impossible to obtain such

a data set under ®eld conditions so that an unbiased

method was required for the elimination of outliers in

order to obtain meaningful envelope functions.

To assess the sensitivity of the simulated optimal

relationships between grain yield and uptake of N, P

and K in the QUEFTS model, we compared, three sets

of constants (sets I±III, Table 7) representing the

Fig. 2. The relationship between harvest index and grain yield of rice. Data were obtained at experimental stations and from farmer's fields in

six tropical Asian countries between 1992 and 1997 (n � 2928).

Table 7

Constants of envelope functions relating grain yield (GY) to the maximum accumulation (a) and dilution (d) of N, P and K in the above-ground

plant dry-matter of irrigated lowland rice

Nutrient Value of constants

Set I Set II

a (2.5th) d (97.5th) r a (5th) d (95th) r

N 42 96 0 45 91 0

P 206 622 0 220 559 0

K 36 115 0 39 102 0

Set III Set IV

a (10th) d (90th) r a (2.5th) d (97.5th) r

N 49 86 0 43 106 3.0

P 241 503 0 207 632 0.1

K 43 89 0 37 126 3.0

Note: Data with an harvest index of <0.40 were excluded. Constants a and d were calculated by excluding the upper and lower 2.5, 5 or 10

percentiles (2.5th/97.5th, 5th/95th, or 10th/90th) of all internal nutrient efficiency data presented in Table 6 (n > 2000). In case of set IV, the

actual nutrient accumulation was corrected for the minimum nutrient uptake required to produce any measurable GY (r-values). Constants

were then estimated by excluding the upper and lower 2.5 percentile of the newly calculated internal nutrient efficiencies as done for sets I±III.


slopes of the boundary lines for maximum accumula-

tion (a) and maximum dilution (d). By treating the

upper and lower 2.5, 5 or 10 percentiles of the IEs as

outliers, data sets with different degrees of outlier

exclusion were obtained for de®ning the borderlines.

This is demonstrated in Fig. 3 where all IEs are plotted

against the HI. While the internal N ef®ciency was

normally distributed, the distribution of the IEs for P

and K were slightly skewed which appeared to be

related to the HI. As a consequence, constant d

changed relatively more than constant a when greater

percentiles of the internal P and K ef®ciencies were

excluded. With harvest indices ranging from 0.40 to

0.66, however, the mean values of the IEs differed by

only 3±5% from the median (66 vs. 64 kg grain kgÿ1

N, 371 vs. 358 kg grain kgÿ1 P, 66 vs. 63 kg

grain kgÿ1 K, Table 6).


accumulation in plant DM at maturity of rice (i.e.,

internal ef®ciency) is shown in Fig. 4 for data with a

HI > 0.40. As expected, the slope of each boundary

line forming the envelopes was greatly affected by the

stepwise exclusion of the 2.5th, 5th and 10th percen-

tiles of the IEs (Fig. 4(a)±(c)). However, the optimal

nutrient requirements calculated by the model (curves

of YN, YP and YK) were similar for all three sets of

constants (Fig. 4(d)±(f)). Apparently, eliminating a

greater percentage of the upper and lower IE values

only narrowed the envelopes and the skewed distribu-

tion of the IEs for P and K had little effect on the model

output. The relation between nutrient requirements

and grain yield target for the three sets of constants

differed only in the upper yield range (i.e., >7 t haÿ1)

since envelopes narrowed with stepwise data exclu-

sion forcing YN, YP and YK to follow a steeper curve.

Differences were greatest at yield targets that were

close to the yield potential. For example, N, P and K

requirements to achieve 8 t haÿ1 would be 6±11%

lower if envelope functions were based on constants

of set III (exclusion of 10th and 90th percentiles)

Fig. 3. The relationship between harvest index and internal efficiency (IE, kg grain yield per kg N, P or K in total above-ground plant dry-

matter). Data with a harvest index of <0.40 were excluded before the upper and lower lines representing the constants of maximum dilution (d)

and accumulation (a) of nutrients were determined by excluding the upper and lower 2.5, 5, and 10 percentiles of the IE data (for constants, see

sets I±III, Table 7).


instead of set I (exclusion of 2.5th and 97.5th percen-

tiles). However, considering the great variation in

internal ef®ciencies in farmers' ®elds, we presume

that any set of constants would lead to more balanced

fertilizer recommendations.

Theoretically, the envelope functions cannot go

through the origin since a minimum uptake of nutri-

ents (rN, rP, rK) is required to produce any measurable

grain yield (Janssen et al. (1990). However, these r-

values remain uncertain since they are experimentally

dif®cult to determine and extrapolation is question-

able. In order to test the sensitivity of the model to the

inclusion of r-values, it was assumed that 3 kg N,

0.1 kg P and 3 kg K would be needed to produce any

measurable grain yield. Correcting the actual nutrient

accumulation data using these r-values, a set of con-

stants was derived by excluding the upper and lower

2.5 percentile of the newly calculated internal nutrient

ef®ciencies (set IV, Table 7). The nutrient require-

ments as calculated by QUEFTS were almost identical

whether r-values were applied or not (data not shown).

Applying r-values, however, forced YN, YP and YK to

follow a steeper curve due to the offset of the envelope

functions caused by the r-values. As a consequence,

the IEs for the predicted nutrient requirements would

be too low at yield levels of <3 t haÿ1. For example,

QUEFTS predicted IEs of 60 kg grain per kg plant N

at a yield target of 2 t haÿ1 but 70 kg grain per kg plant

N at 6 t haÿ1. It is, however, more likely that IEs are

greater at lower yield levels where plant growth is

mainly limited by nutrient supply. Thus, we recom-

mend not to use any r-values in the QUEFTS model

which also simpli®es many of the equations used.

We propose to use the model parameters of set I

(Table 7) for a standard version of QUEFTS focusing

on practical decision making on fertilizer require-

ments of irrigated rice. Proposed standard slopes

describing the envelope of grain yield vs. nutrient

Fig. 4. Relationship between grain yield and accumulation of N, P and K in total above-ground plant dry-matter at maturity of rice based on

the data set presented in Fig. 3 after exclusion of data with an harvest index <0.40. The regression lines in the left of each figure represent the

boundary of maximum dilution (YND, YPD and YKD), while the lines on the right indicate the boundary of maximum accumulation (YNA,

YPA and YKA). Slopes of the boundary lines were calculated by excluding the upper and lower 2.5, 5 or 10 percentiles of all internal nutrient

efficiency data (n � 2200). For constants, see sets I±III, Table 7. In Fig. 4(d)±(f), YN, YP and YK represent the balanced uptake requirements

of N, P and K to achieve a certain rice grain yield target for the given boundaries as predicted by QUEFTS. The yield potential was set to

10 t haÿ1 (Ymax).


uptake in rice are aN � 42, dN � 96, aP � 206, dP �622, aK � 36 and dK � 115. For comparison, values

proposed for maize were aN � 30, dN � 70, aP �200, dP � 600, aK � 30 and dK � 120 (Janssen et al.,

1990). Apparently, rice has a greater IE of N than

maize, whereas IEs of P and K appear to be similar.

The ratio of the slopes of maximum dilution to max-

imum accumulation (d/a) in rice was smaller for N

(2.3) than for P (3.0) and K (3.2), con®rming that grain

yield of rice is very tightly related to N uptake (Kropff

et al., 1993). Since such a strong correlation cannot be

expected between grain yield and plant P or plant K

accumulation, approaches like QUEFTS are needed

for calculating nutrient requirements based on nutrient

interactions.

4.5. Nutrient requirements as affected by the

potential yield

The QUEFTS model calculates the nutrient uptake

requirements to achieve a certain yield target depend-

ing on the potential yield as shown in Fig. 5. Depend-

ing on season and site, the potential yield of currently

grown rice varieties in the countries represented in our

database ranged from about 6 to 11 t haÿ1. For com-

parison, the maximum grain yields recorded at IRRIs

Mega Project sites ranged from 6.0 t haÿ1 for a wet

season rice crop (measured at Suphan Buri, Thailand),

to 9.9 t haÿ1 for a dry season rice crop (measured

in North-Vietnam and Central Luzon, Philippines).


accumulation as predicted by QUEFTS is linear at

lower yield levels re¯ecting a situation where plant

growth is mainly limited by nutrient supply (Fig. 5).

The model also calculates a decrease in internal

nutrient ef®ciencies when target yields are close to

the yield potential (Table 8), in consistency with

results obtained from fertilizer trials at experimental

stations (Cassman et al., 1993, 1995; Dobermann

et al., 1996a, b).

Regardless of the selected yield potential, the opti-

mal N : P : K ratio in plant DM as recommended by

Fig. 5. The balanced N, P and K uptake requirements (YN, YP and YK) for targeted grain yields depending on the yield potential (Ymax) as

calculated by QUEFTS. See Fig. 4 for explanation of YND, YPD, YKD, YNA, YPA and YKA. Boundaries were calculated using constants of

set I (Table 7).


QUEFTS was ca. 5.7 : 1 : 5.6 (Table 8, Fig. 5) which

is similar to the average plant N : P : K ratio of

6.1 : 1 : 5.6 derived from farmers' ®elds. For the linear

part of the relationship between grain yield and nutri-

ent accumulation (Fig. 5), QUEFTS calculates that

14.7 kg N, 2.6 kg P and 14.5 kg K haÿ1 would be

needed to produce 1000 kg grain yield, i.e., internal

ef®ciencies of 68 kg grain kgÿ1 N, 385 kg grain kgÿ1

P and 69 kg grain kgÿ1 K could be achieved under

optimum conditions at yield levels of about up to 80%

of Ymax (Table 8). For comparison, the average inter-

nal nutrient ef®ciencies in farmers' ®elds were 59 kg

grain kgÿ1 N, 354 kg grain kgÿ1 P and 64 kg

grain kgÿ1 K. This difference was probably due to

both nutrient imbalances in farmers' ®elds as well as

differences in yield potentials at the various experi-

mental sites. The threshold yield level beyond which

the internal nutrient ef®ciency starts to decrease

mainly depends on the climate-adjusted potential

yield if other factors are not limiting (Fig. 5). Another

reason may be that factors other than nutrient supply

affected the IE in farmers' ®elds. The future challenge

will be to increase IEs in farmers' ®elds at constant or

increased grain yield levels by a balanced N, P and K

nutrition and improved cropping management.

Caution is needed in using an empirical model such

as QUEFTS for de®ning nutrient requirements in the

nonlinear range of the relationship between grain yield

and nutrient uptake. For elevated yield levels of 9.1±

9.9 t haÿ1, QUEFTS predicted plant N requirements

of 163±217 kg N haÿ1 at a yield potential of 10 t haÿ1

(Table 8). This was similar to measured values of

165±205 kg N haÿ1 in the same yield range in the

Philippines (Cassman et al., 1997; Ying et al., 1998a,

b). However, the accuracy in predicting nutrient

requirements for elevated yields is greatly affected

by the seasonal variation of the yield potential. For

example, if the yield potential in a particular season

was 10.5 t haÿ1 instead of 10 t haÿ1, plant N require-

ments to achieve a target yield of 9.9 t haÿ1 would

drop from 217 to 187 kg N haÿ1 in that season as

predicted by QUEFTS. We need more data in the high-

yield range to further improve the model. Presumably,

mechanistic crop growth models are more suitable to

handle such situations, although none of the existing

rice models is capable of simulating the nutrition of N,

P and K.

We argue, however, that nonlinear situations cur-

rently have little relevance for practical decision mak-

ing under normal economic conditions as farmers

Table 8

Balanced uptake requirements, internal efficiencies (kg grain per kg nutrient), and reciprocal internal efficiencies (kg nutrient per 1000 kg

grain) of N, P and K for irrigated lowland rice as calculated by QUEFTS to achieve certain grain yield targets

Yield Required nutrient uptake Internal efficiency Reciprocal internal efficiency

(kg haÿ1)N P K N P K N P K

(kg haÿ1) (kg kgÿ1) (kg 1000 kgÿ1)

1000 15 2.6 15 68 385 69 14.7 2.6 14.5

2000 29 5.2 29 68 385 69 14.7 2.6 14.5

3000 44 7.8 43 68 385 69 14.7 2.6 14.5

4000 59 10.4 58 68 385 69 14.7 2.6 14.5

5000 73 13.0 72 68 385 69 14.7 2.6 14.5

6000 88 15.6 87 68 385 69 14.7 2.6 14.5

7000 104 18.4 103 67 380 68 14.8 2.6 14.7

7500 115 20.4 114 65 368 66 15.3 2.7 15.1

8000 127 22.6 126 63 354 64 15.9 2.8 15.7

8500 142 25.1 140 60 339 61 16.7 3.0 16.5

9000 159 28.2 157 57 319 57 17.6 3.1 17.4

9500 182 32.2 180 52 295 53 19.2 3.4 19.0

9800 205 36.3 203 48 270 48 20.9 3.7 20.7

9900 217 38.6 215 46 256 46 21.9 3.9 21.7

9990 243 43.1 240 41 232 42 24.3 4.3 24.1

Note: The model was run using constants of set I (Table 6). The grain yield potential was set to 10 t haÿ1.


rarely aim at yield levels that are beyond 80% of the

maximum yield potential (Cassman and Harwood,

1995). The demand for increasing rice production,

however, may increasingly force farmers to operate in

the non-linear range of the relationship between grain

yield and nutrient uptake, although future advances in

increasing Ymax may offset this need.

4.6. Genotypic variation in nutrient requirements

A crucial issue was whether a generic model relat-

ing nutrient uptake to grain yield would be applicable

for all modern, high yielding, short-to-medium dura-

tion cultivars. The ef®ciency of DM production per

unit of incident global radiation appears to be similar

as shown in cross-location experiments (Horie et al.,

1997), but great uncertainties remain about nutrient

requirements of speci®c rice cultivars. Genetic selec-

tion and plant breeding techniques were primarily

used to develop rice cultivars that are high yielding

or resistant to pests, diseases, or adverse environmen-

tal conditions. It was only recently that attempts have

been made to identify superior N-ef®cient rice geno-

types but data on genotypic variation in IEs of P and K

are lacking (Broadbent et al., 1987; Tirol-Padre et al.,

1996; Singh et al., 1998).

It has to be kept in mind that the IEs as calculated by

QUEFTS are based on the average IE values of

numerous modern, high-yielding indica cultivars

grown at the various experimental sites. Thus, if the

IE of a certain cultivar was greater than that of another,

the envelope functions for the two should differ. In

other words, if a single cultivar had a narrower range

of IEs and, thus, formed a narrower envelope than

anticipated, the standard envelope functions may

re¯ect the maximum IE of a certain cultivar but the

Fig. 6. Genotypic variation in the relationship between grain yield and accumulation of N in total above-ground plant dry-matter (DM) at

maturity of rice. Data depicted in Fig. 6(a)±(c) derive from long-term fertility experiments with IR64 in Vietnam (Omon), Indonesia

(Sukamandi), and India (Aduthurai) in 1995 to 1997 (this study). Data of Fig. 6(d) and (e) originated from an experiment with 10 different

medium-duration cultivars grown in the 1993 dry-season at IRRIs experimental farm (adapted from Singh et al., 1998). Data depicted in

Fig. 6(d) derive from treatments receiving 0, 50, 100, 150 or 200 kg fertilizer-N haÿ1, while only 0 and 150 kg fertilizer-N treatments (N0 and

N150) are considered in Fig. 6(e). The yield potential was estimated with 10 t haÿ1. See Fig. 4 for explanation of Ymax, YN, YND, YNA,

YPD, YPA, YKD and YKA.


minimum IE of another. Overlaying data from differ-

ent cultivars that describe the relationship between

grain yield and plant N obtained would then result in

inappropriate standard envelope functions. A compar-

ison of the varieties in our database, however, indi-

cated that the modern, high yielding cultivars

currently grown in farmers' ®elds have a wide and

very similar range of internal N, P and K ef®ciencies

as demonstrated in Fig. 6(a)±(c) for IR64. The stan-

dard envelope functions for N, P and K are based on

the model parameters of set I (Table 7). The internal N

ef®ciency of IR64 appeared to be relatively low at

elevated yield levels (Fig. 6(a)), but the data set was

too small to determine whether this was genetically

determined or due to site- or season-speci®c condi-

tions.

We further evaluated the standard envelope

functions for N using recently published data on grain

yield and plant N accumulation in above-ground plant

DM of 10 different medium-duration cultivars

(Fig. 6(d) and (e)). Full details of the experiment

are given by Singh et al. (1998). The material in this

experiment had been selected from a larger ®eld

screening trial (Tirol-Padre et al., 1996), and included

cultivars as well as advanced breeding lines. Using

the ORYZA1 model (Kropff et al., 1994b), we

estimated a yield potential of 10 t haÿ1 for the 1993

DS in which the experiment was conducted at IRRI

(Fig. 6(d) and (e)).

It appears that the standard envelope functions for N

are generally valid for the current generation of mod-

ern, high yielding cultivars as our estimated range of

internal N ef®ciencies, represented by YND and YNA,

was also valid for advanced breeding lines of selected

medium-duration cultivars (Fig. 6(d)). At low and

medium yield levels, almost all cultivars ef®ciently

used the N acquired to produce grain yield but the

estimated maximum IE of 96 kg grain per kg plant N

accumulation (i.e., constant d; set I, Table 7) was

generally not exceeded.

Despite similar ranges of internal N ef®ciencies,

though, some cultivars may produce more grain than

others at comparable levels of N supply from indi-

genous sources (Broadbent et al., 1987; Tirol-Padre et

al., 1996), and/or applied fertilizer-N due to genotypic

differences in N uptake, HI, nitrogen HI, or IE (Singh

et al., 1998). We argue, however, that the presented

approach using QUEFTS for practical decision

making on fertilizer requirements of irrigated rice is

applicable to all modern cultivars despite differences

in above mentioned plant parameters. Even though

grain yields in N unfertilized (N0, Fig. 6(e)) plots may

vary greatly as shown for the 10 different medium-

duration cultivars used by Singh et al. (1998), geno-

typic variation of grain yield and internal N ef®cien-

cies were rather small in treatments receiving 150 kg

fertilizer-N haÿ1 (N150, Fig. 6(e)). The only excep-

tion was the older, and less N ef®cient cultivar IR20.

The HI in the N150 treatments averaged 0.55 kg kgÿ1

(ranging from 0.51 to 0.60 kg kgÿ1) while the IE was

on average 68 kg grain per kg plant N (ranging from

65 to 78 kg kgÿ1). However, some cultivars produced

more grain at medium fertilizer-N (or yield target)

levels as they acquired N more ef®ciently than others.

At these yield levels, N supply was actually limiting

yield as most data points were close to the borderline

of YND (Fig. 6(d)). If this was the case and if geno-

typic variation in the IE of N was low as the results

indicate, the actual fertilizer-N requirement of culti-

vars that are more ef®cient in taking up N from

indigenous sources and/or fertilizer-N would slightly

be overestimated. However, this could be corrected

with a N management that is using plant-based tech-

nologies such as chlorophyll meter or the leaf color

chart. The optimal N rate for a certain season, site and

yield target should not be considered as a ®xed value

because crop N requirements may change due to

yearly variation in solar radiation and temperature.

4.7. Season- and site-specific differences in nutrient

requirements

A comparison of internal nutrient ef®ciencies from

sites in the Philippines and India indicates that the

average potential yield could be used as the only site-

or season-speci®c parameter for estimating nutrient

requirements (Fig. 5) as it is not advisable to use

different envelope functions for different sites or

climatic seasons (Fig. 7). The WS yield potential is

slightly lower in Maligaya, Central Luzon, Philip-

pines, than in Aduthurai, Tamil Nadu, India (8 vs.

8.5 t haÿ1) as simulated with crop models while the

DS yield potentials were ca. 10 t grain haÿ1 at both

sites (Kropff et al., 1994a; Mohandass et al., 1995).

These estimates corresponded well with the highest

yields observed at each site during the respective


season except for the WS data in the Philippines

(Fig. 7).

If two separate DS and WS envelope functions were

chosen for N in Maligaya, the DS functions would be

largely towards the line of maximum dilution while

the WS lines were closer to the line of maximum

accumulation (Fig. 7(a)). Adjusting the envelope

functions would, therefore, cause a corresponding

shift of the optimum line of N accumulation as pre-

dicted by QUEFTS (YN, Fig. 7(a)). This would,

however, not lead to an improved nutritional balance

of the plants. The climatic conditions are more favor-

able for growing rice in the DS than the WS, and there

are clear indications that plants were even N limited in

the DS since most data points were closer to the line of

maximum N dilution (YND, Fig. 7(a)). In contrast,

most WS data points were below the optimum line of

N accumulation as predicted by QUEFTS (YN,

Fig. 7(a)) and, independent of fertilizer-N application,

closer to the line of maximum accumulation. The WS

results in Maligaya were probably caused by unfavor-

able weather conditions especially during the grain

®lling period since the general plant N accumulation

was suf®cient to sustain higher yields. This was well

re¯ected by the lower HI of the WS than the DS crops

(0.42 vs. 0.48). If season-speci®c envelope functions

were chosen at this site, the fertilizer-N recommenda-

tion would be to apply less N to DS crops but more N

to WS crops. Instead, it is economically reasonable to

apply more fertilizer-N to the DS than the WS crops.

Likewise, the P accumulation seems to be generally

close to the line of maximum dilution in both DS and

WS crops in Maligaya which indicates insuf®cient

supply to the rice crops. This supports results of a

recent survey where >60% of a 19 200 ha survey area

of irrigated rice farm land in the same region, were

classi®ed as low in available soil P reserves (Dober-

mann and OberthuÈr, 1997). Thus, if fertilizer-P recom-

Fig. 7. Relationship between grain yield and accumulation of N, P and K in total above-ground plant dry-matter at maturity of rice in dry- and

wet-seasons (DS, WS) in Maligaya, Central Luzon, Philippines (Fig. 7(a)±(c)), and Aduthurai, Tamil Nadu, India (Fig. 7(d)±(f)), 1995±1997.

Data derive from experimental stations and farmers' fields. See Fig. 4 for explanation of abbreviations. Envelope functions were calculated

using constants of set I (Table 7). The yield potentials were estimated with 10 and 8 t haÿ1 (DS, WS) in Maligaya, and 10 and 8.5 t haÿ1 (DS,

WS) in Aduthurai. Thus, YN, YP and YK differed in DS (straight lines) and WS (broken lines). Data with a harvest index of <0.40 were

excluded.


mendations were based on site-speci®c envelope func-

tions for P in Maligaya using the data in Fig. 7(b), the

apparent P depletion of the soils would be further

enhanced.

The nutrition of the rice plants appeared to be well-

balanced in Aduthurai, India. Most P and K uptake

data were close to the optimum line as predicted by

QUEFTS (YP, YK, Fig. 7(e) and (f)). Traditionally,

farmers in Aduthurai apply higher rates of K through

fertilizer and farmyard manure than those in Maligaya

which explains the less scattered distribution of the

K uptake data (Fig. 7(f) vs. Fig. 7(c)). However, the

internal nitrogen ef®ciency in Aduthurai differed

from the optimum N line (YN) depending on the

yield level (Fig. 7(d)). In plots without N application,

grain yields averaged 4.4 t haÿ1 in the DS (n � 138)

and the average IE was very high (>80 kg grain per

kg N). In fertilized plots, grain yields averaged

6.5 t haÿ1 during the DS with an IE of 58 kg grain

per kg plant N (n � 161) which was lower than the

target IE of 68 kg kgÿ1 as predicted by QUEFTS

(Table 8). Plants therefore seem to acquire suf®cient

nitrogen to sustain even higher yields. Additional

information would be needed to decide whether the

fertilizer ef®ciency could be improved by choosing a

different nitrogen split application in order to meet

the crop N demand or whether less fertilizer-N should

be applied.

5. Conclusions

The presented approach using QUEFTS allows not

only the estimation of nutrient requirements to achieve

a certain yield target, it also provides a useful tool for

identifying nutritionally optimal yield targets. The

calibration of the QUEFTS model for rice required

the estimation of the slopes of two borderlines describ-

ing the maximum accumulation (a) and dilution (d) of

N, P and K in the plant in relation to grain yield. We

propose to use aN � 42, dN � 96, aP � 206,

dP � 622, aK � 36 and dK � 115 as standard model

parameters in QUEFTS for all irrigated rice varieties

with a HI of �0.50. We suggest not to use constants

assumed to represent the minimum nutrient uptake

requirement (r-values) to obtain any measurable grain

yield when determining the envelope functions

because internal nutrient ef®ciencies would be under-

estimated at low target yields.

On condition that plant growth was only limited by

nutrient supply, the model predicted a linear increase

in grain yield if nutrients are taken up in balanced

ratios of 14.7 kg N, 2.6 kg P and 14.5 kg K per

1000 kg of grain until yield targets reached ca. 70±

80% of the climate-adjusted potential yield (Ymax). In

this yield range, optimal IEs for a balanced nutrition

were 68 kg grain kgÿ1 N, 385 kg grain kgÿ1 P and

69 kg grain kgÿ1 K. With yield approaching Ymax, IEs

of nutrients decreased. The optimal IEs as predicted

by QUEFTS were greater than previously used litera-

ture estimates and also exceed those measured in

many farmers' ®elds. Low IEs in the farmers' practice

were related to nutritional imbalances, inadequate

irrigation, or problems with pests. It may be more

pro®table for farmers to maximize nutrient ef®cien-

cies by a more balanced nutrition than to aim for

higher yield targets in seasons with yield levels

approaching maximum yields.

Compared to commonly used `rules of thumb' for

estimating crop nutrient uptake requirements, the

main advantages of our modeling approach were (i)

wide geographical coverage and use of on-farm data

for model development, (ii) treatment of the relation-

ship of grain yield vs. nutrient uptake in a linear to

non-linear fashion and (iii) simultaneous optimization

of the IEs of N, P and K based on their interactions.

The envelope functions determined by the constants a

and d are applicable to all irrigated rice crops grown in

tropical and subtropical Asia regardless of the method

of crop establishment, site or growing season. Envel-

ope functions may have to be modi®ed only if a new

generation of modern high-yielding varieties with

different crop characteristicswas introduced.Thus, site-

or season-speci®c information other than Ymax is not

required for the crop-speci®c part of a SSNM approach,

abolishing theneed for expensive calibration research of

that component. Site-speci®c nutrient management in

rice will, however, require more farm- or soil-speci®c

estimates of the indigenous nutrient supply.

Appendix A

De®nitions and origin of variables needed for

calculating the plant N, P, and K requirements to

achieve a certain grain yield target using QUEFTS

(modi®ed after Janssen et al., 1990).


Appendix A

Model input data and parameters Origin of variables

INS Potential indigenous soil N supply (kg haÿ1) � crop

N uptake in a plot without N application but ample

P and K supply

Field-specific estimation of INS, IPS and IKS. Values

depend on soil type and field management and may

change with time.

IPS Potential indigenous soil P supply (kg haÿ1) � crop

P uptake in a plot without P application but ample

N and K supply

IKS Potential indigenous soil K supply (kg haÿ1) � crop

K uptake in a plot without K application but ample

N and P supply

RFN

RFP

RFK

Recovery fraction of applied N (%)

Recovery fraction of applied P (%)

Recovery fraction of applied K (%)

Soil specific target values depending on timing and

mode of application considering possible residual

effects. Initial values may be obtained from previous

fertilizer trials.

FN Recommended N Fertilizer rate (kg haÿ1) Initial value � 0, optimized by model

FP Recommended P Fertilizer rate (kg haÿ1)

FK Recommended K Fertilizer rate (kg haÿ1)

aN

dN

Maximum accumulation of N in the plant (slope

of envelope function grain yield vs. N uptake)

Maximum dilution of N in the plant (slope of

envelope function grain yield vs. N uptake)

Generic constants or region- and/or season-specific

constants for each site. Season-specific constants would

account for differences in climatic yield potential and

possible differences in internal nutrient efficiency

aP Maximum accumulation of P in the plant (slope

of envelope function grain yield vs. P uptake)

dP Maximum dilution of P in the plant (slope of

envelope function grain yield vs. P uptake)

aK Maximum accumulation of K in the plant (slope

of envelope function grain yield vs. K uptake)

dK Maximum dilution of K in the plant (slope of

envelope function grain yield vs. K uptake)

rN Minimum N uptake to produce any measurable

grain yield (kg haÿ1)

Variety-specific, obtained from experimental data or

estimation

rP Minimum P uptake to produce any measurable


rK Minimum K uptake to produce any measurable


Ymax Climatic � genetic yield potential (kg haÿ1) Region and season-specific, obtained from crop

simulation models or expertise

Model-calculated variables

SN Potential supply of N (kg haÿ1), SN � INS � RFN � FN

SP Potential supply of P (kg haÿ1), SP � IPS � RFP � FP

SK Potential supply of K (kg haÿ1), SK � IKS � RFK � FK

SNy Potential yield-producing supply of N (kg haÿ1), SNy � SN ÿ rN

SPy Potential yield-producing supply of P (kg haÿ1), SPy � SP ÿ rP

SKy Potential yield-producing supply of K (kg haÿ1), SKy � SK ÿ rK

UN(P) Actual N uptake as a function of N and P supply (kg haÿ1)

UN(K) Actual N uptake as a function of N and K supply (kg haÿ1)

UP(N) Actual P uptake as a function of P and N supply (kg haÿ1)

UP(K) Actual P uptake as a function of P and K supply (kg haÿ1)

UK(N) Actual K uptake as a function of K and N supply (kg haÿ1)

UK(P) Actual K uptake as a function of K and P supply (kg haÿ1)

UN Final estimate of actual N uptake (kg haÿ1), UN � minimum (UN(P),UN(K))


Acknowledgements

This paper could not have been written without the

dedicated work of many people participating in the

Mega Project on `Reversing Trends of Declining

Productivity in Intensive Irrigated Rice Systems'.

We thank Kenneth G. Cassman for initializing and

leading the project during 1994 to 1996. Researchers

in the Philippines, Thailand, Indonesia, India, Viet-

nam and China deserve credit for their successful

implementation of the project. In addition to those

listed as co-authors, we wish to thank E.M. Punzalan,

R.T. Cruz, J. Bajita and F. Garcia (PhilRice), S.

Chatuporn, J. Sookthongsa, and M. Kongchum

(PTRRC), I. Juliardi (RIR), P. Muthukrishnan and P.

Stalin (TNRRI), He Yunfeng, Sun Qinzhu and Ding

Xianghai (ZU/Jinhua Agric. Research Center), Cao

Van Phung (CLRRI), Nguyen Van Chien and Vu Thi

Kim Thoa (NISF), Le Quoc Thanh (VASI), and P.C.

Sta. Cruz and M.A.A. Adviento (IRRI).

The data from the INSURF LTFE were collected in

1993 and we wish to acknowledge the support of J.P.

Descalsota(IRRI),E.M.Imperial(Bicol,BRIARC),S.P.

Palaniappan (Coimbatore, TNAU), P. Lal (Pantnagar,

G.B. Pant University), R. Djafar Baco, R. Le Cerff, and

Ir. Rauf Mufran (Maros and Lanrang, MORIF), Li

Jiakang (Jinxian, Qingpu, Shipai), Lai Qingwang (Jin-

xian, Red Soil Institute), Wang Yinhu and Zhou Xiu-

chong (Soil and Fertilizer Institute, GAAS).

The authors thank John Sheehy (IRRI), Shaobing

Peng (IRRI), and an unknown reviewer for their helpful

comments on an earlier draft of this paper.The Swiss

Agency for Development and Cooperation (SDC), the

International Fertilizer Industry Association (IFA), the

Potash and Phosphate Institute Canada (PPIC), and the

International Potash Institute (IPI) provided funding for

different parts of the presented research.

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Appendix A (Continued )

Model input data and parameters

UP Final estimate of actual P uptake (kg haÿ1), UP � minimum (UP(N),UP(K))

UK Final estimate of actual K uptake (kg haÿ1), UK � minimum (UK(N),UK(P))

UNy Actual yield-producing uptake of N (kg haÿ1), UNy � UN ÿ rN

UPy Actual yield-producing uptake of K (kg haÿ1), UKy � UK ÿ rK

UKy Actual yield-producing uptake of K (kg haÿ1), UKy � UK ÿ rK

YNA Estimated GY for the predicted UN at max. accumulation of N in the plant (kg haÿ1), YNA � aN * (UNy)

YND Estimated GY for the predicted UN at max. dilution of N in the plant (kg haÿ1), YND � dN * (UNy)

YPA Estimated GY for the predicted UP at max. accumulation of P in the plant (kg haÿ1), YPA � aP * (UPy)

YPD Estimated GY for the predicted UP at max. dilution of P in the plant (kg haÿ1), YPD � dP * (UPy)

YKA Estimated GY for the predicted UK at max. accumulation of K in the plant (kg haÿ1), YKA � aK * (UKy)

YKD Estimated GY for the predicted UK at max. dilution of K in the plant (kg haÿ1), YKD � dK * (UKy)

YNP Estimated GY for UN as limited by GYT that can be achieved with UP (kg haÿ1)

YNK Estimated GY for UN as limited by GYT that can be achieved with UK (kg haÿ1)

YPN Estimated GY for UP as limited by GYT that can be achieved with UN (kg haÿ1)

YPK Estimated GY for UP as limited by GYT that can be achieved with UK (kg haÿ1)

YKN Estimated GY for UK as limited by GYT that can be achieved with UN (kg haÿ1)

YKP Estimated GY for UK as limited by GYT that can be achieved with UP (kg haÿ1)

GYT Grain yield target (kg haÿ1), GYT � mean (YNP,YNK,YPN,YPK,YKN,YKP)

YPUEN Yield-producing uptake efficiency of N, YPUEN � UNy/SNy

YPUEP Yield-producing uptake efficiency of P, YPUEP � UPy/Spy

YPUEK Yield-producing uptake efficiency of K, YPUEK � UKy/SKy

TYPUE Total yield producing uptake efficiency, TYPUE � mean (YPUEN,YPUEP,YPUEK)


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Internal nutrient efficiencies of irrigated lowland rice in tropical and subtropical Asia

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