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A two-dimensional simulation model of phosphorus uptake including crop growth and P-response

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Page 1: A two-dimensional simulation model of phosphorus uptake including crop growth and P-response

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e c o l o g i c a l m o d e l l i n g 2 1 0 ( 2 0 0 8 ) 453–464

avai lab le at www.sc iencedi rec t .com

journa l homepage: www.e lsev ier .com/ locate /eco lmodel

two-dimensional simulation model of phosphorusptake including crop growth and P-response

lain Molliera,∗, Peter De Willigenb, Marius Heinenb, Christian Morela,ndre Schneidera, Sylvain Pellerina

INRA, UMR1220 TCEM, 71 avenue Edouard Bourlaux, F-33883 Villenave d’Ornon Cedex, FranceALTERRA, P.O. Box 47, NL-6700 Wageningen, The Netherlands

r t i c l e i n f o

rticle history:

eceived 18 July 2006

eceived in revised form

0 July 2007

ccepted 15 August 2007

ublished on line 20 September 2007

eywords:

rop growth

ynamic model

aize

utrient uptake

hosphorus

ea mays L.

a b s t r a c t

Modelling nutrient uptake by crops implies considering and integrating the processes con-

trolling the soil nutrient supply, the uptake by the root system and relationships between

the crop growth response and the amount of nutrient absorbed. We developed a model that

integrates both dynamics of maize growth and phosphorus (P) uptake. The crop part of the

model was derived from Monteith’s model. A complete regulation of P-uptake by the roots

according to crop P-demand and soil P-supply was assumed. The soil P-supply to the roots

was calculated using a diffusion equation and assuming that roots behave as zero-sinks.

The actual P-uptake and crop growth were calculated at each time step by comparing phos-

phate and carbohydrate supply–demand ratios. Model calculations for P-uptake and crop

growth were compared to field measurements on a long term P-fertilization trial. Three P-

fertilization regimes (no P-fertilization, 42.8 kg P ha−1 year−1 and 94.3 kg P ha−1 year−1) have

led to a range of P-supply. Our model correctly simulated both the crop development and

growth for all P-treatments. P-uptake was correctly predicted for the two non-limiting P-

treatments. Nevertheless, for the limiting P-treatment, P-uptake was correctly predicted

during the early period of growth but it was underestimated at the last sampling date (61 day

after sowing). Several arguments for under-prediction were considered. However, most of

them cannot explain the observed magnitude in discrepancy. The most likely reason might

be the fact that biomass allocation between shoot and root must be modelled more precisely.

Despite this mismatch, the model appears to provide realistic simulations of the soil–plant

dynamic of P in field conditions.

. Introduction

n the last 40 years several mathematical models simulatinghosphorus (P) uptake by roots from soils have been devel-ped. Following the work of Nye and Marriott (1969), these

odels described transport of P to individual roots by mass

ow and diffusion. P-uptake is assumed to be a function ofhe P-concentration in the soil solution, of transport rates in

∗ Corresponding author. Tel.: +33 557 12 25 20; fax: +33 557 12 25 15.E-mail address: [email protected] (A. Mollier).

304-3800/$ – see front matter © 2007 Elsevier B.V. All rights reserved.oi:10.1016/j.ecolmodel.2007.08.008

© 2007 Elsevier B.V. All rights reserved.

the soil liquid phase, and of the soil solid phase to bufferthe solution. Models based on this theory were first devel-oped for single roots and later adapted to the entire growingroot system (Baldwin et al., 1973; Claassen and Barber, 1976;De Willigen and Van Noordwijk, 1987). Such modelling efforts

have led to a better understanding of nutrient uptake by rootsin the absence of other limiting factors. Model-based inves-tigations have confirmed diffusion and mass flow processes
Page 2: A two-dimensional simulation model of phosphorus uptake including crop growth and P-response

i n g

454 e c o l o g i c a l m o d e l l

of soil nutrient transport to the root. The existence of a con-centration gradient around roots, which provides the drivingforce for P-diffusion, was confirmed by calculations and obser-vations (Jungk and Claassen, 1997; Hinsinger, 2001; Singh andSadana, 2002).

Evaluations of these models, either at the field scale orin pot experiments, have shown that they were able toclosely predict P-uptake in various soil–plant systems withmedium to high soil P-content for relatively short periods(Schenk and Barber, 1979; Lu and Miller, 1994; Teo et al., 1995).However, at low soil P-content, these models often underes-timate the experimentally measured P-uptake (Brewster etal., 1976; Schenk and Barber, 1979, 1980; Ernani et al., 1994).These discrepancies were due to the fact that some root sur-face processes (Hinsinger, 2001), mycorrhizae contribution(Gavito and Varela, 1995) and plant regulations (Raghothamaand Karthikeyan, 2005), which are obviously more importantat low soil P-content, were not included. Recent develop-ments have focused on integration of the contribution ofother rhizospheric processes to the soil P-supply such as pHchanges, organic anions and phosphatase release in the rhi-zosphere (Trolove et al., 2003). According to these models, theexudation of such compounds could greatly increase soil P-availability (Hoffland et al., 1990; Geelhoed et al., 1999; Kirket al., 1999). Nevertheless, these processes did not occur forall plant species and their efficiency is highly dependent onsoil physico-chemical properties and experimental conditions(Jones and Farrar, 1999). As these dependencies have beenshown to occur under extreme experimental conditions, it isquestionable to what extend they contribute to the crop P-nutrition in usual agricultural situations. There is still littleevidence that these root exudates mechanisms actually playa significant role in plant P-acquisition (Jones and Farrar, 1999).

While much efforts have been devoted to the aspects thataffect P-availability in soil, plant functioning aspects have gen-erally received less attention (Itoh and Barber, 1983). In mostmodels, plant growth is a fixed input irrespective of P-uptake,which does not account for the ability of the plant to reactto P-deficiency. As a consequence, the model underestimatedplant growth and P-uptake (Barber, 1995). Recent progresseshave been made in modelling crop growth and in understand-ing crop responses to P-deficiency. Models for crop growthrange in complexity from a simple, direct conversion of theamount of light energy into an amount of biomass (Goudriaan,1977; Monteith, 1977; Porter, 1984; Williams et al., 1989), todetailed mechanistic models including gas-exchange proper-ties of leaves and profile of light interception (e.g., Marcelis etal., 1998). In absence of limiting growth factors such as nutri-ents, water, pests and diseases, these models have provedto be able to predict correctly potential crop growth accord-ing to environmental conditions such as light, temperature,and carbon dioxide (CO2). Recent progresses have been madein understanding how P-deficiency affects the potential plantgrowth (Halsted and Lynch, 1996; Rodriguez et al., 1998; Plenetet al., 2000a, 2000b; Chiera et al., 2002), shoot–root allocationof the biomass and root growth (Mollier and Pellerin, 1999;

Pellerin et al., 2000; Vance et al., 2003; Wissuwa et al., 2005).Until now, this knowledge has rarely been used in the contextof uptake models. For instance a plant growth model based onempirical data measured for highly P-deficient conditions was

2 1 0 ( 2 0 0 8 ) 453–464

developed to investigate genotypic differences in P-efficiencyfor rice (Wissuwa, 2003). In this model, the soil part was over-simplified. It is important to link such a model to a soil–rootmodel to gain a better understanding of the soil–plant pro-cesses involved in P-uptake.

The purpose of this study was to develop a mechanisticmodel for the simultaneous simulation of P-supply by the soil,P-uptake by the root system and plant growth response. Thedynamic link between these processes was explicitly takeninto account. The objective assigned to the model was to pre-dict P-uptake and crop response under sufficient P-availabilityor moderate P-deficiency. Severe P-deficiencies were outsidethe scope of the model. The simulations of crop growth and P-uptake were compared to field measurements on young maizecrops and model applications were explored.

2. Model description

The current model consists of three modules closely con-nected. The first one deals with crop growth and cropP-demand. In this version of the model, the shoot part ofthe crop is assumed to be only constituted by leaves. Cropgrowth is described by plant phenology and biomass accumu-lation depending on climatic conditions. Crop P-requirementis derived from the potential plant growth regarding the envi-ronmental conditions. The second module describes P-supplyfrom the soil considering the soil solution concentration andthe soil buffer capacity. The third module deals with crop P-uptake depending on crop P-demand and P-uptake capacitydetermined by the soil P-supply and the root length densitydistribution in soil. The three modules are integrated to simu-late the feedback of effective P-uptake on crop growth. Thus,the model tightly couples crop growth with soil processes. Thethree modules exchanged information at a daily basis. Thecrop growth processes are expressed as a function of ther-mal time per square meter surface area of soil. The input datainclude climate drivers, soil properties and crop parameters.The output includes crop growth, P-uptake, soil P-fluxes andP-status. For convenience, in this paper volume water unit ismL while volume soil unit is designated with cm3.

2.1. Module 1: Modelling crop growth and P-demand

2.1.1. Crop growthThe crop growth module simulates plant phenology and drymatter accumulation as a function of daily weather data. Thedaily biomass production depends upon the photosyntheti-cally active radiation absorbed by the canopy (PARa, MJ m−2)calculated via crop cover from LAI, the leaf area index (m2 m−2)and k, the attenuation coefficient (Bonhomme et al., 1982;Varlet-Grancher et al., 1982), and the radiation use efficiency(Monteith, 1977; Kiniry et al., 1989; Sinclair and Muchow, 1999):

Gwnew = RUE × PARa (1)

�TT

where Gwnew is the total biomass increment rate(g biomass m−2 (◦Cd)−1), RUE the radiation use efficiency(g biomass MJ−1 PAR) and TT is the thermal time (◦Cd) since

Page 3: A two-dimensional simulation model of phosphorus uptake including crop growth and P-response

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pmad

edgitgd

G

w(ia(

G

wG(o

shsr

G

ass

G

2Tbfl

U

w

fpE

S

e c o l o g i c a l m o d e l l i n

lant emergence calculated with daily minimum and maxi-um air temperature with a temperature threshold of 10 ◦C

nd �TT is daily increment of thermal time. The RUE did notepend on nutritional P-status (Plenet et al., 2000a).

During the juvenile phase, the LAI is simulated using anxpo-linear growth function of thermal time. This functionescribes LAI as an exponential phase for early stages ofrowth, which for later stages of growth turns towards linearncrease in LAI (Goudriaan and Monteith, 1990). The poten-ial leaf area index expansion rate (GLAIPot m2 m−2 (◦Cd)−1) isoverned by the air temperature and it is calculated as theerivative of the expo-linear growth function:

LAIPot = dLAIPot

dTT= cm(1 − e−(rm/cm)LAI) (2)

here cm is the maximum GLAI in the linear phasem2 m−2 (◦Cd)−1), and rm is the maximum relative GLAIn the exponential phase ((◦Cd)−1). The maximum GLAIllowed by the carbohydrates availability denoted as GLAIC

m2 m−2 (◦Cd)−1) is calculated from Gwnew (Eq. (1)) as:

LAIC = GwnewSLA (3)

here SLA is the specific leaf area (m2 g−1). The maximumLAI allowed by temperature and carbohydrate availability

GLAImax, m2 m−2 (◦Cd)−1) was assumed to be the minimumf GLAIPot and GLAIC.

The assimilated carbohydrates are partitioned betweenhoot and root assuming that the shoot demand for carbo-ydrates is firstly satisfied. When P-uptake is not limiting, thehoot growth rate (Gshoot, g m−2 (◦Cd)−1) is calculated as theatio of GLAImax to SLA:

shoot = GLAImax

SLA(4)

The root growth rate (Groot, g m−2 (◦Cd)−1) is calculatedssuming that once the shoot demand for carbohydrates isatisfied the remaining carbohydrates are allocated to the rootystem:

root = Gwnew − Gshoot (5)

.1.2. P-demando derive the crop demand for P we used a close relationshipetween LAI and total crop P-uptake (UP, g P m−2) obtainedrom a long-term field fertilization experiment with differentevels of P soil availability:

P = a(LAI)b (6)

here a and b are fitted parameters.The daily crop P-demand (Ssr, g P m−2 (◦Cd)−1) is calculated

rom the maximum leaf area expansion rate allowed by tem-

erature and carbohydrates availability (GLAImax) according toq. (6):

sr = GLAImaxdUP

dLAI(7)

0 ( 2 0 0 8 ) 453–464 455

2.2. Module 2: Modelling soil P-supply to crop

Plants absorb P as orthophosphate from the soil solution. Here,soil P-supply refers to the concentration of P in soil solution(CP, mg mL−1) plus the amount of P (Q, mg cm−3) that canreplenish within 1 day the soil solution under a gradient ofconcentration. The contribution of organic P to the plant nutri-tion is neglected. To predict the evolution of CP following rootabsorption, the P-transfer between liquid and solid phaseswas described by a Freundlich equation (McGechan and Lewis,2002):

Q = kFCb1P (8)

where kF and b1 are Freundlich coefficients determined from asorption/desorption experiment or from an isotopic exchangemethod after 24 h (Schneider and Morel, 2000). The soil buffercapacity is the ratio of changes in solid P to those in solutionP (dQ/dCP).

2.3. Module 3: Modelling P-uptake by root systemaccording to crop P-demand and soil P-supply

The nutrient uptake model is a two-dimensional model: thevertical and horizontal dimensions at right angles to the row.The two-dimensional soil domain is subdivided into squarecontrol volumes. Each of them is characterised by soil prop-erties and root length density (Lrv, cm cm−3). The microscopicmodel for nutrient uptake developed by De Willigen and VanNoordwijk (1987) is used for each control volume. Phospho-rus transport within the solution of the soil cylinder aroundthe root is driven by mass flow and diffusion. The equationfor transport of P in soil of constant water content reads incylindrical coordinates:

(dQ

dCP+ �

)∂CP

∂t= D

R

∂RR

∂CP

∂R− V

∂CP

∂R− SS (9)

where dQ/dCP is the soil buffer capacity (mL cm−3), � the soilwater content (mL cm−3), t the time (day), R radial distanceto the root center (cm), D the diffusion coefficient in soil(cm2 day−1), V the flux of water towards the root (cm day−1)and Ss is the uptake rate (mg cm−3 day−1). The diffusion coef-ficient D is calculated using the following equation proposedby Barraclough and Tinker (1981):

D = D0�fl (10)

where D0 is the P diffusion coefficient in free water, and fl isthe tortuosity factor which accounts for the increased pathlength in soil. The tortuosity factor fl is given by a broken-linefunction of � (Barraclough and Tinker, 1981):

fl =

⎧⎨⎩

f1� + f2, � ≥ �l

�(f1� + f2), � < �l

(11)

�l

where �l is the water content where the two lines intersect(mL cm−3), f1 and f2 are dimensionless parameters dependingon soil properties.

Page 4: A two-dimensional simulation model of phosphorus uptake including crop growth and P-response

i n g

456 e c o l o g i c a l m o d e l l

It is assumed that roots are regularly distributed withineach control volume and all roots have the same radius R0

(cm) and length �z (cm) corresponding to the thickness of thecontrol volume. A radial soil cylinder of height �z and radiusRl is assigned to each root. Rl is given by

Rl = 1√�Lrv

(12)

The boundary condition at the root surface follows from thecrop demand for P. We assumed that root P-uptake is dictatedby crop P-demand denoted as Ssr (Eq. (7)) and converted tomg cm−2 day−1. The flux of P (F, mg P cm−2 day−1) at the rootsurface accordingly reads:

R = R0, F = − Ssr

2�R0 �zLrv(13)

The outer boundary condition is that of vanishing P-flux F:

R = Rl, F = −D∂CP

∂R+ VCP = 0 (14)

Required uptake cannot occur when the diffusion and massflow processes in the soil cannot replenish enough P to theroot. We assume that the maximum uptake rate equals themaximum possible rate of transport (by diffusion and massflow) to the root, i.e. the root behaves as a zero-sink. Themaximum nutrient uptake rate per unit surface area Ssm

(mg cm−2 day−1) is derived from the steady-rate approximatesolution for the concentration profile around the root for thezero-sink condition (De Willigen and Van Noordwijk, 1994)

Ssm = 2� �zLrvD(�2 − 1)2G(�, �)

CP (15)

where CP is the average CP in the soil surrounding the root(mg mL−1), � the dimensionless normalized radius defined asRl/R0, G(�,�) is the geometry function given as

G(�, �) = 12(� + 1)

(1 − �2

2+ �2(�2� − 1)

2�+ �2(�2� − 1)(� + 1)

2�(�2�−2 − 1)

+ (1 − �2�+4)(� + 1)(2� + 4)(�2�+2 − 1)

)(16)

where � is the dimensionless uptake of water as given by

� = ql

4 �z�LrvD(17)

where ql is the flow of water across the root surface(mL cm−2 day−1).

Actual P-uptake may or may not satisfy crop P-requirements. We assume that the actual P-uptake rate Ss

equals the required P-uptake rate Ssr as long as Ssr is lessthan the maximum P-uptake rate Ssm, otherwise Ssr equalsthe maximum P-uptake rate Ssm. The total P-uptake by theentire root system is the sum of P-uptake from all control

volumes. It may occur that in some parts of the soil (controlvolumes) roots are not able to take up P at the required rate.It is known that the root system can compensate such localshortage by increasing uptake at more favorable locations (e.g.,

2 1 0 ( 2 0 0 8 ) 453–464

De Jager, 1985). To determine if the other roots can take upthis shortage an iterative scheme is used. Indeed, as this pro-cess continues, more and more roots may reach the maximumpossible uptake rate and further compensation needs to belooked at.

2.3.1. Integration and feedbackThe crop growth processes are driven by the amounts of carbo-hydrates and P-supply to the crop. The crop growth is thereforecalculated from the actual carbohydrate assimilation and theactual P-uptake as follows.

If the crop P-demand is satisfied (Ss = Ssr), the actual leafarea index expansion rate (GLAIA, g m−2 (◦Cd)−1) equals theleaf area index expansion rate allowed by the current air tem-perature and the carbohydrate assimilation (GLAImax). Theassimilated carbohydrates are partitioned between shoot androot assuming that the shoot demand for carbohydrates isfirstly satisfied and Gshoot and Groot are calculated followingEqs. (4) and (5), respectively.

If the actual P-uptake is less than required (Ss < Ssr), theleaf area index expansion rate is reduced according to the P-shortage. Many results have shown that when P-uptake waslimited, the leaves appearance and morphology were modi-fied. For low P-treatments, the leaves were smaller (Plenet etal., 2000b), thicker and the specific leaf area SLA was decreased(Grimoldi et al., 2005) most likely because of increases in cellwall material (Jacob and Lawlor, 1991) and of storage car-bohydrates, especially starch (Fredeen and Terry, 1988; Raoand Terry, 1989; Khamis et al., 1990). The SLA decreased in alesser extend than the leaf area index expansion rate whenP is limiting (Rao and Terry, 1989). A reduction factor, i.e.Ss/Ssr is therefore applied to the GLAImax when P-uptake islimited. The actual leaf area index expansion rate (GLAIA)equals:

GLAIA = Ss

SsrGLAImax (18)

We assumed that the SLA of the leaf area index increment(SLAnew) decreased according to the Ss/Ssr ratio but that itshould not be less than one-half of SLA:

SLAnew =

⎧⎨⎩

Ss

SsrSLA,

Ss

Ssr≥ 0.5

0.5SLA,Ss

Ssr< 0.5

(19)

The Gshoot and the Groot are calculated with Eqs. (4) and (5)according to GLAIA, SLAnew and Gwnew. Because of reducedleaf area index expansion rate, fewer carbohydrates are allo-cated to the shoot so that more carbohydrates are directed tothe root system.

The amount of assimilates partitioned to roots determinesnew root growth (Van Noordwijk, 1983). The increase in rootlength is obtained by the daily carbon allocated to the root sys-tem multiplied by the length/weight ratio (specific root length,

m g−1). This new root length is distributed in the soil based onthe diffusion-type root growth model proposed by De Willigenet al. (2002) and Heinen et al. (2003). In two dimensions (carte-sian coordinates with no gradient in the Y direction), the
Page 5: A two-dimensional simulation model of phosphorus uptake including crop growth and P-response

g 2 1

r

wtddcii(Hrisal

Q

wtdfvTip

3

TTc2wumfsawt

e c o l o g i c a l m o d e l l i n

oot-growth diffusion equation reads:

∂Lrv

∂t= ∂

∂X

(DL,X

∂Lrv

∂X

)+ ∂

∂Z

(DL,Z

∂Lrv

∂Z

)− �LLrv + QL(X, Z, t)

(20)

here Lrv is the root length density (cm cm−3), X the horizon-al coordinate (cm), Z the vertical coordinate (cm), DL,X theiffusion coefficient in the X direction (cm2 day−1), DL,Z theiffusion coefficient in the Z direction (cm2 day−1), �L the spe-ific root decay rate (day−1), and QL is the root length densitynput rate (cm cm−3 day−1). This diffusion equation is numer-cally solved using the control-volume-finite-element methodPatankar, 1980; Heinen and De Willigen, 1998; Heinen, 2001;einen et al., 2003). For each of the control volumes, the input

ate of root length density QL for each of the control volumess computed from the total input of root dry mass per timetep in the soil where root mass origins (for maize 5 cm deptht the plant location). The root mass input is converted to rootength input according to (Heinen et al., 2003):

L(X, Z, t) = QM(X, Z, T)

�R20�rdr

A

VT(21)

here QM is the rate of root biomass input (g cm−2 day−1), R0

he mean root radius (cm), �r the bulk density of root (g cm−3),

r the dry matter content of root (g (dry) g−1 (fresh)), A the sur-ace area occupied by a single plant (cm2), and VT is the sum ofolumes of all control volumes where root input occurs (cm3).he R0, �r, dr, A, and VT are assumed to be constant and QM

s time-varying rate of root biomass input derived from wholelant carbohydrate budget.

. Model operation

he model was programmed using Fortran 77 and Fortran 90.he crop growth model included the crop P-response. It wasoupled to FUSSIM2 model (Heinen and De Willigen, 1998,002; Heinen, 2001), a two-dimensional simulation modelhich described water movement, solute transport and rootptake of water and nutrients in partially saturated porousedia. In this paper, FUSSIM2 was used with transient dif-

usive P-transport under steady-state water conditions. The

tudy was carried out on irrigated field experiment (see below)nd we assumed that water availability was no limiting. Theater uptake and the mass flow were not considered here. So,

he P-transport was only by diffusion (� = 0) and the Eq. (16)

Table 1 – Measured soil physico-chemical properties and Freun

Depth (cm) Soil texture

Clay(g kg−1)

Loam(g kg−1)

Sand(g kg−1)

Organic matter(g kg−1)

0–25 60 134 806 17.725–40 69 157 774 12.440–60 82 181 737 7.1

0 ( 2 0 0 8 ) 453–464 457

became:

G(�, 0) = 12

(1 − 3�2

4+ �4 ln(�)

�2 − 1

)(22)

The input data include climate (daily minimum and maxi-mum temperature, solar radiation), soil features (soil texture,bulk density, water content, P-concentration, P-adsorptionisotherm, P-transport parameters) and crop genetic param-eters (potential leaf area growth, radiation use efficiency,specific leaf area, mean root radius, root diffusion parameters).The crop growth parameters are calibrated based on observedfield data under non-limiting P-conditions. The output vari-ables are the daily P-uptake from each soil control volume andcumulated P-uptake, the shoot and root growth, the leaf areaindex, the root length density and P-bioavailability distribu-tion within the soil.

4. Validation analysis

4.1. Field crop experiment

We selected a long-term P field experiment to evaluate theproposed model for the newly developed parts of the model,including mainly leaf growth, biomass production and cropP-response to P-uptake. The long-term P-fertilization exper-iment located at Carcares Sainte Croix in the Southwest ofFrance (43◦52′N, 0◦44′W, 55 m above sea level) has been con-tinuously cropped with irrigated maize since 1972. ThreeP-fertilization regimes were arranged in a randomized com-plete block design with four replicates: 0 kg P ha−1 year−1

(treatment P0); 42.8 kg P ha−1 year−1 applied on average whichcorresponded to about 1.5 times the amount of P exportedannually by grains (treatment P1.5); and 94.3 kg P ha−1 year−1

applied on average which corresponded approximately tothree times the amount of P exported annually by grains (treat-ment P3). These treatments have led to a range of P-supply. In1995, the amount of extractable Olsen-P (Olsen and Sommers,1982) in arable layer were 23 �g P g−1 in P0, 49 �g P g−1 in P1.5and 66 �g P g−1 in P3. In this sandy soil, 23 �g g−1 of Olsen-P is considered to limit growth. Tables 1 and 2 give the soilphysico-chemical properties, Freundlich equation parameters(Morel, 2002), and the P-concentration in soil solution mea-

sured on soil samples of the different layers collected atplant emergence. Maize (Zea mays L.), cultivar Volga (Pioneer-France Maıs) was sown on 10 April 1996. Plant density was8.35 plants per m2. Plant samples were taken approximately

dlich equation parameters for P in the different soil layers

Freundlich parameters(Eq. (8))

pH inwater

Bulk soil density(g cm−3)

kF b1

5.8 1.5 6.15 0.726.1 1.7 1.19 0.466.2 1.7 0.41 0.27

Page 6: A two-dimensional simulation model of phosphorus uptake including crop growth and P-response

458 e c o l o g i c a l m o d e l l i n g

Table 2 – Mean P-concentration in soil solution CP(10−3 mg P mL−1) for the three P-treatments at plantemergence in the different soil layers

Depth (cm) P-treatments

P0 P1.5 P3

0–25 0.52 (0.145) 1.61 (0.164) 2.85 (0.092)25–40 0.22 (0.084) 0.52 (0.133) 1.29 (0.241)40–60 0.05 (0.046) 0.12 (0.111) 0.26 (0.085)

Standard error of the mean is given in parentheses (number ofreplicates was 4).

once a week from emergence to flowering. Leaf measurementsand calculations to obtain the LAI were presented in Plenetet al. (2000b). Above-ground and root dry matter were deter-mined by sampling small plots consisting of 14 consecutivesplants from the central rows. Dry matter was determinedafter drying at 80 ◦C for 72 h. The P-content in dry matterwas determined by induced coupled plasma (ICP) after grind-ing, calcination at 550 ◦C and taken in HNO3. More detailson the experimental design were presented by Plenet et al.(2000b).

4.2. Model parameters

The daily weather data used to drive the model, i.e. solar radi-ation (RG0), maximum and minimum temperature (◦C), weremeasured on the experimental site by a global radiation sensor(SDEC, France) and temperature probes (107, Campbell Scien-

Table 3 – Soil and crop parameters used for P-uptake model cal

Symbols Explanation Sou

Soil parametersD0 Diffusion coefficient of H2PO4

− infree water at 25 ◦C

Lide and Frede

fl Tortuosity factor (Eq. (10))�l, f1 and f2 Parameters of tortuosity model

(Eq. (10))Barraclough an

� Soil water content Measured (field

Plant parametersLAIi Initial leaf area Measuredcm rm Leaf area expansion parameters of

Eq. (3)Estimated‡

K Extinction coefficient Bonhomme etRUE Radiation use efficiency as

function of total dry biomass (W)Estimated‡

a and b Parameters of (Eq. (7)) Estimated‡

SLA Specific leaf area Estimated‡

DL,X Root diffusion coefficient in Xdirection

Fitted fromdata ofGrabarnik etal. (1998)

DL,Z Root diffusion coefficient in Zdirection

�L Specific root decay rateR0 Mean root radius Machado and Fdr Dry matter of a root Anghinoni and�r Density of a fresh root

† Dimensionless.‡ Parameters estimated from measurements on P3-treatment in 1996.

2 1 0 ( 2 0 0 8 ) 453–464

tific, UK). The measurements were taken every 15 min and thehourly means were stored in a datalogger (CR10X, CampbellScientific Ltd., Leicestershire, UK).

Table 3 gives the soil and crop parameters estimated eitherfrom the literature or from crop measurements achieved onP3 in 1996.

4.3. Comparison of simulated results withmeasurements

Daily model outputs were compared to field measurements ofP-uptake, shoot and root biomass, leaf area index during theearly growth period (from 22 to 61 days after sowing, i.e. from86 to 336 ◦ Cd with base temperature 10 ◦C). The mean valueof the four replicates of field measurements were comparedto model outputs.

The modelling efficiency statistic (EF), between measuredand simulated variables was used as indicator of goodness ofpredictions (Mayer and Butler, 1993; Tedeschi, 2006):

EF = 1 −∑n

i=1(Pi − Oi)2∑n

i=1(Oi − Oavg)2(23)

where Pi is the ith simulated value, Oi the ith observed value,Oavg the average of the observed values, respectively, and n is

the number of data pairs. For a perfect model prediction EF = 1.The (theorical) lower bound of EF is minus infinity. When EFis negative, the model-predicted values are worse than theobserved mean (Loague and Green, 1991).

culations

rce Value Units

rikse, 1996 0.759 cm2 day−1

–†

d Tinker, 1981 0.12, 1.58 and −0.17 mL cm−3, –, –

capacity) 0.35 mL cm−3

0.045 m2 m−2

0.020, 0.024 m2 m−2 (◦Cd)−1, (◦Cd)−1

al., 1982 0.7 –†

0.85 × W0.24 g MJ−1

0.38 and 1.16 –†

0.011 (LAI)−0.35 m2 g−1

3.60 cm2 day−1

2.15 cm2 day−1

0.0001 day−1

urlani, 2004 0.01 cmBarber, 1980 0.04 g g−1

1.0 g cm−3

Page 7: A two-dimensional simulation model of phosphorus uptake including crop growth and P-response

e c o l o g i c a l m o d e l l i n g 2 1 0 ( 2 0 0 8 ) 453–464 459

Fig. 1 – Time courses of predicted P-demand and P-uptaker

5

5

TgdosPegtdaiagduP

dsEt

Fig. 2 – Measured (open symbols) and simulated (lines)time courses of cumulated P-uptake (g P m−2) by maize cropin the three P-treatments. Data points represent the meanand vertical bars show the 95% confidence intervals of the

ate (g P m−2 day−1) in the three P treatments.

. Results

.1. Crop P-demand and P-uptake

he simulated P-demand (Eq. (7)) was dependent on croprowth governed by climatic conditions (temperature, inci-ent radiation). It was also affected by soil P-supply becausef indirect effects of P-uptake on crop growth and its sub-equent P-demand (Fig. 1). For non-limiting conditions of-nutrition for maize (P3 and P1.5), the actual P-uptake ratequals the P-demand which is controlled by maximal croprowth according to carbohydrates assimilation and tempera-ure. For high P-conditions the P-demand increased rapidlyuring the early growth period to reach a maximum valuet around 0.11 g P m−2 day−1. When crop P-nutrition is lim-ted by soil P-supply as for P0, the simulated P-demand waslmost never satisfied from 100 to 400 ◦Cd. Consequently, croprowth and P-demand were reduced for P0. Although the P-emand was reduced for P0, the soil P-availability and rootptake were even then too small for the P-uptake to satisfy the-demand.

Fig. 2 shows the time courses of the measured and pre-

icted total P-uptake for the three P-treatments. For P3, theimulated and measured P-uptake were similar (Table 4;F = 0.97). For P1.5, the predicted P-uptake was very similaro measured P-uptake (Table 4; EF = 0.91) and was slightly

Table 4 – Model efficiency (EF) obtained from the comparison ofbiomass and leaf area index

P-treatment

P-uptake Shoot biomas

P0 0.661 0.787P1.5 0.912 0.975P3 0.970 0.979

mean.

reduced compared to P3. Moreover, the period when P-uptakedecreased for P1.5 compared to P3, i.e. from about 220 to400 ◦Cd, was correctly predicted. For P0 the model predicteda severe reduction in P-uptake. The predicted and measuredP-uptakes for P0 were similar during the early growth period.Nevertheless, at the last sampling date the predicted P-uptakewas underestimated. Due to this discrepancy, the model effi-ciency for P-uptake prediction was lower for P0 (Table 4;EF = 0.66) compared to the other treatments.

5.2. Crop growth response to P-uptake

Fig. 3 shows the measured and simulated leaf area index (LAI)for the three P-treatments. For P3 the simulated LAI was veryclose to observations and model efficiency was high (Table 4).As P was non-limiting, the leaf area expansion was only gov-erned by climatic conditions and biomass partitioning withinthe plant. For P1.5 the predicted leaf area expansion wasslightly reduced compared to P3 after 220 ◦Cd. Moreover, LAI

reduction for P1.5 was correctly predicted. For P0 the modelpredicted a severe reduction in the leaf area expansion asso-ciated to the P-uptake decrease. After 336 ◦Cd the predictedvalue of LAI for P0 was only 17% of that for P3. The period and

simulated with measured P-uptake, shoot biomass, root

Model efficiency (EF)

s Root biomass Leaf area index

0.928 0.7610.929 0.9790.978 0.988

Page 8: A two-dimensional simulation model of phosphorus uptake including crop growth and P-response

460 e c o l o g i c a l m o d e l l i n g 2 1 0 ( 2 0 0 8 ) 453–464

Fig. 3 – Measured (open symbols) and simulated (lines) timecourses of maize crop leaf area index (m2 m−2) in the three

Fig. 5 – Comparison of measured (open symbols) andsimulated (lines) shoot dry weight (g m−2) to leaf area index(m−2 m−2) relationship in the three P-treatments. Datapoints represent the mean and bars show the 95%confidence intervals of the mean.

P-treatments. Data points represent the mean and verticalbars show the 95% confidence intervals of the mean.

the reduction of LAI were well predicted excepted for the lat-est sampling date. However, the simulated leaf area index wasslightly underestimated at 336 ◦Cd.

For the three P-treatments, the predicted and measuredshoot biomass production agreed closely (Fig. 4 and Table 4).Both values were not different for P3 and P1.5. The period andthe order of magnitude of shoot growth reduction were veryclosely predicted for P0.

As P became limiting factor of crop nutrition, the predictedSLA decreased so that more biomass was required for leafarea expansion (Fig. 5). Predicted shoot biomass associated

Fig. 4 – Comparison of measured (open symbols) andsimulated (lines) time courses of shoot biomassaccumulation (g m−2) in the three P-treatments. Data pointsrepresent the mean and vertical bars show the 95%confidence intervals of the mean.

Fig. 6 – Comparison of measured (open symbols) andsimulated (lines) time courses of root biomassaccumulation (g m−2) in the three P-treatments. Data points

represent the mean and vertical bars show the 95%confidence intervals of the mean.

to a LAI value of 0.6 m2 m−2 were 36 and 60 g m−2 for P3 andP0, respectively. This predicted response to P-shortage was inaccordance with measurements.

The values of root biomass and root growth response toP were correctly predicted (Fig. 6 and Table 4). The simulatedroot growth for P3 and P1.5 were similar and higher than for

P0. As P was limiting for P0 the model predicted a reductionof root growth. This predicted reduction in root growth (rel-ative root biomass P0/P3 at the last sampling date was 0.52)was less severe than for shoot growth (relative shoot biomass
Page 9: A two-dimensional simulation model of phosphorus uptake including crop growth and P-response

g 2 1

PmPtl

6

Cumahart

ds1bfrTutpcB1TiuauPuioddutiarstsBttct

S

TC

e c o l o g i c a l m o d e l l i n

0/P3 at the last sampling date was 0.30). Consequently, theodel predicted higher root–shoot ratios for P0 in response to

-shortage compared to P3. The field measurements indicatedhat the root–shoot ratio increased for P0-treatment but to aesser extent than predicted.

. Discussion

rop parameters determined for P3 were used to predict P-ptake and crop growth prediction for P1.5 and P0, so thatodel evaluations in Figs. 2–6 for the P1.5- and P0-treatments

re proper tests of the model hypotheses. The core of theseypotheses are basically those of FUSSIM2 model (De Willigennd Van Noordwijk, 1994; Heinen, 2001), but extended with theesponse of shoot and root growth to P-uptake, so as to enablehe simulation at whole plant level under field conditions.

In nutrient uptake models root uptake is generallyescribed as a function of the concentration of the nutrient inolution at the root surface (Claassen and Barber, 1976; Barber,995). Numerous studies have shown that the relationshipetween root P-uptake and the P-concentration was satis-actory described either by a linear relationship in a limitedange of P-concentrations or by a Michaelis–Menten equation.he Michaelis–Menten kinetics parameters were determinednder controlled conditions (Claassen and Barber, 1974) or fit-ed from soil-grown plants (Mullins and Edwards, 1989). Thesearameters vary with plant species, genotype, plant age, soilonditions and nutritional status of the plant (Jungk andarber, 1975; Anghinoni and Barber, 1980; Jungk and Claassen,989; Teo et al., 1992; Kumar et al., 1995; Dunlop et al., 1997).he variations of these parameters were rarely considered

n nutrient uptake models. In addition, modifications of rootptake kinetics parameters according to plant demand werelmost never considered. In our proposed model the root P-ptake is determined by both the crop P-demand and the soil-availability. The crop P-demand determines the current P-ptake rate by the whole root system when the soil P-supply

s sufficient, that is when the current potential uptake ratesf all roots under a zero-sink assumption exceed crop P-emand. Transport in the soil by diffusion to the root surfaceetermines current P-uptake rate when the current potentialptake rates of all roots under zero-sink assumption is lesshan crop P-demand. We assumed that the crop maximizests uptake rate and, therefore that the roots are able to behaves a zero-sink, taking up P at the same rate as it arrives at theoot surface, thus keeping the concentration there zero. Manytudies on P-uptake absorption kinetics of roots show the exis-ence of a minimal concentration (Cmin) at which root P-uptaketops. Its value is closed to (3–6) × 10−6 mg P mL−1 (Schenk andarber, 1979; Bhadoria et al., 2004) and is very low comparedo commonly measured soil solution concentration in agricul-ural soils of temperate area. In the model, it is possible toalculate P-uptake for situations with Cmin > 0. Eq. (15) thenakes the form:

2

sm = 2� �zLrvD(� − 1)2G(�, �)

(CP − Cmin) (24)

he predicted P-uptake values for P0 and for P3 with

min = 6 × 10−6 mg P mL−1 were lower compared to those with

0 ( 2 0 0 8 ) 453–464 461

Cmin = 0 mg P mL−1. However, the relative P-uptake decreasewas lower than 0.1%. So, in the studied conditions the zero-sink assumption did not affect predicted value of P-uptake.

The model included several direct and indirect feedbackson P-uptake, biomass production and partitioning betweenshoot and root. Increases in root-to-shoot ratio were com-monly reported when P is limiting factor (Lynch et al., 1991;Rosolem et al., 1994; Ciereszko et al., 1996; Horst et al., 1996;Nielsen et al., 2001). The simulated increases in root-to-shootratio at lower P-levels are thus consistent with field data andthis lends further support to model hypotheses. The causesof these increases are consistent with the observations ofWissuwa et al. (2005) and Mollier and Pellerin (1999). Limita-tion in soil P-supply reduces first leaf area, and assimilates nolonger needed for leaf expansion rate are partitioned to theroots. Once these excess assimilates are used up, the smallerleaf area no longer supplies enough carbohydrates and rootgrowth decreases due to carbohydrate limitation.

The proposed model correctly simulated the crop devel-opment and growth under non-limiting P-conditions (i.e.P3 and P1.5). For all predicted variables, model efficiency(EF) ranged from 0.91 to 0.98 (Table 4). For P0 the cropgrowth processes, which were affected, were also correctlysimulated (EF = 0.76–0.92), but the predicted P-uptake wasunderestimated (EF = 0.66) at the last sampling date (336 ◦Cdafter emergence). For P0 according the simulations, the rootsbehaved almost always as a zero-sink for P-uptake and rootbiomass was correctly simulated (Fig. 6). Thus, mismatchbetween measured and predicted P-uptake and crop growthfor limiting conditions of P-nutrition may be attributed to P-mobilizing processes not taken into account by the model.The signification of these processes may be indicated bythe importance of the underestimation of the simulatedP-uptake.

Three factors were mainly neglected for the simulations:the P-transport by mass flow to the root, the contribution ofrhizospheric processes of P-acquisition, except the gradientof P concentration; and mycorrhizal infection. Regarding P-transport by mass-flow Roose et al. (2001) showed that forP-uptake the water flux into the root would have to be muchhigher than 4.5 × 10−5 cm s−1 for advective solute uptake tobe important. Typical water flux values are on the order of10−7 cm s−1, so that water uptake has to increase by about 100times before advection becomes even comparable to diffusion.Moreover, when water movement and uptake were consid-ered, the calculated cumulated P-uptake was lower than in theabsence of water movement (Roose et al., 2001). This is prob-ably because water uptake leads to a reduction in soil watercontent � in rhizosphere with a consequent reduction in P-diffusion transport (cf. Eq. (10)). Accordingly, if we consideredboth root water and mass-flow in P0-simulation, the predictedP-uptake would have been reduced and the difference withmeasurements would have been increased.

Regarding the role of rhizospheric mechanisms of P-acquisition, other than the gradient of concentration occur-ring around the root when they absorb P, it is still questionableabout their quantitative contribution in field conditions. The

exudation of organic acids like citrate and oxalate (Geelhoed etal., 1999) or of proton (Hinsinger et al., 2003) may increase soilP-supply and thus predicted P-uptake. Studies demonstrated
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i n g

r

462 e c o l o g i c a l m o d e l l

that organic acids can cause a significant enhancement ofcrop P-uptake. However, the magnitude of the P-mobilizationresponse is likely to be highly context-dependent (Strom et al.,2002). This P-mobilization is probably important in calcare-ous soil. For maize, the contribution of exuded organic acidsto rhizosphere acidification was rather negligible, not exceed-ing 0.2–0.3% (Petersen and Bottger, 1991). Exuded organic acidanions might affect the speciation of both Fe (Marschnerand Romheld, 1994) and Al (Heim et al., 1999) via complexa-tion reactions. Their possible implication in the dynamic ofP ions in the rhizosphere is thereby possible, although nodirect evidence for increasing P-availability has been reported(Hinsinger, 2001).

The exudation of enzymes hydrolyzing organic soil P mayalso increase P-availability in soil (Jungk et al., 1993; Seelingand Jungk, 1996). In our considered field experiment thesoil organic matter and P-organic contents were 1.8% and100.1 mg P kg−1, respectively. If we assume an organic mattermineralization of 1% per year and that P is released at thesame rate as the organic matter decomposition then, on aver-age, 0.137 mg P kg−1 should be released during the 50 days ofsimulation. This amount represents only 0.25% of the amountof P-mineral available in P0 (38.9 mg P kg−1) and could be rea-sonably neglected.

Regarding the mycorrhizal interaction on maize P-uptake,the Miller et al. (1995) works showed that mycorrhizal infec-tion increased early maize P-uptake. Maize is considered tobe a low-dependent, facultative mycorhizal plant (Howeler etal., 1987) that responds to mycorrhizal inoculation at low fer-tility levels (Gavito and Varela, 1995). In our proposed model,the mycorrhizae development and its contribution to P-uptakewere not considered. This model simplification should notimpair model prediction when P-availability in soil is high orslightly limiting. In the low P-conditions of the P0-treatment,modelling of P-uptake without considering root mycorrhizalinfection might explain underestimation of predicted of P-uptake and crop growth.

The simulation results indicate that some aspects of themodel hypotheses require further development. Root biomasswas correctly simulated. However for P0, P-uptake was slightlyunderestimated at the last sampling date (Fig. 2). This dis-crepancy could be due to an imperfect description of soilP-buffer power. Indeed, soil sorption and desorption of P arehighly time-dependent processes. P-buffer power increaseswith time (Morel, 2002). In this work we choose to use theFreundlich isotherm after 1 day of contact between soil andsolution. This choice may explain the underestimation ofuptake for P0 at last sampling date.

For P0, root biomass was correctly simulated whereas shootbiomass was eventually underestimated (Fig. 4). This underes-timation of shoot biomass could be due to an over prediction ofthe specific leaf area SLA eventually visible at the last samplingdate (Fig. 5). Indeed, when the actual P-uptake is less thanrequired (Ss < Ssr), the way chosen to describe the influence ofthis situation on SLA (Eq. (19)) is important. Other simulationsthan that proposed here showed significant modifications of

the biomass partition between shoot and root.

Another way to improve the model could be to take intoaccount a root demand for biomass. Including a root biomassdemand in the model depending on root potential growth as

2 1 0 ( 2 0 0 8 ) 453–464

proposed by Thaler and Pages (1998) would lead to a morerealistic biomass partitioned between shoot and root.

7. Conclusions

The proposed model correctly simulated the crop develop-ment and growth under non-limiting P-conditions. The cropgrowth processes, which were affected in the low P-treatment,were also correctly simulated. Nevertheless, for the low P-treatment, the P-uptake was correctly predicted until 43 dayafter plant emergence (259 ◦Cd) and underestimated 50 dayafter plant emergence (336 ◦Cd). In order to clarify this under-estimation of cumulative P-uptake in low P treatment, moredetailed accurate simultaneous measurements of root mor-phology and distribution together with crop growth andP-uptake should be carried out. Despite these discrepancies,the model appears to be an appropriate basis for develop-ing P-fertilization strategies based on soil properties, croprequirements for P and other environmental conditions. How-ever, ongoing testing with detailed data for P-uptake and cropgrowth acquired under well-documented site conditions isnecessary to establish the domain of validity of the model.

Acknowledgements

The authors are grateful to S. Thunot, C. Barbot and S. Niol-let for their excellent technical assistance during the study.We also thank A. Vives and E. Martin for help with chemi-cal analysis. The department Environment and Agronomy ofthe Institut National de la Recherche Agronomique (INRA) pro-vided financial support for this study.

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