Modelling plant nutrition of horticultural crops: a reviewplantstress.com/Articles/min_deficiency_i/modelling nutrition.pdf · Scientia Horticulturae 74 1998 47–82 . Modelling plant

Ž .Scientia Horticulturae 74 1998 47–82

Modelling plant nutrition of horticultural crops:a review

J. Le Bot ), S. Adamowicz 1, P. Robin 2

INRA, Unite de Recherche en Ecophysiologie et Horticulture, Domaine St. Paul, Site Agroparc,´84914 AÕignon, Cedex 9, France

Accepted 19 September 1997

Abstract

In this review, studies in plant nutrition are classified according to their time scales and micro-or macroscopic level of approach. Short-time scale studies are mostly dealt by plant physiologistswith the prospect of building mechanistic models. They describe elementary plant functionsimplicated in, or dependent on ion uptake, with the goal of explaining the mechanisms underneaththe functions. The concept of ‘active ion transport’ across the root plasma membrane derives fromprecise analyses of uptake ‘isotherms’ describing nutrition as a function of ion concentration in theroot medium. Attempts to introduce feedback mechanisms, as required to model whole-plantresponse to the environment, are reviewed. Similarly, the response of plant photosyntheticcapacity to leaf nitrogen status is extremely rapid and the role of nitrogen in regulatingphotosynthesis seems to hold for a large number of species. Therefore, it appears possible tointroduce nitrogen regulation on leaf photosynthesis, thus allowing better simulations of plantgrowth under nitrogen limiting conditions. Long-time scale studies are dealt by agronomists andhave long been the basis of fertilization advice. They attempt to predict crops’ mineral nutrientrequirements over the entire cycle from the empirical knowledge of ‘general laws’ governing cropgrowth. Recent advances propose to manage nutrition on the basis of crop structure independentlyfrom species and give opportunities to develop mechanistic concepts at this time scale. Fornitrogen, this has been formalized extensively in crops such as cereals and grasses. It deserves tobe carefully looked at for horticultural crops. These models also provide a sound basis to diagnosisthrough plant analysis. In horticultural agrosystems, such as those found for hydroponic culturesunder commercial glasshouses, the use of on-line sensors is currently an alternative to cropmodels, since fertilization is induced by the immediate response of the sensors. This practice made

) Corresponding author. E-mail: [email protected] E-mail: [email protected] E-mail: [email protected]

0304-4238r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved.Ž .PII S0304-4238 98 00082-X

( )J. Le Bot et al.rScientia Horticulturae 74 1998 47–8248

possible by technological breakthrough is meant to correct drifts but lacks anticipation. q 1998Elsevier Science B.V.

Keywords: Efflux; Functional equilibrium; Influx; Mineral ions; Model; Nitrogen; Photosynthesis; Plantgrowth; Regulation; Uptake rates

Contents

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

2. Proximate functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 522.1. Nutrient uptake . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

2.1.1. Influx isotherms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 532.1.2. Efflux measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 542.1.3. Net uptake isotherms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

2.2. Feedback regulation of uptake . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 562.2.1. Influx . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 572.2.2. Efflux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 582.2.3. Net uptake . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

2.3. Nutrient use efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 592.3.1. Nutrients and photosynthesis: a casual relationship? . . . . . . . . . . . . . . . . . . . . 592.3.2. Several models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 612.3.3. Nutrients and water fluxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

2.3.3.1. Is there a casual relationship between PNUE or mineral concentrations andWUE? Is mineral uptake, in particular nitrogen, controlled by plant water fluxes? . . . . 63

3. Ultimate functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 643.1. Nutrient uptake and functional equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 643.2. Growth control by nutrients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 653.3. Growth demand of nutrients. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

3.3.1. Statistic approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 663.3.2. Mechanistic approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

4. Operational approach of nutrition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 694.1. Diagnostic of nutritional status . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 694.2. Managing the cultural system: the greenhouse as an example . . . . . . . . . . . . . . . . . . . 70

5. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

1. Introduction

Plants acquire from their aerial and root environments all constituents of their tissues.In particular, soil fertility governs plant growth and thereby the quantities of mineralnutrients taken up by the roots. In natural ecosystems, the minerals absorbed by growingorganisms return to the soil after organic matter decomposition, and soil fertility is moreor less maintained through nutrient cycling. In cultivated ecosystems, however, all

( )J. Le Bot et al.rScientia Horticulturae 74 1998 47–82 49

harvested biomass withdrawn from the field contains nutrients that no longer return tothe soil. Hence, maintenance of soil fertility and plant yield production depend ofcounterbalancing fertilizer inputs. Considering all the nations in the world, grain yield

Ž .increases linearly with the doses of NqPqK fertilizers applied to cereals and thisŽ .accounts for more than 80% of the variance in yield Greenwood, 1990 . From the

viewpoint of agricultural productivity, it means that mineral nutrition is the main factorlimiting growth and therefore high fertilizer inputs are necessary to produce largequantities of biomass. This idea explains the peculiarity of horticulture where fertiliza-tion is extremely intensive: although nitrate concentration in the soil solution of a fertile

y3 Ž .field ranges between 2 to 20 mol m Mengel and Kirkby, 1987; p. 365 , the nutrientsolution used to grow tomatoes in soilless cultures is maintained in between 15–25 molmy3 NOy. Meanwhile, 1 ha of fertile wheat field yielding 8 tonnes of grains produces3

around 14 tonnes of aerial dry biomass, whereas 1 ha of greenhouse yielding 450 tonnesof tomatoes produces around 40 tonnes of total aerial dry biomass.

Since the XIXth century, it is well known that plant growth is always limited by thefirst factor whose availability in the environment starts missing. This fundamentalconcept has guided research to render modern agriculture more efficient. The contempo-

Žrary research in crop physiology has identified the factors limiting plant growth Table.1 , tempted to delay their upcoming limitation or change their order of appearance, and

quantified their potential productivity increase when economically profitable.These lines of research resulted in increasingly more complex models of plant growth

Ž .processes and yields which offer today the operational bases for strategic long-termŽ .and tactical short-term crop management. Meanwhile, industrialization and break-

through in technology have given growers powerful and sophisticated tools to manipu-late these factors. Moreover, for highly profitable potential productivity increases, newagrosystems have been developed to manipulate the naturally fixed limiting factors. Forinstance, the development of horticulture in protected environments proceeds from thistechnical breakthrough and growers use in their greenhouses CO enrichment, soilless2

cultural techniques, artificial lighting and heating and cooling to increase productivity.It may seem a paradox to trace the first reports on plant water and mineral nutrition

back to the XVIIth century and state that today there is still controversy about themechanisms of ion uptake, and moreover, the use of mineral nutrition in crop modelsŽ .Fig. 1 ; Table 2 .

Table 1Factors limiting plant yield. For non-fixed factors, the names expensive and cheap refer to the cost in energy

Ž .required to set-up the desired factor modified after Mohr and Schopfer, 1995

Fixed factors Non-fixed factors

Expensive factors Cheap factors

CO concentration Irrigation Plant density2

Light integral Fertilization Time of sowingTemperature Crop protection GenotypeType of soil Nutritional value External yield quality


w xFig. 1. Different approaches for modelling the uptake of a nutrient X . All numbers refer to models listed inŽ .Table 2. The direction of the arrows indicate which factor is explained target by an explicative factor.

Dashed lines refer to regulatory processes.

Agronomists and plant physiologists have developed a dual approach to characterizew xthe uptake of a mineral nutrient X by a plant. A ‘mechanistic’ approach describes

Ž w x .uptake as successive steps: uptake per se i.e. the entrance of X inside the root ,Ž .assimilation if any andror transport in the plant and at last utilisation in plantŽ .metabolism Fig. 1; groups 1, 2 and 3 . Research along these lines aims at explaining the

‘proximate’ factors controlling mineral uptake. Hence, modelling is set at fine spatio-temporal scales: short-time studies at the cellular and molecular levels. The uppermostimportant question concerns the identification of uptake regulatory processes likely tohappen in one or several successive steps. In the end, only the integration of thesesuccessive steps will simulate adequately the behaviour of a whole plant. The second‘statistic’ approach has anteriority and proceeds from higher levels of integration. Thisresearch focus on the ‘ultimate’ factors governing the equilibrium between mineral

Ž .uptake and plant demand considered through growth Fig. 1; groups 4 and 5 . From thisŽviewpoint, modelling is set at a broad spatio-temporal scale: long-time studies months,

.year at the whole plant or field levels. This approach has resulted in the actualŽfertilization practices, which attempt simultaneously to maintain soil fertility by a

. Ž‘maintenance’ fertilization and to fulfil the crop-growth demand by a ‘growth’.fertilization . Table 2 is a non-exhaustive compilation of the authors which have

developed the main concepts used as starting points for models dealing with plantmineral nutrition.

This review will concentrate on the main models of plant mineral nutrition publishedin the literature with an attempt to explicate the hypotheses underneath the concepts. Itreflects our view of agronomists seeking for a leading thread in the plentiful literature onplant nutrition. Thereby, we have tried here to organize the current hypotheses into alogical conceptual frame suitable for whole-plant physiologists and agricultural engi-

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Table 2Ž . Ž .A brief history of plant nutrition modelling. In the ‘model’ column, s and m refer to statistic and mechanistic models. The ‘group’ column refers to the place of the

models in Fig. 1

Explained Explicative factors Model Group Authorsfactorrfunction

Ž . Ž .Growth: final yield dose of one element Ø law of minimum s 4 von Liebig 1841Ž . Ž .dose of one element Ø diminishing return s 4 Mitscherlich 1909

Ž . Ž .plant nutrient content Ø critical concentration s 5 Ulrich 1952Ž . Ž .dose of two or more elements Ø nutrient equilibrium s 4 Homes and van Schoor 1982`

˚Ž . Ž . Ž .dynamic rate of supply of one element Ø relative addition rate m 4 Ingestad and Agren 1992 ; Larsson 1994Ž . Ž .plant N, P, K contents Ø critical concentration s 5 Burns 1990

NutrientŽ . Ž . Ž . Ž .content: KqCaqMg thermodynamic activity ratio Ø selectivity constant m 14 Hansen 1972 ; Nielsen and Hansen 1984 ; Nielsen and Sørensen 1984

Ž . Ž . Ž .N total aerial biomass Ø diminishing N demand s 68 Greenwood et al. 1990 ; Lemaire and Gastal 1997Ž . Ž .N plant compartments Ø 2 compartments m 68 Caloin and Yu 1984

Ž . Ž .N plant compartments Ø core-skin m 68 Hardwick 1987

UptakeŽ . Ž .rate: K, Na, Cl, solution ion content Ø Michaelis–Menten m 1 Epstein 1972

SO , NO ,4 3

NH 4Ž . Ž . Ž .K, Cl plant and solution contents Ø feedbackrMichaelis s 17 Siddiqi and Glass 1982 ; Cram 1983

Ž . Ž .NO plant NO content Ø pump–leak–buffer m 17 Scaife 19893 3Ž . Ž .NO plant NO content Ø feedbackrMichaelis s 17 Buysse et al. 19963 3

Ž . Ž . Ž .NO root respiration Ø C–N interaction m 18 Le Bot 1991 ; Andriolo 19953Ž . Ž .PO root length Ø C–N interaction s 18 Sanders 19934

q y Ž . Ž . Ž .H rOH excretion NO , NH and Ø cytoplasmic pH-stat m 1238 Dijkshoorn et al. 1968 ; Ben Zioni et al. 19713 4

SO assimilation4Ž . Ž . Ž . Ž .Root respiration anion uptake Ø energy requirement m 8 Veen 1980 ; Lambers et al. 1983 ; van der Werf et al. 1988

Ž . Ž .Photosynthesis specific leaf N Ø C–N interaction s 3 Sinclair and Horie 1989


neers interested by the subject. The scheme of this paper is set on the description of thedual spatio-temporal approach mentioned above, which is in our view the mostinteresting for horticulture. For reasons of conciseness, we will not develop extensivelythe role of each nutrient in plant metabolism, information on the implication of mineral

Ž .nutrition in crop production being reviewed elsewhere Le Bot et al., 1994 . At last, thispaper aims to unify different modelling approaches by exploring the diversity of speciesand environments studied so far. This is a reason why we will not confine our analysisto horticultural plants. Moreover, modelling in this field is too scarce to justify aseparate study from other agrosystems.

2. Proximate functions

2.1. Nutrient uptake

In productive agrosystems, ion concentration at the root surface level is determinedboth by the properties of the rooting medium and by the plant ion uptake kinetics.

Ž .Clarkson 1985 reviewed these interface aspects ‘between plant physiology and soilŽ .science’. For example, he reported on the work of Silberbush and Barber 1983

showing that root elongation rate and soil diffusion coefficient are the main determinantsof phosphorus uptake rate by roots. Thus, although these aspects are not dealt with inthis paper, it is important to stress that the knowledge of nutrient distribution andmobility in soils or substrates, as well as uptake capacity distribution and architecture of

Ž .roots for review, see Habib et al., 1991 are required to model nutrition. Furthermore,these determine the root units that plant physiologists should prefer. However, althoughfor phosphorus most works relate uptake to root surface or length, for other nutrientsonly more accessible units such as root dry or fresh weights are commonly used, whichmay be a limit for models.

Plants regulate their tissue mineral composition against electrochemical gradientsthrough active and passive processes. This explains why mineral concentrations are

Ž . Ž .sometimes lower e.g. Ca, Na, and toxic elements or higher e.g. N, P, S, K in theplant than in the soil solution. Extensive research on ion uptake has been dedicated tocharacterizing plant ability to extract nutrients from the soil solution. In particular,uptake velocity has been related to external nutrient concentration, thus, yielding theso-called ‘uptake isotherms’, most of the time using young plants grown in well definedenvironmental conditions or excised roots. While results have proven useful in definingsound ecological properties of the transport systems, they are questionable in the contextof rich soil environments, typical of intensive horticultural systems. In fact, technicaldifficulties seriously limit the accuracy of uptake rate measurements when the nutrient

Ž .concentration is elevated, and or with older plants.Ž q q 2q y q y 2y 2y.For most ions K , Na , Ca , Cl , NH , NO , PO , SO , uptake is the net4 3 4 4

result between simultaneous influx from the solution to the roots and efflux from theŽroots to the solution, these processes being considered independent Clarkson, 1986;

.Aslam et al., 1996a . Many studies are concerned with net uptake or influx, but since


high values of efflux have been reported, it influences significantly net uptake andshould be considered in its regulation.

Influx of anions being mostly ATP-dependent, the existence of a significant amountof efflux is puzzling, as it may be seen as an energy-wasting process. Indeed, due toefflux, net anion uptake could require 25 to 100% more energy than expected from

Ž .theoretical values van der Werf et al., 1988; Bouma and De Visser, 1993 . As aŽ .consequence, in addition to growth and biomass maintenance, Johnson 1990 proposed

two supplemental specific components for root respiration, one being the energy cost ofŽion uptake and the other the energy cost of ion re-uptake i.e. the uptake needed to

.balance efflux . Some data also suggest that efflux occurs through specialized specificŽ .systems requiring both RNA and protein synthesis Aslam et al., 1996a . To date, the

physiological role of efflux, if any, is unclear. It might be an essential process, the mostŽ .direct way to regulate internal ion concentration Miller and Smith, 1996 , and the

respiration re-uptake component would be the cost of homeostasis.

2.1.1. Influx isothermsŽInflux kinetics are established by measuring the accumulation rate of an isotope e.g.

13 15 . Ž y q .N or N for nitrogen or an analogue e.g. ClO for nitrate, Rb for potassium in3

plant tissues. To minimize efflux, the shorter the experiments the better, experimentsŽ .shorter than 10 min being preferable Clarkson, 1986; Nissen, 1991 . However, due to

sensitivity limits, many published data were obtained over 30 min to 1 h periods, leadingto large influx rate underestimation.

Ž y3 y q q.For low concentrations e.g. under 1 mol m for NO , NH or K influx rate3 4

increases with ion concentration following an hyperbola. Since the early work of EpsteinŽ .and Hagen 1952 , the mechanistic enzyme kinetic formula of Michaelis and Menten

Ž ŽTable 3 is widely accepted as best describing this behaviour. Two parameters, I alsom. Ž .notated V and K also notated K or C characterize this model. The former, them m 0,5

maximal rate of influx, is a capacity parameter which can be approached at high externalconcentrations. Its value is related both to the number of transporters per root unit and to

Ž y3 .their intrinsic characteristics. The latter is the ion concentration mol m for whichinflux rate is half the maximum. The lower its value the higher is the affinity of thetransporter for a particular ion. It does not depend on the root units but it is determinedonly by intrinsic characteristics of the transporter.

Table 3Ž .Formulas used for ion influx I into roots. I , I and I maximum influx, K , K and Km m1 m2 m m1 m2

Michaelis–Menten constants, x nutrient solution concentration of ion Xs

Formula Type Authors

xs Ž .Is I = Michaelis–Menten Epstein and Hagen 1952m x q Ks mx xs s Ž .Is I = q I = Dual Michaelis–Menten Epstein et al. 1963m1 m2x q K x q Ks m s m2

xs Ž .Is I = q b = x Michaelis–MentenqLinear Kochian and Lucas 1982m sx q Ks m


Ž y3If kinetic measurements are made at higher concentrations above 1 mol m fory q q.NO , NH or K , influx rate increases again and reaches much higher values than3 4

predicted by I . Such a complex pattern has been described for Kq, Naq, Cly, Mg2q,m2y 2y y q ŽPO , SO , NO , NH and most micro nutrients Berlier et al., 1969; Laties, 1969;4 4 3 4

.Epstein, 1972; Hodges, 1973; Nissen, 1974; Rao and Rains, 1976 . The molecularinterpretation of influx kinetics over a wide range of concentration has led to consider-

Žable debate Laties, 1969; Epstein, 1972; Hodges, 1973; Nissen, 1974, 1991; Borstlap,. Ž .1981; Smart et al., 1996 , but the dual transport mechanism of Epstein 1972 is the

Ž .most widely accepted. Mechanism I or HATS for high affinity transport systemoperates in the low concentration range, obeys simple Michaelis–Menten kinetics andshows very low K values. Reported K and I values are greatly variable with plantm m m

Žage, species or varieties and growth conditions Glass and Siddiqi, 1984a; Clarkson,.1985; Schenk, 1996 , but also due to resolution of the measurement set-up. For nitrate,

ammonium and potassium, most K values lay between 5 and 100=10y3 mol my3m

Ž . y3Glass and Siddiqi, 1984a; Peuke and Kaiser, 1996 , but values as high as 985=10y3 Ž .mol m have also been reported for nitrate Pace and McClure, 1986 . Mechanism II

Ž .or LATS for low affinity transport system operates mostly in the higher concentrationrange and its kinetic is not clearly characterized. There are reports that influx rate fits the

Ž .saturable Michaelis–Menten kinetics with lower affinity i.e. higher K and higher Im mŽ .than HATS Peuke and Kaiser, 1996 . Observed K values for LATS reach 25 molm

y3 Ž . y3 Žm for nitrate Peuke and Kaiser, 1996 and 3 to 19 mol m for potassium Benlloch.et al., 1989; Maathuis and Sanders, 1996; Smart et al., 1996 . However, most published

data on NOy, NHq, PO2y, and Kq describe a linear influx in the high range of external3 4 4Ž .ion concentration. According to Bieleski 1973 when experimental concentrations are

far below the K value of LATS, a linear expression is an adequate approximation of am

Michaelis–Menten hyperbola. Only one parameter characterizes the linear LATS kinet-Ž .ics i.e. the slope between uptake rate and nutrient concentration and it should be

expressed in m3 hy1 per root unit. Reported values, in m3 hy1 gy1 of fresh root, rangey6 Ž . y3 Ž .from 150=10 Kronzucker et al., 1995a to 14=10 Peuke and Kaiser, 1996 for

y6 y3 Ž .nitrate, from 670=10 to 1.3=10 Wang et al., 1993b for ammonium, and fromy6 Ž . y6 Ž .160=10 Kochian and Lucas, 1982 to 540=10 Kochian et al., 1985 for

potassium.Overall influx is usually computed as the sum of HATS and LATS components

Ž .Table 3 , referring either to the dual Michaelis–Menten kinetics with four parametersŽ .two for maximum influx and two for affinity or single Michaelis–Menten plus a linear

Ž .component, with three parameters I and K of HATS, and slope of LATS .m m

2.1.2. Efflux measurementsThe use of isotopes in influx studies allows the determination of efflux by monitoring

Ž .the accumulation of natural isotope originating from the roots into the nutrient solutionŽ .Morgan et al., 1973 . As for influx, experiments should be as brief as possible but dueto low analytical sensitivity, nitrate efflux determinations for concentrations above 0.1mol my3 last for about 1 h, thus resulting in underestimated values. To overcome thisproblem, efflux is usually computed rather than measured, either by subtracting net

Ž .uptake from influx Deane-Drummond, 1986; Macduff and Jackson, 1992 , or through


Ž .compartmental analysis Cram, 1968; Pitman, 1971; Devienne et al., 1994a which mayappear too cumbersome a procedure. Therefore, little information is available on efflux

y3 Žin the high concentration range, above 1 mol m for nitrate and ammonium Macklon.et al., 1990; Devienne et al., 1994b . It should also be emphasized that efflux values

may be largely artefactual. Usually, experimental set-ups require the transfer of theplants from their cultivation medium prior measurements. In some cases, the resulting

Žtransplant shock has been shown to inhibit net uptake for several hours Bloom and.Sukrapanna, 1990 , due to a dramatic enhancement of efflux, while influx remained

Ž .unchanged Delhon et al., 1995a; Aslam et al., 1996b .Ž y1 y1Depending on growth conditions and species, efflux rates mol h g root fresh

. y9 Ž . y6weight range from 4=10 Kronzucker et al., 1995b to 10=10 for nitrateŽ . y9 y6Deane-Drummond and Glass, 1983 , and from 100=10 to 4=10 for ammoniumŽ . ŽWang et al., 1993a . Expressed in percentage of influx, efflux ranges from 5% Siddiqi

. Ž .et al., 1991; Kronzucker et al., 1995b to 93% Devienne et al., 1994b for nitrate, fromŽ . Ž9–10% Wang et al., 1993a; Kronzucker et al., 1995c to 33–35% Macklon et al.,

.1990; Kronzucker et al., 1995c for ammonium, and values of 30% have also beenŽ .reported for phosphate and sulphate Lee, 1993 . Efflux is mostly seen as an unidirec-

tional leak, depending only on the root ion content, but independent of the external ionŽ .concentration Breteler and Nissen, 1982; Mackown, 1987; Teyker et al., 1988 .

2.1.3. Net uptake isothermsUnder near constant ion concentrations, net uptake is measured by the difference

between initial and final ion content in the nutrient medium. Some experimental set-upsallow the continuous monitoring of ion concentrations and solution volume which are

Žmaintained at set points through automatic additions Clement et al., 1974; Andre et al.,´1979; Blom-Zandstra and Lupijn, 1987; Alloush and Sanders, 1990; Freijsen et al.,

.1990 . Plant ion and water uptake are computed as the added amounts. Depending onthe sensitivity of the experimental set-ups and ion concentrations, their time-scale rangesfrom a few minutes to 3 h. Accumulation of an isotope in plant tissues during a long

Ž .time of exposure 1 h at least can also be used as an estimate of net ion uptakeŽ .Macduff and Jackson, 1992; Ourry et al., 1996 . Uptake isotherms are usually obtainedunder variable ion concentrations, following the depletion method of Claassen and

Ž .Barber 1974 . Plants are transferred to a small solution volume and are allowed todeplete a particular ion until its concentration becomes constant. Manual or automaticŽ .Goyal and Huffaker, 1986 ion titration allows to compute net uptake rate against ionconcentration. However, the time necessary to complete an experiment increases withincreasing initial ion concentrations, which seriously limits isotherm studies to a verylow range. Experiments may last for about 10 h for nitrate and phosphate at respectiveinitial concentrations of 250=10y3 mol my3 and 30=10y3 mol my3 and 4 h forpotassium at initial concentration of 200=10y3 mol my3. However, since net uptakeshows diurnal variations even under constant ion concentrations, we believe that theseisotherms probably happen to be distorted.

Net uptake characteristics are mostly the same as those deduced from the influxstudies, i.e. existence of two uptake mechanisms, the first being saturable. The

Ž .Michaelis–Menten kinetics have been adapted to take efflux into account Table 4 .


Table 4Ž .Formulas used for net ion uptake In into roots


xs Ž . Ž .Ins In = y E Influx minus efflux E Claassen and Barber 1974m x q Ks m

x y xŽ .s cp Ž . Ž .Ins In = Compensation point x Nielsen 1976m cpx y x q KŽ .s cp m

Ž .Claassen and Barber 1974 proposed a model where net uptake is the mere differencebetween influx, following simple Michaelis–Menten kinetics, and efflux, considered as

Ž .a constant. The model of Nielsen 1976 does not include efflux explicitly, but considersthat the ion concentration necessary for null net uptake, as measured at the end ofdepletion experiments, is an ion compensation point. Both models are currently used tofit the data, but in view of the stated mechanistic independence of influx and effluxŽ .Clarkson, 1986; Aslam et al., 1996a , the formulation of Claassen and Barber should bepreferred.

2.2. Feedback regulation of uptake

Evidence has accumulated showing that uptake characteristics of both HATS andLATS are not fixed values, but are closely dependent on experimental conditions andplant growth demand. Under near constant ion concentrations, net uptake of nitrateŽClement et al., 1978; Triboı-Blondel, 1979; Pearson et al., 1981; Le Bot and Kirkby,¨

. Ž1992; Delhon et al., 1995a; Andriolo et al., 1996; Ourry et al., 1996 , ammonium Wild. Žet al., 1987; Ourry et al., 1996 and potassium Wild et al., 1987; Le Bot and Kirkby,

.1992; Macduff and Dhanoa, 1996; Ourry et al., 1996 undergo continuous variations, theŽ .pattern being roughly an increase during the light period and a decrease during the

night. For nitrate, these variations have been stated for concentrations as low asy3 y3 Ž . y3 Ž20=10 mol m Ourry et al., 1996 and as high as 5 mol m Pearson et al.,

. Ž1981 . Nitrate and ammonium net uptake rates are strongly reduced by defoliation Wild.et al., 1987; Macduff and Jackson, 1992 in less than 90 min, and reduction in nitrate

Ž .uptake rate becomes significant within 20 min Wild et al., 1987 . These continuous andrapid variations in uptake rates cannot be explained by changes in the root system sizeor by synthesis of new transporters. In addition, different ions share common uptakepatterns in these experiments. For these reasons, it has been suggested that uptake ratesare controlled by a common, non-specific, mechanism, presumably transpiration or theflow of carbon compounds from leaves to roots, necessary to the respiration-dependent

Ž . Ž .influx Wild et al., 1987 . Today, the former hypothesis is rejected see Section 2.3while the latter is not. However, as variations of uptake rate take place even whennutrient concentration is limiting, the second hypothesis seems also unlikely. What ismore, homeostasis can hardly be explained by non-specific mechanisms, and underneathmost studies, regulation lays on negative feedback from internal specific components.


Given its relative importance and sensitivity to internal ion concentration, effluxŽ .might explain both homeostasis and net ion uptake regulation Miller and Smith, 1996 .

Ž .Since the early work of Morgan et al. 1973 introduced efflux as a regulatoryŽ .component of net nitrate uptake and Deane-Drummond and Glass 1983 suggested that

it might be the main short-term regulator, experimental results have led to contradictoryand much debated results. During the day–night cycle under constant ion concentrations,

Žnet nitrate uptake variations have been stated to be due only to efflux Pearson et al.,. Ž .1981 , or mostly to influx Delhon et al., 1995a . In experiments involving nutritional

pre-treatments, net nitrate uptake regulation has also been explained by either effluxŽ .Breteler and Nissen, 1982; Deane-Drummond and Glass, 1983; Mackown, 1987 , influxŽ . ŽLee and Drew, 1986; Lee, 1993 or both Teyker et al., 1988; Devienne et al., 1994b;

.Kronzucker et al., 1995b . While different results may be explained by specificdifferences and experimental peculiarities, it remains that modelling both fluxes is anecessity. Successful incorporation of nutrition dynamics in a crop model requirescorrect and simultaneous simulation of homeostasis, energy cost and net uptake.

2.2.1. InfluxThe simplest, most general and selective regulation mechanism lays on the sensitivity

of the transport systems to the internal concentration of the particular transported ionŽ . Ž .Glass and Siddiqi, 1984a . Indeed, inverse relationships between root non-metabolized

Žion concentration and influx rates have been stated for nitrate Siddiqi et al., 1990;. Ž . Ž .Delhon et al., 1995a , ammonium Wang et al., 1993b , sulphate Clarkson et al., 1983 ,

Ž . Ž . Žphosphate Lefebvre and Glass, 1982 , chloride Cram, 1983 and potassium Siddiqi.and Glass, 1987 . Most studies focused on the HATS, for which I appears to bem

inversely related to root ion concentration. K has been found positively correlated tomŽ . Žroot ion concentration for ammonium Wang et al., 1993b and potassium Siddiqi and

. Ž .Glass, 1987 , or constant for sulphate Clarkson et al., 1983 , while reports areŽ .conflicting for nitrate Lee and Drew, 1986; Siddiqi et al., 1990 . For a linear LATS, it

Ž . Žhas also been reported, both for ammonium Wang et al., 1993b and nitrate Siddiqi et.al., 1990 that the slope parameter is lower when root ion concentration is high.

A model of root ion concentration negative feedback on HATS has been introducedŽ . Ž .by Siddiqi and Glass 1982, 1986 for potassium uptake Table 5 . For this particular

ion, the relationships of I and K with root potassium concentration are exponentialm m

with negative and positive parameters, respectively. Therefore, the original I and Km m

values of the Michaelis–Menten model have been replaced by their statistical relation-ship with root potassium concentration so that I and K become, respectively, them m

Ž .maximum and minimum values reached for a null root potassium content. Cram 1983Ž .compared various models involving feedback on the I component only Table 5 . Theym

are of the proportional type, influx being greater when root concentration is either farŽ .from a set point concentration error actuated feedback or close to a minimum

Ž . Ž .concentration reciprocal feedback . Cram 1983 concluded that error-actuated feedbackbest simulated both influx and homeostasis for chloride. This choice has been criticized

Ž .by Glass and Siddiqi 1984b, 1985 , and indeed a molecular mechanism for sensing a setpoint concentration is hardly imaginable. However, a similar approach has been recently

Ž .proposed for nitrate influx regulation by Buysse et al. 1996 .


Table 5Ž .Some feedback formulas used for ion influx I into roots. I absolute or relative maximum influx, Km

Michaelis–Menten constant, x , x , x nutrient solution, cytoplasm and root concentrations of ion X, xs cyt r min

and x minimum and set point root concentrations of ion Xsp


xsb x r Ž .Is I e = feedback on I and K Siddiqi and Glass 1982, 1986Xm m mb x rx q K es mXwith b-0 and b )0

x xr sŽ . Ž .Is I 1y = error actuated feedback on I Cram 1983m mx x q Ksp s m

x xmin s Ž .Is I = reciprocal feedback on I Cram 1983m mx x q Kr s mxsŽ . Ž .Is I x y x = error actuated feedback on I Buysse et al. 1996m sp cyt mx q Ks m

From a mechanistic viewpoint, a direct negative feedback of internal potassium andchloride on their respective transporters is currently admitted. This is mostly supported

Ž q y 2yby the absence of metabolism for these ions. Instead, other ions NH , NO , SO ,4 3 42y.PO are metabolized, and feedback from their assimilation products is under examina-4

Ž .tion. Indeed, when plants are treated with L-cysteine an S-containing amino acid ,Ž .sulphate uptake is strongly depressed Clarkson et al., 1983 . Similarly, treatments with

Žvarious amino acids reduce nitrate or ammonium uptakes Lee et al., 1992; Muller and¨.Touraine, 1992 while malate, a by-product of leaf nitrate and sulphate assimilation,

Ž .stimulates nitrate uptake Touraine et al., 1992, 1994 . However, reports on correlationŽbetween root amino acid content and nitrate uptake rates remain conflicting Delhon et

.al., 1995a,b; Laine et al., 1995 . As a matter of fact, the same problems arise to proveéither a direct effect of the transported ion itself or an indirect effect by its assimilationproducts. Split-root experiments where part of the root system is deprived of a particularion, result in an increase of ion uptake by normally fed roots. For nitrate, this

Ž .enhancement is not correlated to root amino acid content Laine et al., 1995 . For both´Ž . Ž .nitrate Laine et al., 1995 and sulphate Clarkson et al., 1983 , uptake rate is usually´

better correlated with the non-metabolized ion content of shoots than roots. Interestingly,Ž .the same arises for potassium Claassen and Barber, 1977 , showing that such experi-

ments are not decisive in proving a direct or indirect effect on the transporters. Evenexperiments involving the use of treatments affecting nitrogen assimilation, or nitrate

Ž .reductase deficient mutants, do not prove decisive Lee et al., 1992; King et al., 1993 .Experimental uncertainties arise from the difficulty to devise experiments involving onlyshort-term regulations, and from the analytical significance of root ion or amino acidcontent, as only the cytoplasmic content of cortical cells is expected to act on thetransporters.

2.2.2. EffluxFew experimental data are available for efflux. A positive linear relationship between

Žroot ion content and efflux has been demonstrated for nitrate Breteler and Nissen, 1982;


.Mackown, 1987; Teyker et al., 1988 , and a correlation between cytoplasmic ion contentŽ .and efflux have been reported for nitrate Kronzucker et al., 1995b and ammonium

Ž .Wang et al., 1993a; Kronzucker et al., 1995c . Efflux being considered as a passiveleak, it is usually computed as the mere product of internal concentration and a

Ž .permeability constant Cram, 1983 .

2.2.3. Net uptakeNet uptake can be modelled by subtracting efflux from influx in the above models

Ž .Cram, 1983; Siddiqi and Glass, 1986 . However, an interesting endeavour to simulateŽ .nitrate uptake under constant ion concentrations should be mentioned here. Scaife 1989

showed realistic nitrate uptake rate patterns in the diurnal cycle using a model based ona constant influx rate, an efflux proportional to the plant nitrate content and a nitrogenassimilation rate proportional to photosynthesis. This model even predicted the time-lagusually observed between maximum photosynthesis and maximum nitrate uptake rate.

Ž .Our own simulations unpublished showed that this time-lag is not constant, butincreases from day to day when diurnal photosynthesis increases, or decreases on the

Ž .reverse situation. This behaviour is consistent with published data Clement et al., 1978 .Furthermore, diurnal variations of plant nitrate concentration are also realistic. It shouldbe emphasized that all these properties are typical of a capacitive model, where fluxesare controlled by the buffer content. In fact, Scaife proposed that net nitrate uptake benegatively correlated to plant nitrate concentration. His interpretation of parameters canbe turned round in terms of regulated influx and constant efflux; eventually both fluxescan be regulated without changing the model’s behaviour. The energy cost of net uptake,however, should be strongly affected by these different options. Most important of all,

Žmodels based on feedback from internal ion concentration Cram, 1983; Siddiqi and.Glass, 1986; Scaife, 1989; Buysse et al., 1996 are potentially able to simulate both ion

uptake and homeostasis. However, they were formulated in a context of low ionconcentration and further studies are needed in the high concentration range correspond-ing to horticultural practice.

2.3. Nutrient use efficiency

2.3.1. Nutrients and photosynthesis: a causal relationship?There is an intimate relation between plant nitrogen or phosphorus status and the

carbon metabolism. Hence, N and P deficiencies in plants induce changes in carbo-Žhydrate synthesis and degradation pathways Rufty and Huber, 1983; Vessey and

.Layzell, 1987; Rufty et al., 1988; Fredeen et al., 1989; Paul and Stitt, 1993 . Forinstance, nitrogen-deficient tomato plants accumulate starch in their leaves which

Ž 2 y1 . Ždecreases rapidly their SLA specific leaf area in m g leaf Suniaga Quijada, 1991;.Gary and Bertin, 1992 . Many observations made over a range of nitrogen availability in

the environment suggest the existence of a compulsory balance between nitrogen andcarbon nutritions. This explains why plants optimize their carbon gains in relation to

Žnitrogen available for photosynthesis Field, 1983; Hirose and Werger, 1987a,b; Lawlor,. Ž .1994 . This optimization implies a tight relation between leaf nitrogen concentration N

Ž .and its maximum photosynthetic activity A , measured at saturating light intensitymax


under optimum temperature and humidity conditions at ambient CO levels. Similarly,2

phosphorus deficiency progressively stops aerial plant growth, decreases phosphorusŽ .concentration in the dry biomass P and diminishes leaf maximum photosynthetic

Ž .activity Brooks, 1986; Fredeen et al., 1989; Halsted and Lynch, 1996 . The decrease ingrowth, however, results more from a lack of phosphorus for new tissue biosynthesesŽ .leaf expansion for instance than from a drop in photosynthesis. Thus, the observed

Ž .close A –P relation Lynch et al., 1991 comes from the indirect effect of phosphorusmaxŽ .on leaf expansion, which in turn affects photosynthesis. Sanders 1993 discussed this

argument and reckoned that a shortage in phosphorus affects growth via changes in theroot:shoot ratio. Reference to photosynthesis is therefore not essential in modelling plantphosphorus nutrition. The A –N relationship has been investigated thoroughly, espe-max

cially in ecological studies where nitrogen availability in the soil influences speciesadaptation to their ecosystems. At the present time, only statistical models account for

Ž .the A –N relationships Table 6 . They are based on several hypotheses about the rolemaxŽ .of nitrogen in several photosynthesis-limiting reactions Field and Mooney, 1986 .

Ž .1 A could be regulated by one or several processes functioning at ratesmax

determined by leaf nitrogen content. For instance, the rate at which CO is transported2

from gaseous to liquid phases depends on the activity of carbonic anhydrase and CO2

fixation depends on the activity of the enzyme Rubisco, on RuBP, NADPH, ATPregenerations. All these steps require enzymes, in which the constitutive nitrogen maybe the rate limiting factor. As a consequence, the optimization of nitrogen efficiency forphotosynthetic use is made through the function of nitrogen distribution between plantorgans and between classes of nitrogen compounds.

Table 6Mathematical functions used for modelling the effect of nitrogen on photosynthesis

Ref. Model Description

Ž .1 A s a= Nq b a and bsconstantsmaxa = N0 nsŽ .2 As Asphotosynthetic rate,SLA=T

SLA sspecific leaf area,T sproportion of incident light inthe horizon where the leaf lies,a sconstant, N snon-structural0 ns

nitrogen concentration2

Ž . Ž .3 A s A = y1 A smaximum A , asconstant, N s N at zero Amax x x max 0 maxyaŽNyN .01q e2Ž .4 A s a= N q b= Nqc a, b and csconstantsmax

yk N y NŽ .0Ž . w x5 A s A = 1y e A smaximum A , ksconstant, N s N at zero Amax x x max 0 maxkA = NxŽ .6 A s A smaximum A , ksconstant, K s N at A r2max x max p xkK q Np

Ž . Ž . Ž . Ž . Ž .1 Field and Mooney 1986 ; Hirose and Werger 1987b ; Sage and Pearcy 1987b ; Hirose et al. 1988 ;Ž . Ž . Ž . Ž . Ž . Ž .Evans 1989b . 2 Charles-Edwards et al. 1987 . 3 Sinclair and Horie 1989 ; Connor et al. 1993 ;

Ž . Ž . Ž . Ž . Ž . Ž . Ž .Muschow and Sinclair 1994 ; Bellert 1995 . 4 DeJong and Doyle 1985 . 5 Cromer et al. 1993 . 6 LimŽ .et al. 1990 .


Ž . Ž2 A could be regulated independently from nitrogen by stomata, CO diffusionmax 2.resistance, etc. but leaf nitrogen content could be adjusted to maximum leaf photosyn-

thetic activity. In case of nitrogen shortage, the plant would optimize nitrogen invest-ment since any enzyme activity or nitrogen compound in excess of that strictly requiredfor maximum rate would be useless, only the limiting factor being worth upraising. As aconsequence, nitrogen use efficiency is highest when the distribution of nitrogen to allnon-limiting plant growth processes is regulated towards the critical N concentration.

Ž .3 A and N could not be adjusted one to another but be both regulated by one ormax

several leaf parameters. In this case, A and N would be invariant when expressedmax

relative to the appropriate leaf unit but would vary proportionally based on other units.Ž . Ž .Hypotheses 1 and 2 may be put forward since they are backed by a number of

observations concerning nitrogen distribution and use in plant leaves. In a leaf, thefraction of nitrogen used in photosynthesis is determined by the orientation of assimi-lates towards compounds required by photosynthesis. The latter are numerous andalmost identical in all plant cells. Hence, structural N is associated with the protection ofcell walls against biotic or non-biotic attacks, and cells contain various nitrogen solutes

Ž .such as vegetative storage proteins VSP , peptides, polyamines, alkaloids, etc.Ž .Lambers and Poorter, 1992 . On the other hand, up to 75% of leaf nitrogen may beassociated with the functioning of the chloroplast. Nitrogen is constitutive of proteinsŽ .16 to 18% N in average involved in CO fixation and CO acceptor replacement2 2Ž . Ž .Field and Mooney, 1986 . Ribulose-1,5-bisphosphate carboxylaseroxygenase Rubisco ,the CO fixing protein, represents more than 50% of the chloroplast soluble proteins2Ž .Evans, 1983, 1989a; Makino and Osmond, 1991 . Nitrogen is also constitutive of

Ž y1 .pigments associated with the light-harvesting machinery 50 mol N mol chlorophyll ,Žproteins of the electron transport chain and proteins of the Calvin–Benson cycle Abadia

.et al., 1987; Nishio et al., 1985; Wong et al., 1985 . Moreover, nitrogen is found innucleic acids, the peroxisome and in mitochondria enzymes responsible for the renewalof products during photorespiration. At last, according to environmental conditionsŽ .incoming radiation , nitrogen may be allocated in priority to compounds involved in the

Ž .light phases of photosynthesis pigments, photosystems, etc. or those concerned withŽ .the dark reactions Rubisco, Calvin–Benson cycle proteins, etc. . Acclimatization to

Ž .shade induces a lower nitrogen investment in light harvest Evans, 1989a .

2.3.2. SeÕeral modelsIn a comparison of a plentiful number of plant species characteristic of natural

Ž .ecosystems, Field and Mooney 1986 observed a tight linear relationship between Amax

and N when both parameters were expressed per unit of leaf dry matter. This couldindicate a general ‘law’. However, expressing data per unit leaf area, which is moresatisfactory from a physiological viewpoint, may result in differences which areattributed to SLA variations between plants of different leaf N status. Several models

Ž .have been proposed so far to account for the A –N relation Table 6 . For severalmax

species, this relation is not linear but hyperbolic. Hence, for these species, from low leafN onwards, A increases rapidly with increasing N but reaches a plateau where Nmax

Ž .accumulation is no longer beneficial to photosynthesis. According to Evans 1989a , thecurvature of the relationship does not reflect an inactivation in Rubisco at high leaf N


Ž . Ž .but could result either from 1 an underestimation of A or 2 a decrease in COmax 2

partial pressure in the leaf between the intercellular space and the site of carboxylationbecause of an increase in the resistance of cell walls to CO transport. According to2

Ž .Sage and Pearcy 1987b , the loss of linearity in the A –N relation proceeds from themaxŽ .appearance of nitrogen storage compounds in the leaves nitrate, asparagine, etc. .

Ž .The ratio A rN is called the photosynthetic nitrogen use efficiency PNUE . Itmax

removes the effects of fluctuating SLA and allows the comparison between species to becarried out. Several studies have shown that the efficiency of C species is higher than4

that of C species, which has been interpreted as the result of a better acclimatization to3Ž .environments low in nitrogen Brown, 1978; Sage and Pearcy, 1987a,b . However, the

reduced rates of photorespiration in C species gives also these plants higher A4 max

values than C plants. In this case, higher PNUE may also proceed from a better use of3

carbon. The difficulty of interpreting PNUE data comes from the fact that in a ratio,similar data may result from equal changes either in the numerator or the denominator.Within a similar photosynthetic type, however, changes in PNUE have been reportedŽ .Field and Mooney, 1986; Lambers and Poorter, 1992 . These could reflect interspecificdifferences in Rubisco activity or nitrogen allocation towards the functioning of this

Ž .enzyme Evans, 1989a as well as intra-specific differences in nitrogen allocationtowards compounds not involved in photosynthesis or involved but not limiting photo-synthesis.

Most horticultural crops being fast growing species, it is reasonable to assume thattheir leaf nitrogen is invested in priority towards photosynthetic compounds. Therefore,leaf nitrogen analysis is a potential tool for assessing the limiting or non-limiting natureof nitrogen in crop photosynthesis using the A –N relationship typical of the species.max

Moreover the calculation of the PNUE index indicates the closeness of nitrogen supplyto the demand of the crop. Any supra-optimal nitrogen availability results in nitrogenaccumulation in plant tissues and thereby decreases PNUE compared with pre-definedoptimal value. This index could therefore be used as an indicator for nitrogen fertiliza-tion decision making. This index, however, should be considered with care since aPNUE increase is not necessarily beneficial to plants. For instance a PNUE increase has

Ž .been observed in nitrogen-deprived rose plants Bellert, 1995 together with a decreasein A . In this case, the decrease in leaf N concentration more than offset the decreasemax

in A , thus yielding higher PNUE. This was interpreted as the result of a greatermax

remobilization of non-photosynthetic nitrogen under nitrogen shortage, hence, renderingthe remaining nitrogen more efficient for photosynthesis.

2.3.3. Nutrients and water fluxesStomata are a compulsory passageway for CO and H O gas exchanges between the2 2

plant and the atmosphere. Therefore, in order to fix carbon, the plant looses water to theatmosphere, the ratio being variable depending on species and growing conditions. This

Ž .ratio is called the ‘water use efficiency’ WUE , i.e., the quantity of water transpired perunit carbon fixed in the dry matter. Plants under conditions of low water availabilityandror great water demand have low stomatal conductance and low leaf CO partial2

pressure. Therefore, these plants have low WUE because the decrease in their rate oftranspiration is larger than the decrease in CO fixation. Under such circumstances, the2


low A values associated with normal leaf nitrogen concentrations, also give thesemax

plants low PNUE indices. The measurement of the isotopic ratio 13Cr 12 C is anassessment of plant WUE. It has been introduced as a tool for geneticists in breeding

Ž .programs to select plants with low water use efficiency Evans and Farquhar, 1991 .Ž .Similarly, Masle et al. 1992 suggested that plant breeders use plant mineral concentra-

tion as an alternative measurement, simpler and economically more viable than isotopicratio determinations. Hence, these authors observed positive correlation between WUEand mineral concentration in the dry matter of several C and C species.3 4

2.3.3.1. Is there a causal relationship between PNUE or mineral concentrations andWUE? Is mineral uptake, in particular nitrogen, controlled by plant water fluxes? In a

Ž .study made on several herbaceous species, Lambers and Poorter 1992 were able toobserve the doubling of PNUE index in plants of constant WUE. Similarly, Field and

Ž . 13 12Mooney 1986 measured the same isotopic ratio Cr C in C species of markedly3

different PNUE index. Therefore, in light of the present evidences, we may seriouslydoubt a causal and general relation between PNUE and WUE. Moreover, Barthes et al.Ž .1995 observed for two wheat species widely different rates of mineral accumulation inthe whole plant, and concluded that the measurement of mineral concentration in the

13 Žtissues could not be proposed as an alternative measurement to the d C isotopic ratio.normalized against an absolute reference and thereby to WUE. At last, Tanner and

Ž .Beevers 1990 found that two lots of maize plants grown in controlled cabinets underŽ .two contrasting regimes of relative humidity RHs60 or )95% had on the one hand

a WUE differing by a factor 3.3 and on the other hand, a same dry matter yieldproduction and a similar plant mineral content at the end of the crop cycle.

The questions addressed above are fundamental in horticulture. For instance, in thepractice of soilless culture, the frequency of delivery of nutrient solution doses to thecrop is determined almost solely by plant water demand estimated from incoming solarradiation. Underlying in this practice is the hypothesis that the requirements for waterand for minerals are always intimately correlated. The experiments made over long

Ž . Žperiods of time weeks, months generally support such an hypothesis Brun and Blanc,.1987; Schacht and Schenk, 1990; Bar-tal et al., 1994 and have led agronomists to

empirical determinations of recipes for ideal ion mixtures adapted to plant growthŽstages. On the contrary, experiments made over short periods of time hour, dayrnight

.cycle demonstrate clearly that the ratio of water to nutrients taken up by the plants varyŽwidely with time of the day Triboı-Blondel, 1979; Le Bot, 1991; Ferrario et al., 1992;¨

.Le Bot and Kirkby, 1992; Andriolo, 1995; Brun et al., 1997 . Moreover, during summer,and in particular under Mediterranean conditions, growers observe frequently a sharpand rapid increase in the nutrient solution salinity, potentially at risks for both the plantsand the environment. This happens because during such periods of time, plant waterdemand increases more than mineral requirement.

All these evidences support the idea that the transpiration flux is not essential to ionuptake and transport in plants, and therefore in plant nutrient uptake modelling it isnecessary to dissociate mineral fluxes from water fluxes. A model of ion uptake simplybased on plant transpiration flux has no scientific grounds, neither does the calculation

Ž .or use of ‘uptake concentrations’ i.e., the ratio of ions to water taken up over time . In


spite of these statements, the actual practice of fertilization of soilless cultures grownunder greenhouses with drainage-to-waste bases the supply of nutrients on plant water

Ž .demand models de Villele, 1972 . This modelling of nutrient supplies is successfullyòperative in most commercial greenhouses yet it has extremely poor predictive proper-

Ž .ties as proven by 1 the occurrence of the drifts in nutrient solution salinity requiringŽ .heavy washing of the rockwool slabs with diluted nutrient solution and 2 the poor

Žcoefficients of fertilizer use i.e. the ratio of fertilizer taken up by the plants to that. Ž .applied in the slabs , especially for nitrate van Noordwijk, 1990 , which are of serious

environmental concern, especially in intensive areas of greenhouse production. Theseconclusions, however, should not hide the fact that in soil, the transpiration flux is thedriving force for the transport of most mineral ions from the soil layers to the roots, andtherefore, it is essential for modelling nutrient availability at the soilrroot interface.

3. Ultimate functions

3.1. Nutrient uptake and functional equilibrium

Plant nutrient uptake rate is computed as the product of net uptake rate per root unitŽ .Section 2.1. by the size of the root system. The latter, usually characterized by the

Ž . Ž .RSR root:shoot ratio or RWR root:whole plant weight ratio , varies greatly betweenŽ .species, edaphic conditions and with plant age. For instance, Laine et al. 1993 found a´

Žnegative relationship between nitrate uptake capacity per root unit and RSR from 0.1 to.1 in ten catch crop species grown under non-limiting constant nutrition. However, when

we computed their data to express them per total plant fresh weight, uptake capacity wasroughly the same for all these species, showing that a similar absorption rate can beachieved by various plant strategies. Similarly, it is commonly observed that most plants

Žincrease the size of their root system when water or nutrients particularly nitrate and.phosphate are limiting, or decrease it under low light conditions. However, under

non-uniform nutrient supplies, root growth is usually stimulated in the well-fed zone,Žwhile it can be depleted in the restricted zone for review, see Habib et al., 1991;

.Robinson, 1994 . From the nutritional viewpoint, the importance of these strategiesŽ .depends upon if the root medium is homogeneous e.g. hydroponics or heterogeneous

Ž .e.g. natural soil . From a carbon utilization viewpoint, high RSR differences areŽnecessarily important since roots represent from 1 see Table 1 in the work of Marcelis

. Ž .and De Koning, 1995 to 50% Laine et al., 1993 of plant dry weight.´ŽMechanisms involved in RSR elaboration are unclear for review of opinions, see the

.special issue of Plant and Soil, 185, 1996 . They include specific root growth regulationŽ .by plant hormones cytokinins and abscisic acid or sucrose, and non-specific determina-

Žtion by the so-called functional equilibrium Brouwer, 1962; see also Marcelis et al., this.issue . In the latter, RSR may be seen as an emergent property, resulting from the

balance between root and shoot growth necessary to acquire the limiting resources,nutrients and carbon, respectively. To achieve such models, it is necessary to formalizedry mass production under nutrient limitation, nutrient uptake under carbon limitation,and rules of carbon and nutrient exchanges between roots and shoots.


It is beyond the scope of this review to develop all these aspects but it should bestressed that existing models lay on unregulated root uptake activity. The latter is either

Žexpressed as only proportional to the size of the root system Cheeseman, 1993;.Reynolds and Chen, 1996 , or following the Michaelis–Menten kinetics of Epstein and

Ž .Hagen Lim et al., 1990 . Although such models do predict the right tendency of RSRvariations, such oversimplified assumptions should result in exaggerated changes, as theonly way to increase nutrient uptake rate is to increase the size of the root system. A

Žmore realistic approach requires the use of nutrient uptake feedback regulation Section.2.2. , which implies, therefore, the modelling of nutrient accumulation and assimilationŽ .rates Buysse et al., 1996 . This should result in more realistic effects of nutrient

Ž .limitation, i.e. increase of both RSR and SAR specific absorption rate . Furthermore,more research is required on transport of resources between compartments. It is viewedas a purely diffusive process where flux is along a concentration gradient affected by a

Ž .resistance parameter Thornley, 1972, 1995 , an active process following a Michaelis–Menten relationship whose substrate is the concentration in the source compartmentŽ .Cheeseman, 1993 , or the much-controversial xylemic water transport process where

Ž .flux is determined by transpiration for review, see Tanner and Beevers, 1990 .Choosing between these possibilities is uneasy, as nitrate concentration in the shoots ofseveral species has been reported to be higher than, equal to or lower than that of rootsŽ .Laine et al., 1993 . This might explain why less mechanistic approaches may be´preferred. These include a simple partition coefficient where a constant proportion of the

Ž .mineral is allocated to roots and shoots Siddiqi and Glass, 1986 , or sophisticatedmodels of source–sink relationships, where flow between compartments is governed by

Ž .the size of the source and growth rate of the sink Ran et al., 1994 .

3.2. Growth control by nutrients

The general idea that nutrient availability in the root medium determines plant growthŽ .arises from the general concepts of the limiting factor von Liebig, 1841 . An original

use of this concept has been developed since the seventies by Ingestad and Cottorkers˚Ž .for review, see Ingestad and Agren, 1992 : their technique consists in supplying

Ž .nitrogen at constant relative addition rates RAR to hydro- or aeroponically grownplants. As long as nitrogen remains limiting, they show that the plant relative growth

Ž .rate RGR equals RAR, and that whole-plant nitrogen concentration is nearly constant.On this ground, Ingestad introduced the term of ‘steady-state nutrition’. This techniquehas been used on a large number of plants and was shown to hold also for phosphorusŽ .Ericsson and Ingestad, 1988 , and is probably generalizable to other macronutrients.

On the one hand, there is no doubt that this technique is a valuable tool to monitorgrowth under controlled conditions. On the other hand, theoretical considerations havebeen derived to interpret the relationship between plant nutrient content and RGR˚Ž .Agren, 1985, 1988 . Whether these have sound physiological background or not is

˚Žunder debate for opinions, see Macduff et al., 1993; Burns, 1994; Wikstrom and Agren,¨.1995; Hellgren and Ingestad, 1996; Burns, 1997 and their use for diagnostic procedure

Ž .for crop nutrient management Burns, 1997 or for modelling nutrient uptake byŽ .horticultural crops Willits et al., 1992 are far from being straightforward. Hence, the


parameters of the relationship linking plant nutrient content to RGR are not unique, but˚Ž .vary according to plant species Agren, 1988 , plant age and environmental conditions

Ž .Willits et al., 1992 .

3.3. Growth demand of nutrients

3.3.1. Statistic approachŽ .Minerals are taken up by the roots and eventually assimilated in order to fulfil plant

growth requirements. For nitrogen, phosphorus and potassium it has been demonstratedat all times of the vegetative crop cycle, that a critical concentration is required in planttissues to sustain 90% of the maximum growth rate potentially obtained by the amount

Ž .of radiation intercepted by the crop Ulrich, 1952; Burns, 1990 . Below the criticalconcentration, growth is impaired. On the contrary, if nutrient availability is excessive,nutrients accumulate in the plant without concomitant increase in dry biomass. The

Ž .implicit relationship between nutrient uptake and dry matter accumulation sgrowthduring the vegetative development of a crop is particularly well expressed for nitrogen

Ž y1 .in the ‘law’ of progressive decline of %N g total N 100 g dry matter during cropŽ .growth Lemaire and Salette, 1984; Justes et al., 1994 :

%Nsa=DMyb

Ž y1 .where: DM tonnes ha is the total dry aerial biomass, %N is the critical nitrogenconcentration, coefficient a represents the nitrogen concentration in the dry biomass atthe end of the exponential growth period, and b is a statistical parameter governing theslope of the relation.

Ž y1 .This relation implies an allometry between nitrogen uptake by the crop N, kg haand the dry matter biomass accumulation:

Ns 10=a =DM1ybŽ .Ž .where: 1yb is the ratio between the relative rates of N uptake and dry matter

Ž . Ž . Ž .accumulation allometric parameter and 10=a is the amount of nitrogen kg takenŽ y1up by 1 ha of the crop at the end of the exponential growth i.e. about 1 tonne DM ha

.for most crops .The practical interest of such a relationship comes from the prediction of the

minimum nitrogen fertilization required by the crop to produce a targeted dry matterŽ .yield. Greenwood et al. 1990 have established that critical N concentration of a great

number of plant species fit one out of two possible relationships providing that theybelong either to the C or C type of photosynthesis. Many authors agree on the idea3 4

that the parameter b is identical for C and C species while a is specific for the type3 4

of photosynthesis. Various estimates of the parameters have already been published inŽ .the literature but the later review on the subject Lemaire and Gastal, 1997 proposes the

following average relations:

for C species: %Ns4.8=DMy0 .343

y0.34for C species: %Ns3.6=DM4


These findings may be interpreted as an indication that under non-limiting nitrogensupplies, C species are 25% more efficient than C species in accumulating the same4 3

amount of dry matter with a same quantity of nitrogen taken up. This better nitrogen useefficiency determined at the large time scale supports the findings of higher PNUE indexof C species measured over short time scales, as already discussed in Section 2.3.4

However, the argumentation developed earlier of a higher carbon use in C species4

because of low photorespiration also leads to the same conclusions. The finding of aunique parameter a between C and C species grown on 1 ha of land suggests that3 4

nitrogen use is identical in all plants, irrespective of their carbon metabolism, and isessentially determined by light interception.

The general relationship of progressive decline in %N in the dry biomass of plantshas been verified for a large set of crop species which confers this relation the status of‘law’, at least for non-ligneous plants free of storage organs. A more detailed analysis of

Ž .the literature can be found in the work of Justes et al. 1994 and Lemaire and GastalŽ .1997 . For horticultural crops, to our knowledge, only tomato has been evaluated. Forthis species, the progressive decline in %N has been shown to hold both for vegetative

Ž .and fruiting plants Andriolo, 1995; Le Bot et al., 1997a; Bellert et al., 1997 , althoughfor the time being, a precise relationship using critical nitrogen values has not yet been

Ž .established. However, under non-limiting nitrogen supply, Andriolo 1995 determinedthe following relation: %Ns5.77=DMy0.33. For this particular species, it is interest-ing to note that the concept of progressive decline in %N values, which was firstdeveloped over the vegetative growth of field crops having a closed canopy structure,also holds for the entire cycle of a row crop with indeterminate growth.

3.3.2. Mechanistic approachTwo mechanistic models explain the progressive decline of %N in the dry biomass in

Ž .terms of plant compartmentalization. For Caloin and Yu 1984 plant nitrogen contentvaries during growth according to the proportion of two conceptual compartments in the

Ž .plant. The first compartment is physiologically active for growth; its dry mass M is1Ž .related to the rate of total dry mass increase E MrE t by the following relation:

E MsRGR =Mmax 1E t

RGR being measured during the exponential growth phase. Along growth, themax

proportion of M in plant is:1

M 1 1 E M RGR1p s s = = s1 M RGR M E t RGRmax max

Ž .The second compartment has a mass M sMyM . It is involved in the other2 1Ž .metabolic activities of the plant, including structures and storage. Caloin and Yu 1984

Ž .propose to give both compartments M and M different nitrogen concentrations1 2Ž y1 . Ž .although constant over time, i.e. n and n g N 100 g DM . At any time t of the1 2

Ž .crop growth, total plant nitrogen content N may be calculated from the size of the twocompartments:

N t sn =M t qn =M tŽ . Ž . Ž .1 1 2 2


Ž .therefore, total nitrogen concentration n is:

N t RGR RGRŽ .n t s sn =p qn = 1yp sn = qn = 1yŽ . Ž .1 1 2 1 1 2 ž /M t RGR RGRŽ . max max

that is,

n yn1 2n t s =RGRqn sa=RGRqbŽ . 2ž /RGR max

Ž .In contrast to other approaches see Section 3.2. , in this model the relative growthrate is not a forcing variable for nitrogen uptake but its measurement gives a gooddetermination of the sizes of the two compartments. From practical viewpoints, thelinear relationship between RGR and plant nitrogen concentration has been verified inthe case of several cultivated species. However, a generalization of the model parame-ters has not been established yet, which appears as a limitation compared with the

Ž .statistical approach developed above Section 3.3.1. .Ž .A second model Hardwick, 1987 has been developed from studies on woody plants.

It assumes that plants are composed of an external ‘skin’ of energetically active tissuescovering a three dimensional inner ‘core’ which does not engage in energy exchange. In

Ž .a closed canopy structure, the mass of skin K is proportional to the area of lightŽ .interception; it is therefore proportional to the square of plant’s length l .

Ž .Moreover, the mass of the whole plant W is proportional to the volume of the plant,i.e. the cube of plant’s length:

Ksc= l 2 Wsd= l 3

where c and d are constants of proportionality. Replacing l in the first equation resultsin the following expression:

2

3KAW

Some evidence supports the idea that the amount of skin is proportional to plantŽ .nitrogen content Sylvester-Bradley et al., 1990; Le Bot et al., 1997b . In this case, for a

young plant in which the mass of core is negligible, increase in the amount of skin isŽ .mirrored by a similar increase in plant nitrogen content N :

E Ns1 that is, NAW

E W

For an adult plant, however, the core becomes predominant. Therefore, the total plantmass is a good estimate of the mass of core, which implies that:

E N 20.66s that is, NAW

E W 3

Ž .According to Hardwick 1987 , for a given species, there is a curvilinear relationshipbetween the nitrogen content of a plant and its total biomass, the slope of the curve


varying between 1 and 0.66. Hardwick proposes the following mathematical formula tofit the relationship:

yspq q=x q r=eyxŽ . Ž .Ž . Ž .where: ys log nitrogen mass per plant , xs log total plant biomass , r, p and q are

constants determined by the initial plant biomass and allometric parameters relatinglength to surface and volume plant dimensions. Rewriting this equation leads to:

r

W qNsk=e =WŽ .Therefore, when W™` , as is the case in an adult plant, this expression yields the

Ž .same formula expressed by Lemaire and Salette 1984 and already developed above:

Nsk=W q

Ž . Ž .In conclusion, both models of Caloin and Yu 1984 and Hardwick 1987 explicatedynamically the reasons for the progressive decline of %N in the dry matter from theexistence of two compartments having different physiological functions and biochemicalcompositions. In both models, however, the two compartments are virtual and remain tobe studied further. Hardwick associates the skin with the tissues responsible for the‘process of life’, which include the foliage, responsible for energy income, but also thefractions of roots, responsible for ion uptake, while the core is associated with tissuescomprising cellulose, starch and lignin which do not require maintenance ‘costs’. In themodel of Caloin and Yu, compartment M presumably comprises foliage and root1

fractions while compartment M should be composed of the structures holding the2

foliage in position and storage tissues. It is only if plant compartmentalization isassociated with a more precise anatomical description of the appropriate tissues that avalidation will be possible. More work is therefore required on that subject, although afirst attempt to fit the model of Caloin and Yu to ageing tomato plants, led Bellert et al.Ž . Ž y1 .1997 to separate the foliage rich in nitrogen 4 g N 100 g DM from the stems,

Ž y1 .petioles and fruits low in nitrogen 1.8 g N 100 g DM .

4. Operational approach of nutrition

4.1. Diagnostic of nutritional status

The appraisal of substrate fertility and the assessment of plant mineral requirementsare fundamental for crop fertilization management. In practice, the cultural system

Žshould be optimized in accordance with expectations on yield, crop quality of harvested. Ž .or transformed organs or environmental concerns residues in the soil for instance . The

estimation of nutrient availability for plant growth is generally achieved through soilŽ .substrate testing, which is more or less convenient depending on the agrosystem, orthrough plant or sap analysis. For soilless cultures, technology is providing on-line

Ž .sensors pH, electrical conductivity EC to monitor ion concentrations, which makeŽ .possible the short-term management of nutrition see Section 4.2. . In orchards, the

measurement of minute changes in stem diameter can be used to manage irrigation


Ž .Huguet, 1985 . Whole-plant testing is also widely used because it gives a directmeasurement of the actual quantities of nutrients taken up by the crop. When testing is

Ž .not possible on the entire plant, analysis of individual organs leaf, petiole, etc. is oftentaken as a substitute. In such cases, the mineral concentration measured in plant tissue iscompared to that of ‘reference’ material obtained from plants grown under non-limitingnutrient supply. The increasingly widespread use of leaf analysis since the fifties hasresulted in exhaustive compilations of ‘normal, deficient or toxic’ nutrient concentra-

Ž .tions in plants Chapman, 1966; Martin-Prevel et al., 1984 . Following this approach, it´seems that each tested plant has its own nutrient deficiency concentrations which mayappear irrational considering the similitude in metabolism between different species.However, it is evident from the modelling approaches developed in Sections 3.2. and3.3. that a sensible interpretation of analytical data for diagnostic purposes requiresknowledge of the plants’ critical nutrient concentrations over the whole growing cycle.For example, the diagnostic of nitrogen nutrition is an immediate and practical output of

Ž .the critical N concentration model see Section 3.3. . Hence, during plant growth,nitrogen concentration in the plant tissues may be compared to the critical nitrogen

Ž .concentration thus allowing calculation of a nitrogen nutrition index NNI :

%NNNIs

%Ncritical

As long as NNI is greater than 1, crop growth is not limited by nitrogen availabilityin the root environment. When NNI is lower than 1, the rate at which the crop grows islimited by nitrogen uptake. Hence, increasing nitrogen availability in the root environ-ment may increase the crop growth rate. In this case, NNI may be used as adecision-making indicator to provide the crop with an extra dressing of nitrogenfertilizer. This approach also provides an ubiquitous rationale for diagnostic that mayprobably be extended to minerals other than nitrogen. Hence, phosphorus and sulphur,

Ž 2y 2y.which are also taken up as anions H PO and SO and undergo a step of reduction2 4 4

in plants, should obey similar ‘laws’ of progressive decline in critical concentrations inthe dry biomass. Moreover, due to similarities in their metabolisms, we may speculatethat the parameters of the progressive decline of %P and %S should be similar to that ofnitrogen. For cations, it is probable that potassium, which is the largest counterbalancingion for nitrate uptake, also follows similar pattern. Calcium and magnesium, however,are likely to require different modelling approach due to the importance of plant cation

Ž .exchange capacity CEC and water fluxes in uptake and transport of these two divalentcations.

4.2. Managing the cultural system: the greenhouse as an example

The actual development of protected cultural systems is characterized by an increasein soilless techniques and the automatic monitoring of climate and fertilization. Suchsystems are costly in respect to hand-power and energy inputs. Optimizing thesehigh-tech systems requires the use of models describing fluxes of mass and energy in the

Žplant in harmony with those described for the environment Baille, 1997; Gary and.Baille, 1997 . In terms of fertilization, the widespread use of on-line programmable


fertilizer injectors gives growers an opportunity to apply the current scientific knowl-edge to greenhouse crop ‘fertigation’, for instance the uncoupling between water andnutrient supplies. The analysis of current practices reveals a dual approach for control-ling plant nutrition, i.e. inductive or deductive regulations.

Ž . Ž .1 In open run-through or closed types of soilless cultures, the actual practice offertigation consists in providing the crop with doses of nutrient solution at pre-set pH

Ž .and electrical conductivity values EC . As long as water and nutrients are taken up attŽ dr . Ž dr .the same rates, EC in the drainage EC remains close to a reference value EC .meas ref

In case of drifts, the nutrient solution concentration can be altered based on thedifference between the reference and measured EC in the drainage. Therefore at any

Ž .time t , EC may be determined from the previous EC of the nutrient solution suppliedŽ .at ty1 :

ECdr yECdrref meas

EC sEC = 1qt ty1 drž /ECref

However, EC measurement is partially relevant to the system since it provides onlylimited control of fertigation. Indeed, it is an indiscriminate indicator of the overallconcentration of fertilizers in solution while the appropriate blending of several mixturesof fertilizers requires a precise adjustment of individual ion concentration. Therefore, the

Ž . Ž .inductive a posteriori regulation exhibits two main limitations: 1 the absence ofŽ .specific sensors reliable in greenhouse conditions, and 2 the time-lag of the horticul-

Ž .tural systems 2–5 days for fertigation in rockwool slabs is incompatible with thehourly control of nutrient feed targeted by the regulator. In our view, the success of thistype of regulation is linked to a straight forward technological breakthrough in theconstruction of reliable ion specific sensors, in particular for nitrate measurements indrainage. Also required are changes in the root system environment. It will be necessaryto find a compromise between the current inertia of the system which is stable andsecure, and the regulation time-lag requirements on which depend the optimization ofthe system.

Ž . Ž .2 The deductive a priori regulation is potentially ideal to optimize the control ofgreenhouse crop mineral nutrition. It is based on the knowledge of plant responses tovarying its environment. Plant water supply based on calculation of potential evapotran-

Ž .spiration ET belongs to this type of approach. It allows the precise short-termp

prediction of plant water demand based on the measurement of current environmentalŽ .parameters. For tomato plants growing under the greenhouse, de Villele 1972 proposed`

to estimate ET from the measurement of global radiation and parameters typical of thep

greenhouse and the crop growth stage. Using this approach in plant fertilization shouldŽ .offer two main advantages: 1 the quality of the regulation is independent of the inertia

Ž .of the system and no compromise is required between security and efficiency; 2 theneeded climatic sensors already exist in most greenhouses since they provide inputs forclimate regulation. It is therefore possible to make use of the actual systems without anymore technological inputs. The success of this approach, however, is linked to theprerequisite knowledge of the relevant parameters; thus, modelling plant response tofluctuating environment is essential. For the time being, no knowledge-based plant

()

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Table 7Examples of deductive models used to control water or nitrogen supply to greenhouse crops

Mathematical formulation Authors

Ž .ET s0.67= R y0.2 de Villele 1972`p g

SLI ySLI DLI yDLI DRH yDRH DT yDT CDC A C A C A C A Ž .N s N = x q x q x q x q . . . q Papadopoulos and Liburdi 1989F I 1 2 3 4SLI DLI DRH DT 100A A A A

Rg dy1y3 y2Ž . Ž .N s0.796=10 = R = q1.435=10 =T Brun and Chazelle 1996u g solRg d

Abbreviations: ET , potential evapotranspiration; R , total incident radiation; N and N , final and initial nitrogen concentration in solution; SLI and SLI , currentp g F I C A

and average seasonal light integrals; DLI and DLI , current and average daily light integrals; DRH and DRH , current and average daily relative humidity; DTC A C A CŽ y1 y1.and DT , current and average daily air temperature; CD, overall growers rating of crop demand for Nitrogen; x , scalars; N , NO uptake rate mg N plant h ;A i u 3

T , temperature of nutrient solution.sol


model is operational to optimize the practice of mineral nutrition. Nevertheless, researchalong these lines is active and most relevant parameters controlling ion uptake areknown. Current deductive regulation of ion concentration in solution is simply based on

Ž . Ž .statistical models Table 7 . For instance, Papadopoulos and Liburdi 1989 use numer-Žous parameters influential for nutrient requirement i.e. light, RH, fruit load, crop age,

.etc. to adjust the base values of nutrient feed for tomatoes. Hence, for nitrogen as anw xexample, the final concentration N in solution equals the initial value beforeF

w x Ž .adjustment N corrected by the difference between current index C and averageIŽ . w x w xindex A values of seasonal light integral SLI , daily light integral DLI , daily relative

w x w xhumidity DRH and daily air temperature DT . The influence of each component is setw x w x Ž .by scalars x to x % and an overall grower’s rating of crop demand for nitrogen1 4

w x Ž .CD . Another illustration is given by the work of Brun and Chazelle 1996 on roses.w x Ž y1 y1.They described the kinetic of nitrate uptake N mg N plant h with a multipleu

w y2 xregression using agroclimatic factors, i.e. global radiation R , W m , global radiationgw x w xof the previous day R , the expected global radiation of the day R and theg gdy 1 d

w xtemperature of the nutrient solution T . This relation was strong enough to fitsolŽ 2 .successfully r s0.71 hourly uptake rate data obtained under greenhouse conditions

over a period of 5 consecutive days.To summarize, the inductive regulation is set on a purely technological breakthrough

and is rapidly operational while the deductive regulation depends on knowledge andrequires models. The use of the former in mineral nutrition implicates that the agrosys-tem undergoes normal climatic fluctuations and that action takes place only after analteration of the system has occurred. In other words, the regulator is set to ‘repair’accidents. The application of the latter regulation, should prevent the occurrence ofalteration in the agrosystem. Moreover, the use of climatic parameters to control plantnutrition should lead to a more integrated greenhouse management, in harmony with theregulation of water and carbon fluxes at the crop level. Since all physiological plantfunctions obey the same stimuli, a global model appears essential to understand truly theinteractions and optimize the functioning of the greenhouse.

5. Conclusions

For the purpose of this review, we segregated nutrient uptake into proximate andultimate functions. This was a mean to classify the concepts according to theirspatio-temporal level of approach, as needed for modelling. Another prerequisite isknowledge of the agricultural system. For instance, in the present understanding of plantphysiology, the role of water fluxes through plants is negligible for uptake of mostnutrients. However, depending on the agrosystem, the flux of nutrients from the bulksubstrate to root surface may be limited by water fluxes, i.e. plant transpiration.Therefore, in field conditions, diffusion barriers may overrule uptake kinetics, while inhydroponics, the solution stirring or circulation ensures nutrient availability at the rootsurface, and transpiration is clearly uncoupled from nutrient uptake. What is more, inintensive horticultural agrosystems, the technology allows, up to a certain extent, themonitoring of plant nutrition without reference to physiological knowledge. In this case,


Žmodels are concerned with optimizing the physical system itself i.e. faster response.time, sensors, etc. rather than understanding plant functioning. This latter approach

should not be neglected as it is probably the nearest to implementation.Among proximate functions, most studies have been based on the concept of ion

transporters and their response to low ion concentrations, which seriously limits their usein horticultural crop models dealing with a rich ionic environment. These studiesgenerally do not take plant demand into account, and therefore, are unable to provide thenecessary feedback regulation of uptake. As a consequence, they cannot make the link

Ž .with environmental conditions irradiance, CO enrichment, etc. , nor predict nutrient2

accumulation, which is a weakness for diagnostic purposes and quality prediction.Furthermore, realistic estimations of respiratory costs of ion uptake, required by carbonmodels, will not be made without a better understanding of uptake mechanisms andregulation. Similarly, we may highlight the lack of models of nutrient transport andpartitioning in tissues, which are required to understand the efficiency of their use forgrowth and RSR equilibrium.

Though plentiful, the literature on plant nutrition rarely serves modellers in thedevelopment of general concepts applicable to agronomic conditions. For instance,under different experimental conditions, i.e., steady-state vs. constant nutrition, the sameformula relates nitrogen concentration in whole plant tissue to relative growth rate:

n t sa=RGRqbŽ .

The parameters of the relation, however, have different values and are interpreted in a˚Ždistinct way according to the context: in terms of nutrient productivity Agren, 1985,

. Ž .1988 or plant compartmentalisation Caloin and Yu, 1984 . The former conceptexplains growth by the plant nutrient content, while in the latter, the nutrient content is aresult of growth. This underlines the weakness of these theories in formulating function-ally the interaction between growth and nutrients. Nevertheless, the steady-state ap-proach shows that at large-time scales, the amount of nutrients added to the medium ismore determinant than their concentration, for growth. It thus turns out that a definition

Ž .of plant demand is the relevant ultimate function for modellers. Mankin and Fynn 1996proposed a general formulation of the demand approach:

U sD "Xn n n

where U and D are the actual uptake and plant demand, respectively, while X isn n n

luxury consumption when positive, and storage mobilisation when negative. Plantdemand, computed from growth rate and a critical nutrient concentration, may be seenas the basis for fertilisation policy. Interestingly, critical concentration has been shownto depend strongly on canopy structure in relation to light interception, and onphotosynthetic metabolism, more than on other species-dependent characteristicsŽ .Hardwick, 1987; Lemaire and Gastal, 1997 . It should thus be emphasized that plantnutrition borrows the concepts used in carbon models. However, in the present nutritionstudies, growth is seen as a mere dry weight increase. We may speculate that furtherimprovements could arise from the use of recent growth models, which introduced theconcepts of structural and non-structural dry matter.


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