Impact of contrasted maize root traits at flowering on water stress tolerance – A simulation study

Impact

of

contrasted

maize

root

traits

at

fl

owering

on

water

stress

tolerance

–

A

simulation

study

Daniel

Leitner

a,1

,

Félicien

Meunier

b,1

,

Gernot

Bodner

c

,

Mathieu

Javaux

b,d,

*

,

Andrea

Schnepf

d

a

ComputationalScienceCenter,UniversityofVienna,Austria

b_{EarthandLifeInstitute,EnvironmentalSciences,UniversitécatholiquedeLouvain,Louvain-la-Neuve,Belgium} c_{DivisionofAgronomy,BOKU-UniversityofNaturalResourcesandLifeSciences,Vienna,Austria}

d

ForschungszentrumJülichGmbH,Agrosphere(IBG-3),Jülich,Germany

ARTICLE INFO Articlehistory:

Received14February2014 Receivedinrevisedform8May2014 Accepted11May2014

Availableonline10June2014

ABSTRACT

Waterstressisamongthedominantyieldlimitingfactorsinglobalcropproduction.Betterdrought resistanceisthereforeakeychallengeforbreedingandcropmanagement.Avoidanceofwaterstressby effectiveroot wateruptakeis consideredapromisingapproachtoyieldstabilityinwaterlimiting environments.Wateruptakeefficiencyistheresultofmultipleplantroottraitsthatdynamicallyinteract withsitehydrology.Rootmodelsarethereforeanessentialtooltoidentifykeyroottraitsforwater efficientcropsinacertaintargetcroppingenvironment.

ã2014TheAuthors.PublishedbyElsevierB.V. ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/3.0/).

Wepresentanovelcombinationofadynamicrootarchitecture model(RootBox)withafunctionalmodelofrootxylemhydraulic propertiesandsoilwaterflow(R-SWMS).Thismodelintegrates structural and functional root traits to simulate water uptake undervariablehydrologicalconditions.Applicationofthemodelis exempli_fied for three different maize root phenotypes. We evaluatetheroleofrootarchitecturalandfunctionaltraitstodeal withwater stress at theflowering stage under two contrasted hydrologicalconditions(deepwaterstoragevs.moistupperprofile layerinsiltloam)fora7-dayperiod.Thephenotypesincludea referencephenotype(P1),onephenotypewithsteepermainroots (P2),andonewithsteepmainrootsandwithlongerlateralroots (P3)Weshowedthatgenerallythosephenotypeswhoserootaxes allocationmatchedwithavailablewaterdistributionwereableto transpiremore.Thissynchronizationisaresultofrootarchitecture (structuralroottraits).Thetemporaldynamicsofwaterdepletion onthe contrary were essentially determinedby root hydraulic properties.Weshowedthatlowerequivalentrootconductanceis essentiallyrelatedtoawatersavingbehaviouroftheplant,while highrootconductancecontributestoawaterspendingtypewith highinitialtranspirationthat decreasesquickly overtime.).We alsoshowedthedramaticimportanceofroothydraulicproperty

distribution, and their relation to root order and root age, in determining equivalent root conductance and water uptake behaviour.Inoursimulations,increasingtheradialconductivity of lateral roots by a factor 10 had more impact in the total transpiration than having different root architecture traits. It emphasizes the importance to consider not only architectural traitsbutalsohydraulicpropertiesindefiningideotypesandtouse quantitativemethodstobuildandtestthem.

Our results confirmedthat functional-structuralrootmodels areappropriate tobetterunderstandtheroleof rootsinwhole plant adaptation to different drought scenarios and their contribution to distinct drought response types. The newly developedmodelcontainsallbasiccomponentstofurtherrefine complexrootprocessessuchasarchitecturalplasticity,dynamic rootconductance(xylemvulnerability,compositeradialtransport) androotexudation.Theseresultscouldfeedintocroppingsystem modelstoseetheeffectoftheseprocessesoncropyield.

1.Introduction

Cropproductionmustdoubleby2050tokeeppacewithglobal populationgrowth(Passioura,1977;OECD/FAO,2012).Extension of cultivated land and further management intensification is limitedbygrowingenvironmentalconcernsandincreasingcostsof productionfactors.Newwaystofoodsecuritythereforerequirea moreefficientresourceuse(Rockströmetal.,2007;Razaet al., 2012), particularlyinwater-limitedenvironmentsthatmake up 45% of global land (Safriel et al., 2005). The improvement of

* Correspondingauthorat:EarthandLifeInstitute-Environmentalsciences,Croix duSud,2,L7.05.02,Louvain-la-Neuve,Belgium.Tel.:+3210473708.

E-mailaddress:[email protected](M.Javaux).

1

Theseauthorscontributedequallytothiswork.

http://dx.doi.org/10.1016/j.fcr.2014.05.009

0378-4290/ã2014TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/3.0/). ContentslistsavailableatScienceDirect

Field

Crops

Research

croppingsystemsbytargetingplant-soilinteractionsisalargely unexploitedfieldofagriculturalmanagement(Sposito,2013).In this context the root system is the key plant organ for more efficient use of available resources (Lynch, 2007), particularly understressconditions (Waines and Ehdaie,2007).Cropshave increasingcompetitiveadvantagefromoptimizedrootsystemsin resource limited environments due to improved water and nutrient uptake efficiency(Lynch,2007; Hinsingeret al., 2011; SmithanddeSmet,2012).

Historic advance in breeding has largely optimized the abovegroundstatureofcropplantsaswellastheirradiationuse (Arausetal.,2008).Itisrecognizedthatsuperiorrootwateruptake canbeacrucialtraitexplainingsuperioryieldofdroughtresistant cultivars, e.g. contributing to (flag) leave duration, optimum pollinationandgrainfilling(e.g.Borrelletal.,2001).Withinthis framework,Blum(2009)pointstowateruptakemaximizationasa focusforbreedingbecauseofitsgeneralcompatibilitywithhigh yield.Takingintoaccounttheexistingvariabilityinroottraitsin differentcrops(e.g.chickpea, Kashiwagiet al.,2005;rice, Kato etal., 2006; durumwheat,Nakhforoosh et al.,2014), it canbe expected that improvement of root water uptake is a feasible agronomicoption.Manschadietal.(2008)demonstrateddiversity ofwheatseedlingrootarchitecture.Basedonfieldevidenceand simulationsstudiesusingAPSIM,theysuggestedthatselectionfor growthangle and number of seminal roots may help identify genotypeswitharootsystemthat isbetteradaptedtodrought conditions.Usinga modeltoexplainhistoric yieldtrendsin US maize, Hammer et al. (2009) found that changes in root architectureassociatedwithhigherwateruptaketobethemain reason for better abiotic stress tolerance. Using APSIM-Wheat

LilleyandKirkegaard(2011)showedthatinsimulationsacross109 years, 5 soils, 6 management options and 6 combinations of (virtual)wheatrootmodificationsofrootsystemtraitscouldresult inmoreyieldgainindrylandcroppingregions.Theroottraitsthat weremodifiedwererateofdownwardrootpenetration,efficiency ofwaterextractionfromthesubsoil,anAPSIMparameterforthe effectsofrootlengthdensity,soildiffusivityandroot-soilcontact ontherateofwaterextraction.Forsystematiccropimprovementit is therefore imperative to understand which root architecture wouldbestcontributetomaximizewateracquisitionunderthe prevalentdroughtstressconditions.Thus,differentauthorshave discussedtheoptimalrootarchitecturetraitsneededtoimprove plantdroughttolerance (Lobetet al.,2014).For rain-fedwheat production with high importance of stored subsoil moisture,

Wassonet al.(2012) showedthat maximumrootingdepthand shiftingofrootingdensitytodeeperlayersweremostrelevantroot traitsforyield.Vadezetal.(2008)ontheotherhanddidnotfinda strongcorrelationbetweenrootlengthdensity distributionand wateruptakeforgroundnutinabreedingprogrammeforatropical residualmoistureenvironment.Theysuggestedtoconsiderroot functionalityviawateruptakeandtoonlysubsequently charac-terizerootmorphological differencesbetweengenotypes.Some authorsdefinedroottraitsofapparentlybroadrelevanceforbetter crop growth under drought stress, such as steep, deep and metabolicallycheaproots(Lynch,2013)orrootsystemswithfine rootdominance(Comasetal.,2013).Rootplasticityitselfhasbeen proposedasabeneficialtraitespeciallywhentherearetrade-offs betweendifferenttraits(Zhangetal.,2011;Trachseletal.,2013). Beyond the architecture itself, different authors have also investigatedthequestionofideal axialandradial conductance in roots. In simulation studies, the ratio between axial and radial conductivity proofed useful for classification, since this numberdeterminesifrootuptakeisuniformly,orpreferentially from topsoil (Doussan et al., 2006; Levin et al., 2007; Draye et al., 2010). Richards and Passioura (1989) showed that reducedaxialconductanceofseminalrootsallowswatersaving

during vegetativegrowth and help alleviate stress during the generativestage ofyieldformation.Other distributionsof root hydraulic propertiesthatfavour wateruptakeare greateraxial andradialconductivitiesin deeprootsin ordertoincreasethe uptake and transport capacity of water from deep soil layers (according to Wasson et al., 2012) and, decrease of axial conductanceinordertosavewaterfortheendofthecropcycle (accordingtoComasetal.,2013).Drayeetal.(2010)pointedout theimportanceoftheroothydraulicarchitectureforrootwater uptake, i.e. the combination of the architecture and of the distribution of the root hydraulic properties between root segments. This implies that root contribution to drought adaptation will depend on how root hydraulic properties are connected and how these eventually affect critical water use trait(Vadez, 2014).

However,theabovecitedstudiesdemonstratedthatnotalways genotypeswithapparentlybetterrootingabilityprovidedbetter wateruptakeand/oryieldimprovement.Apreconditiontoobtain better water stress tolerance via the root system is a precise definitionofthetargettrait(s)foraclearlydefinedenvironment.In thissenserootsystemsdonotdifferfromwhat(Tardieu(2012)) statedforabioticstresstoleranceingeneral–anytraitcanconfer drought tolerance, just design the right drought scenario. In climateswherecropsdependonstoredsubsoilsoilwater,narrow growthangleandlargernumbersofseminalrootsarebeneficial,in climateswithregularin-seasonrainfall,lessnarrowgrowthangles withshallowerrootsystem providebetteradaptation. Seasonal drought during (late) reproductive growth is most effectively mitigated bydroughtescape(early maturity;e.g. Thomsonand Siddique,1997;Franciaetal.,2011)aswellaswatersavingduring the vegetative stages to improve generative water availability (MoriandInagaki,2012).RichardsandPassioura(1989) demon-stratedthatreducingseminalrootaxialconductionsconservedeep water resourcesfor grainfilling. However, thepreconditionfor successful water saving is an effective later uptake to avoid unutilizeddeepwaterafterharvest.Kirkegaardetal.(2007)and

LilleyandKirkegaard(2007)quantifiedthevalueofavailablesoil waterinthesubsoilforyield(i.e.additionalyieldpermillimetre subsoil water use) and showed that its efficiency depends on management strategies that defer water usefrom early in the seasontolateintheseasonsothatthecropuses subsoilwater during grainfilling. Strategies for optimizing agricultural water managementfirstofalldependonthesitespecifichydrology.Yield levelsinrain-fedcroppingsystemfromMediterraneanand semi-aridtropicalclimateslargelyrelyonstoredsoilwaterfrom off-seasonrainfalls(e.g.FrenchandSchultz,1984).Inthesecropping environmentspartofthelater (generative) developmentstages coincidewiththeonsetof thedryseason.Thus,stresssensitive processessuchasfloweringandgrainfillingarestronglyrelatedto theuseofpreviouslystoredsubsoilwater(Kirkegaardetal.,2007). In most crops water shortage during the reproductive stage, particularlywhenflowering,ismostdetrimentalforyield(Farooq etal.,2009).

Maizeisacropgrowinginawiderangeoftargetenvironments fromtemperatetotropicalclimates,butHeiseyandEdmeades (1999) estimated thatone-quarter of the global maize areais affectedbydroughtinanygivenyear.TollenaarandLee(2002)

demonstratedthatmainyieldgainsinmaizedidnotcomefrom higheryieldpotentialorheterosisperse,butmainlyfrombetter stresstolerance.IthasbeenshownthatMaizeismostsusceptible tostressatflowering.Shaw(1977)showedthatstressintheperiod fromabout7daysbeforeto15daysafteranthesisreducesmaize grainyieldtwotothreetimesmorethanatothergrowthstages. Indeed drought stress during this period increases the period betweenmaleandfemaleflowering,wideningtheanthesis-silking interval(ASI)(Camposetal.,2004).Yieldunderstresshasbeen

showed to bestrongly dependent tokernel number per plant, barrenness and ASI in tropical Maize (Bolanos and Edmeades, 1996). Our assumption in this simulation study is that stress occurringduringthisperiodwillhaveamajorimpactonthefinal grainyield.

Facingthiscomplexroottrait–targetenvironmentinteraction andtheinherentadaptiveplasticityofrootsystems,Drayeetal. (2010)suggestedtodevelopin-silicoexperimentstotesthowroot traits may increase drought stress tolerance. To be able to investigate the impact of root architecture on water stress tolerance, models with root growth, soil and root water flow andwateruptakemodulesarethusrequired.Themost sophisti-catedapproachistodescribewatermovementinsoilandroots simultaneously,consideringthe3-dimensionalrootarchitecture, heterogeneouswaterdistributionintherootingzoneandwater potential gradientsbetweensoil androots (Javaux etal.,2011). Rootwateruptakeisthendrivenbythewaterpotentialgradients betweenrootsurfaceandsoil.

Theobjectiveofthisstudyistouseamathematicalmodelto quantitativelycomparehowcontrastingrootsystemsofZeamays affectrootwateruptakepatternandsoilwaterdynamics.Wefocus onthefloweringperiodbycomparinghowthreetypesofmaize root architecture (called phenotypes) with different traits will sufferfromstressundercontrastedwaterconditionsinasiltloam: (a)whenmostof thewater islocatedat thetopof theprofile (SWtop)and (b) whenthe watercontentis increasedin depth (SWbot). A reference phenotype (P1) is compared with two contrasted root system architectures having the same volume (proxyoftheamountofinvestedcarbon):asecondtype(P2)with steepermainrootsandathirdone(P3)basedonP2withlonger lateralroots.

2.Materialandmethods

Inthefollowingweoutlinethemathematicalmodelindetail, includingallparametersandunits.Forthenumerical implemen-tation of the model we refer to the corresponding software packagesthatwe haveused,R-SWMS (Javaux etal., 2008)and RootBox(Leitneretal.,2010a).

2.1.Rootarchitecturemodelling

Foreachroot,weconsiderthreezones:thebasalzonelbatthe

baseoftheroot,thebranchingzone,andtheapicalzonelaatthe

end of theroot (Fig.1).After thebasal and apical zoneshave developedtheirlengthsstayconstantduringrootgrowth,while thebranchingzonedevelops.Newlateralrootsareonlycreated withinthebranchingzonewiththeinter-spacesln.

FollowingPagèsetal.(1989)therootlength

l

,isdependentof therootage

t

by

l

ð

t

Þ¼k1expð_kr

t

Þ; (1) wherek is themaximalrootlength,andr istheinitialgrowth speed.Themaximalrootlengthiscalculatedforeachindividual rootby

k_¼lbþlaþlnðnob1Þ; (2)

wherenobisthemaximalnumberoflateralbranches.Newlateral rootsareinitiatedwithaninsertionangle

g

whichdescribesthe anglebetweentheparentrootandtheinitialdirectionofthenew lateralroot.Eachroothasaconstantradiusa.

Therefore,wedescribeeachroottypeinaspecificsoilbyseven parameters:la[L],lb[L],ln[L],nob[1],r[LT1],

g

[1]anda[L].Toadd

randomness to this deterministic approach each parameter is givenbyitsmeanvalueanditsstandarddeviation.

Additionally,wedescriberandomchangesindirectionduring roottipelongation byrandomly choosing two angles(Fig. 2). First, we choosetheangle

a

,whichdescribestheanglebetweencurrentand newroottipheadingbyarotationaroundthelocalaxis(hy).The

Fig. 1.RootgrowthparametersoftheRootBoxmodel.Eachrootorderorroottypeis describedbythelengthoftheapicalzonela,basalzonelb,inter-rootdistanceln,

branchingangleu,rootradiusa,and(notvisualized)themaximalnumberof branchesnob,androotelongationrater.

Fig.2.Changeofroottipheadingduetotworandomanglesaandb.hx,hyandhz

aretheaxesofthelocalcoordinatesystemofarootsegment,wherehxpointsinto

angle

a

isarandomnumberandnormallydistributedwithamean of0andastandarddeviationof

s

perrootlength.Thus,theexpected angularchangeinroottipheadingperunitlengthis

s

.Second,we choosetheradialangle

b

uniformlydistributedbetween0and2

p

, whichrotatestheroottipheadingaroundthelocalaxis(hx).

To describerootgrowth towardsa preferentialdirection(i.e. tropisms),werandomlycalculateNpairsofangles(

a

,

b

)andthen choosethemostsuitablepairregardingtoanobjectivefunction.N

isthenumberoftrialstofindoptimalvaluesfor

a

and

b

,thelarger

N,themorelikelytherootwillgrowinthepreferreddirection.The objective function is dependent on the type of tropism: for gravitropism headings into the z-direction are favoured, for exotropismheadingsintotheinitialdirection,andfor hydrotro-pismheadingstowardshigherwatercontent.Therefore,tropismis modelledbythreeparametersforeachroottype:

s

[L1],N[1],and

type[1].

Themainrootaxesofthemaizeplantcanbeimplementedas crownorbracerootsthatstarttogrowafterpredefinedtimesand predefined depths. The parameters for the initiation times are calledt0,1–t0,M, and the predefined depths are givenby the

z-coordinatesz1–zM,whereMisthemaximalnumberofmainroot

axes.Therootaxesareinitiatedatapredefinedangle

u

0.

We used the L-System implementation of RootBox (Leitner etal.,2010b)tosimulatetherootgrowthmodelinMatlab.The dynamicgrowthofrootsystemswassimulateduntilrootsystems reacheda givenvolume.Thoserootsystemswerethenusedas inputforsimulatingsoilandrootwaterflow.

2.2.Rootwateruptakeandsoilwater_flowmodelling

To describewater uptake bythe rootsystem we followthe approachofJavauxetal.(2008),whocombinedthemodelofwater movementinsoilofSommaetal.(1998)withthemodeldescribing water flow inside a rootbranching structure of Doussan et al. (1998).Inplants,itiscommontoexpresswaterpotentialasenergy perunitvolume(yieldingpressureunits)whileitiscommonto describethestatusofwaterinsoilsasenergyperunitweight(head units).Formodelcoupling,wechosetoconsistentlyexpresswater potentialinbothsystemsonavolumebasis.

2.2.1.Modellingsoilwaterflow

Water movementin thesoil is calculated withtheRichards equation:

@u

@

t ¼r K

r

gðr

c

m

r

gezÞ S; (3)

where

u

:¼

u

(t,x)isthevolumetricwatercontent[L3_L3_],tistime

[T], x is the spatial coordinate [L], K:¼K(

u

) is the hydraulic conductivitytensor[LT1_],

_cm

_:¼

_cm

_{ðt;xÞisthematricpotential}

[ML1_T2_],

_r

_isthe

fluiddensity[ML3_{],gisthegravitational}

acceleration[LT2_],e

zistheunitvectorpointinginz-direction[1],

and S:¼Sðt;x;

c

Þis a volumetric sinkterm representingwater depletionduetorootwateruptakepervolumeofsoil[L3L3T1]. Atthetopand the bottomof thedomainwechoosea no-flux boundarycondition.Atthesides,weassumeperiodicboundary conditions. As initial condition, we predefine a water content distribution

u

0(x):¼

u

(0,x).

ThesolutionfortheRichardsequationEq.(3)isbasedonthe SWMS_3Dalgorithm(Šimu

neketal., 1995).Thefinitemeshforsoil ismadeofcubicvoxelswhichareautomaticallysubdividedinto6 tetrahedralelements.AGalerkinfiniteelementapproachisapplied thatusestetrahedralelementsfor itsspatialdiscretization.The timecomponentisincorporatedusinganimplicitbackward_finite differencemethod.Asolverbasedonaconjugategradientmethod isintegratedandthesolution

c

m(x,t)isobtainedfromaPicard

iterative numerical scheme. Additional measures are taken to

improve solution efficiency in transient problems, including automatictimestepadjustment.

Eq. (3) togetherwiththeinitialconditionand theboundary conditionsallowustosimulatesoilwaterflow,ifthevolumetric sink term S is known. In the following, we describe how we calculatethesinktermS,takingthesoilwaterpotential,aswellas the water potential distribution inside the root system into account.

2.2.2.Waterpotentialdistributionwithinthexylemnetwork

Wedescribetherootwaterpressure

cp

ðt;

z

Þinthexylemtubes, where

z

isthearclengthofthecentrelineofasinglerootsegment with

z

=0 at the base of each root segment. For each

z

, the corresponding position in Cartesian space is given by its parameterisation xroot(

z

) .For a singleroot segment,we adapt

theequationfortheaxialxylemwaterflowJa(Javauxetal.,2008,

Eq. (2b)): Ja¼Ka

@c

p

@z

r

gj

@

xroot

@z

jz ! ; (4)

whereJa:¼Jaðt;

z

Þdescribestherateofaxialxylemwaterflow[L3

T1_{], K}

a is the axial root hydraulic conductance [M1 L5 T],

cp

:¼

cp

ðt;

z

Þisthepressurepotentialintherootxylem[ML1

T2_],where

_z

_{isthedistancefromtherootbase[L],andj}

_@

_x

root=

@z

jz

istheabsolutevalueofthez-componentoftheunittangentvector atposition

z

[1].Thetotalwaterpotentialinthexylem(neglecting theosmoticpotential)is

c

total:¼

cp

r

g.

FollowingLandsbergandFowkes(1978)theradialwaterflux, whichentersradiallyintorootsegmentsisdescribedby

qr¼2

p

akrð

c

m

c

pÞ; (5)

whereqr:¼qr(t,

z

)istherateofwaterflowintotherootperroot

length[L3_L1_T1_],a:¼að

_z

_{Þistherootradius[L],k}

r istheroot

radialhydraulicconductivity[M1_L2_T],and

_c

m:¼

c

mðt;xrootð

z

ÞÞis

thematricpotentialatthesoilrootinterface[ML1T2]. Whennowaterstorageisconsidered,theconservationofwater withintherootyields

@

@z

Ja¼qr: (6)

This 1-dimensional partial differential equation describes the waterpotentialinasinglerootsectionindependenceonthesoil matricpotentialatthesoilrootinterface.

To describe the flux distribution in a root system we stitch together multiple 1-dimensional root sections. At the nodes between the sections (i.e. the branching points) we apply Kirchhoffs law stating that the water volume flowing into the nodeisequaltothewatervolumeflowingoutofthenode. The remainingboundariesarelocatedattherootcollar,andattheroot tips.Attherootcollarweapplyfluxboundaryconditionunder non-stressedconditions(Neumannboundarycondition,Ja,c=Tpot,

whereTpotisthepotentialtranspiration),changingtoafixedwater

pressure potential when stress appears (Dirichlet boundary condition,

c

total,c=1.5MPa). At the remaining boundaries we

apply a no-flux boundary condition. It results in a system of

nn=ns+1equations(nnandnsbeingrespectivelythenumberof

rootnodesandrootsegments),whichwritesinmatrixnotation (Doussanetal.,1998),

C

c

total¼Q; (7)

where C (dimensions npnp) is calledthe conductance matrix

whichcontainstheroothydraulicscharacteristics,Q(dimensions

np1)containsthetermsrelatedtosoiland

c

total(dimensions np1)istheunknownxylemwaterpressurevector(Doussanetal.,

under a sparse format to reduce memory consumption. A biconjugate gradient method is used to solve this asymmetric linearsystem(Press,1996).

2.2.3.Implementation

The coupling between soil and root and the root water uptake was implemented by Javaux et al. (2008) and the software is called R-SWMS. The sink term S is calculated by summing up the radial uptake qr of the root sections located

withina soil voxel V[L3_]. Sðt;VÞ¼_jV1_j

Z V

d

2ð

x

rootsðxÞÞqrðt;xÞdx; (8)

where jVj is the volume of V [L3],

x

rootsðxÞ is a characteristic

function,whichwedefinetobe0iftheCartesianpointxliesonthe centrelineoftherootsystem,andelse1,

d

2isthe2-dimensional

Diracdeltafunction[L2],andqr(t,x)isthevolumetricwaterflow

perrootlengthifxisontherootsystem,else0[L3_L1_T1_].

Forcouplingthewaterflowinbothsoiland rootsystem,an implicit iterative scheme is used. First the root water flow equationsgivenbyEq.(8)aresolvedgivenaninitialestimateof thepressureheaddistributioninthesoil.Thisgenerates afirst estimateofthexylempotential

c

totalandwaterflowdistribution

(Eqs.(4)and(5)).A3-dimensionalsinktermdistributioncanthus becalculatedfromEq.(8),whichallowsthenumericalsolutionof theRichards equation (Eq. (3)).Wesimultaneously solve these equationsforrootandsoilpressureheadusingfixpointiteration. NotethatsolvingEqs.(5)and(7) requirestheassessmentofthe soilwaterpotentialinthevicinityofeachrootnode

c

m,definedas

theaverageofthesoilwaterpotentialofthe8nodesofthecuboid aroundtherootnodeweightedbytheinversedistancebetween rootandsoilnodes.

2.3.Simulationscenarios

Rootwateruptakescenarioswererunfora7dayora10day periods (for thehigh Krs cases,see hereafter) under sinusoidal

potential transpiration conditions (daily Tpot=5.33mm),

corre-sponding totypicalMediterraneanclimatic conditionsin June–

July.Simulationscenarioswerebuiltfrom(i)threedifferentroot systemarchitectures(P1,P2,andP3),(ii)twodistinctvaluesfor root axial conductance and radial conductivities of the root segments (indicated by the subscripts R and H), and (iii) two hydrologicalsituations(SWtopandSWbot).Thisallowedstudying theinteractionsofrootsystempropertieswiththepedo-climatic environment.Giventhefactthattherootarchitectureparameters areassociatedwithrandomvariation(cf.>2.1),eachscenariowas runinfivereplicatesofrootarchitecture.Eachofthesereplicates sharethesameparametersetsbutdifferinthepreciselocationof eachrootsegment.Thusatotalnumberof60simulationswererun (3 root system architectures5 replicates2 root segment hydraulicproperties2soilmoistureconditions).

2.3.1.Rootarchitecture

Threedifferenttypesofrootarchitectureswereusedandare referredtoasphenotypesP1,P2andP3inthefollowingtext.We simulatedrootarchitecturesofapproximately60daysoldplants, correspondingtothefloweringstage,howeverensuringthatroot volumeswereequalbetweenphenotypes.Forsakeofsimplicity, wemodelled rootsystemsonlybased onfirst (mainroots)and secondary rootorders(laterals). Thefirst P1 is consideredasa standardphenotype.Thesecondone(P2)hadsteeperanddeeper principalroots(assuggestedbyLynch,2013),whileP3wascreated basedontherootsystemarchitectureofP2butwaschangedto haveanotherbeneficialtraitfordroughtresistance,i.e.fewerbut

Fig.3.(A)Architectureandagedistributionoftherootsegmentsforarealizationofeachphenotype(P1,P2andP3,respectively)andtheseparationlinefortheinitialwater content.(B)Agedependentrootradialconductivityandaxialconductanceofprimary(left)andlateralroots(right).InsubplotB,solidanddashedlinesstandforreferenceand increasedconductivities,respectively.

longerlateralrootsatdepth(Wassonetal.,2012).Fig.3ashows onerealisationofthearchitecturalmodelforeachphenotypeP1, P2andP3.

The 15 root systems (3 phenotypes5 replicates) were generatedusingtherootgrowthmodeldescribedinsection2.1

basedon theparameters presented at Table 1.The parameter-isationofP1correspondedtothestandardparametersetformaize accordingtoPagèsetal.(1989).Twoparametersofthemainroot axeswerechangedtoformtheparametersetdescribingP2:initial growthrateof themain axeswasincreasedwhiletheirgrowth anglewasdecreased.Themagnitudeoftheseparameterchanges was evaluated based on available data of the DROPS project (http://www.dropsproject.eu/), which screens maize genotypes foryield and rootsystem traits.Onehundred Maizegenotypes werescreenedinaeroponics(deDorlodot,2005)andtheextentof growthrateandinsertionanglewasestimatedfromimageanalysis (X.Draye,personalcommunication).

Table 2 summarizestheaveraged rootcharacteristicsof the threephenotypes.AsP2hasahigherinitialgrowthrateofmain axis,itsrootsystemisyoungerthanthatofP1whenitreachesthe samevolume.AsP3haslongerlateralswiththesamerootradius, thenumberofrootsissmallerinP3thaninP2.Inthis waywe simulatethesameamountofcarboninvestmentindifferentkinds ofrootarchitectures.Theireffectonsoilwaterdynamicsandroot wateruptakeduringoneweekwassimulatedandinthistimethe rootsystemwastakentobestatic.

When needed, the root length density was calculated by summinguptherootlengthper 5cm-deepsoilcompartments, consideringthesoilsurfaceof75cm15cm.

2.3.2.Roothydraulicproperties

In order to investigate the role of the plant root hydraulic propertiesonrootwateruptakeandstressonset,twocaseswere analysedforeachphenotype:areferencescenariowithhydraulic propertiessimilartoDoussanetal.(1998)andanotherscenario withincreasedrootradialconductivity.Theywillbereferredtoby

thesubscriptsRandH:forinstance,P3Hreferstophenotype3with

higherconductivityvalues.

Thelocalconductivityandconductanceoftherootsegmentfor thereferencescenarioaretakenfromDoussanetal.(1998)with modificationsaccordingtoCouvreuretal.(2012).Fig.3bshowsthe reference(Rscenario)radialconductivityandaxialconductanceof mainandlateralroots,respectivelyinfunctiontosegmentage.The H-scenario isbasedonthesamevalues excepttheradialconductivity ofthelaterals,whichisincreasedbyafactor10(dottedlineinFig.3b, rightsubplot)asthesesegmentsappeartobethemostresistivepart towatertransfer.Thisfactortenisintherangeofvariationsobserved inexperimentalstudies(Drayeetal.,2010).

Byconsideringarootsystemasanetworkofresistancesasinan electrical circuit, theplantrootequivalentconductance (Krs; cf.

Table2forvaluesofthethreephenotypes)canbeestimatedusing the Thevenin theorem (Couvreur et al., 2012). The actual transpiration rate [L3 _T1_{] of the plantcan then be defined as}

(Javauxetal.,2013)

Tact¼Krsð

c

L

c

t;eqÞ; (9)

where

c

Listhewaterpotentialattherootcollarand

ct

;eqisan

equivalent total soil water potential, which is defined as the effectivesoilwater potentialat thesoilroot-interface(Couvreur etal.,2012).Theequivalentrootsoilwaterpotentialisthemean soilwaterpotentialofsoil-rootinterfaces,weightedbytherelative localextractionrateoftherootsegmentsinahomogeneoussoil (seeEq.(17)inCouvreuretal.,2012).Itisaphysicallysoundwayto definearoot-sensedwaterpotentialinaheterogeneoussoil.The higher

ct

_;eqthelessenergyisrequiredtoextractwaterfromthe

soil.Fora givenamountofextractedwater(representedbythe cumulative transpiration),a plant witha higher (lessnegative)

ct

_;eq undergoes a less negative suction, and thus is in more

favourableconditionsofsurvivalorforextractingsoilwater. The evaluation ofphenotype performance is donebased on differentindicators:(i)theequivalentsoilwaterpotentialatthe soil-root interface, (ii) the instantaneous stress fraction being

Table1

Rootarchitecturalparametersforthephenotypes1–3.

Symbol(unit) Meaning Parameters

(primaryroot)

Parameters (secondaryroot)

la(cm) Lengthofapicalzone 18.1(P1),24.2(P2),21.3(P3) 10(P1),10(P2),100(P3)

lb(cm) Lengthofbasalzone 0.5(P1),0.5(P2),2(P3) 0

ln(cm) Lengthofbranchinter-space 0.5(P1),0.5(P2),2(P3) 1.2

nob() Maximalnumberofbranches 324(P1),432(P2),109(P3) 0

r(cmd1

) Initialrootelongation 2.94(P1),3.9(P2),3.55(P3) 0.75(P1),0.75(P2),1.5(P3)

g(rad) Insertionangle 1.4(P1),1.06(P2),1.06(P3) 1.5

a(cm) Rootradius 0.13 0.05

s(cm1

) Standarddeviationoftheroottipheading 0.1 0.1

N() Numberoftrials 2 2

Type() Tropismtype geotropism exotropism

P1:phenotype1,P2:phenotype2,P3:phenotype3.

Table2

Averagedrootstatistics.

Symbol(units) Meaning Meanvaluesa

L0(cm) Totalrootlength 6468(P1)6426(P2)7002(P3)

Lcomp(cm) Totalrootlengthbycompartment 5104(P1)4606(P2)4348(P3)(topb)

1364(P1)1820(P2)2654(P3)(bottom)

Lord(cm) Totalrootlengthbyorder 618(P1)664(P2)759(P3)(primary)

5850(P1)5762(P2)6243(P3)(secondary)

rVol() Relativevolumeoftherootsystem 1(P1)1.02(P2)1.01(P3)

Krs(cm3cm1d1) Equivalentconductanceoftherootsystem 0.06(P1r)0.062(P2r)0.051(P3r)

0.17(P1h)0.166(P2h)0.091(P3h)

Age(d) Ageatthebeginningofthesimulation 64(P1)60(P2)62(P3)

a

Referencesofthescenariosaregivenunderparentheses:P1,P2andP3referrespectivelytophenotype1,phenotype2andphenotype3.Subscriptrandhreferrespectively toreferenceandhighradialconductivityofthelaterals.

b

defined astheratiobetweenwateruptake(i.e.actual transpira-tion)andpotential transpiration,and (iii)thecumulativewater uptakeasanindicatorofthecarbonacquiredfortheperiod.

2.3.3.Soilhydraulicproperties

The soil was defined as a silt loam with soil hydraulic parametersfromCarselandParrish(1988)(seeTable3).Itswater retentioncurve,whichrelatesthesoilmatrichead h¼cm

rg

tothe volumetricsoilwater content

u

,and thefunctionalformof the hydraulicconductivitytensorK(h)areshowninFig.4.Theywere modelledusingthevanGenuchten–Mualemfunctions(Mualem, 1976;vanGenuchten,1980)usingsixparameters:saturatedwater content

u

s[L3L3],residualwatercontent

u

r[L3L3],thesaturated

hydraulicconductivityKsat[LT1]andtheparameters

a

vg[L1],nvg

[1],and

l

vg[1],whichdescribethecurvatureofthefunction. 2.3.4.Hydrologicalregimes

Toaccount fordifferentclimaticconditions ina verysimple way, we consider two possible conditions for the initialwater content

u

0(x).Inthefirstcase(calledSWbot),mostofthewateris

locatedatthebottomoftheprofile.Thishydrologicalconditionis representativeforsummerdryclimateswithhighimportanceof subsoilwater,e.g.aMediterraneanclimateoranoceanicclimate duringasummerdryspell.Theseparationbetweenthewetsoil (

c

m,bot=100hPa)andthedryone(

c

m,top=3000hPa)wassetat

the_firstthird of thesoildepth (42cm).In thesecondscenario (SWtop), the boundary is in the same location but the water contentishigherclosetothesoilsurface(

c

m,top=100hPaand

c

m,bot=3000hPa).Thissecondcasemimicsaclimaticsituation

withdominantroleofregularrainfallinputforplantwatersupply and low subsoil water reserves. Such conditions are found particularlyforclimateswithdominantin-seasonrainfallduring thevegetationperiod(e.g.semi-aridcontinentalclimatesinthe temperatezone),semi-aridtropicalconditionsbeforerefillingof deepsoilprofilelayersduringtherainyseasonandforirrigation duringadryseason.

3.Results

Wewillfirstpresenttheimpactofdifferenttypesofroottraits (phenotypes)usingthereferencehydraulicproperties,whileinthe secondpartwewillcomparetheimpactofincreasedrootradial conductivity.Forthesakeofclarity,thethreephenotypeswillbe associatedwithauniquecolourcodeinthesubsequentplots:P1 willbeinred,P2,ingreenandP3inblue.

3.1.Influenceofrootsystemarchitecture

Fig. 5 shows the distribution of the water content for the scenario SWbot after 6.5 days for one given replicate of each phenotype.VideoS1(supplementarymaterial)showsthe evolu-tion of the water contentdistribution for 7 days for the same scenario. We observe that the impact of the initial water distributionremainsvisibleoverthewholeperiod,andthatthe high hydraulic pressure gradient between the two soil layers generatesupwardwaterflux.Theeffectoftherootwateruptakeis also clearly visible, and we can distinguish through the water depletionpatternthemainfeaturesoftherootarchitecturesofthe threephenotypes.Inthevideos,theday–nightdynamicsisvisible throughtheredistributionofthewatercontentduringnight.

To investigate thedifferencebetweenphenotype behaviours better, we can lookat the transpirationdynamics of the three phenotypesunderthetwooppositehydrologicalregimes.InFig.6, theaveragedtranspirationofthefivereplicatesisshownforeach phenotypeandfortheSWbotcase(Fig.6a)andfortheSWtopcase (Fig. 6b). As standard deviations between replicates are small (alwayssmallerthan3%ofthemeanvalue),theyarenotshownon the plots. For all phenotypes and cases, a water stress (i.e. a decreaseoftheactualtranspirationascomparedtothepotential demand) is observed after the beginning of the first day of simulationanditsmagnitudeincreaseswithtime.

Ifwecomparebothscenarios,wecanseethatgenerallythese threephenotypestranspiremorewhentheupperlayeriswetter: allthephenotypestranspiremore than25mmafter7daysfor SWtop conditions (Fig. 6b), while none of them could reach 25mmforSWbot(Fig.6a).Whenwecomparethechangeoftotal transpirationbetweenSWbotandSWtop,weobservedifferences betweenphenotypes.For P3,thechangeofcumulative transpi-rationisverysmall(2mm),forP2ofabout5mmandforP1of about 8mm, demonstrating a different sensitivity to climatic conditions.

IntheSWbotscenario(Fig.6a),therankingbetweenthethree phenotypetranspirationratesevolveswithtime.WhileP1andP2 havethehighesttranspirationrateatthebeginningoftheperiod, transpirationofP3ishighestattheend.HereP1withasurface near root distribution undergoes a more severe stress and transpiration falls below the other phenotypes at the second day.Thephenotypeswithdeeperrootsystemallocationbehaved similar,withthephenotypeP3havingasimilarbehaviourbetween daysofthewholesimulationperiod.

Inthescenariowithwettertopsoillayer(SWtop,Fig.6b),itis observed that the two phenotypes P1 and P2 behave similarly whilethephenotypeP3suffersfromamoredrastictranspiration decrease.

Fig.7showsthechangeoftheequivalentsoilwaterpotential

ct

_;eq with increasing water extraction from soil between the

beginning and the end of the period, expressing the global moisturedeficitthatbuildsupattheroot–soilinterface.Logically, weseethat

ct

_;eqhasadecreasingtrendwithtimeandcumulated

uptake.Duringthenighthowever,

ct

;eqgetslessnegative,asthe

system relaxes: water potential gradients built up during day aroundtherootsegmentsdecreasesastheuptakeisreducedand soilwaterredistributionoccurs.

Fig.4.Waterretentionandhydraulicconductivitycurvesofthesoilusedforthe simulation.

Table3

ParametervaluesfortheMualem–VanGenuchtenmodel.

Symbol(unit) Meaning Parametervalues

Ksat(cmd1) Saturatedhydraulicconductivity 10.8

us(cm3cm3) Saturatedwatercontent 0.45

ur(cm3cm3) Residualwatercontent 0.067

avg(cm1) Shapeparameter 0.02

nvg() Shapeparameter 1.41

IntheSWbotcase(continuouslines),allphenotypesexperience alowersoilwaterpotential(andalowertotaltranspiration)than intheSWtopscenario.However,inSWbotthephenotypeP3is mostefficient,asittranspiresalmostthesameamountofwateras P2 and experiences higher (less negative) soil water potential. Thus,itcouldbeexpectedthatP3wouldbeabletosustainahigher transpirationcomparedtoP2overalongerperiodofstressasitcan accesswatermoreeasilyatdepth.Inthecasewherethewaterisin the upper layer (dashed lines), P1 has always a higher (less negative)total equivalentwater potential thanP2 and P3for a similar given amount of cumulated transpiration. As can be expected,thedeeprootedphenotypeP3(continuousblueline)not onlytranspiresless(i.e.experiencesamoreseverestress)butalso undergoes a lower (more negative) total equivalent water potential. However, as already observed for the transpiration

dynamics,P3hasarelativelysimilarbehaviour betweenSWbot andSWtopcases.

Fig.8aandbshowtheaveragedsinktermprofilesofthethree phenotypesattwodifferenttimes(t=0.5and6.5days)andunder variable hydrologicalconditions. Fig. 8d shows theroot length densityprofileofthethreephenotypes:P1hasmorerootsatthe top, P3 deeper rooting distribution and P2 an intermediate distribution. When the water is in the bottom layer (SWbot scenario,Fig.8a),allplantphenotypesdecreasetheirwateruptake in theupperlayer after6.5 dayswhile remainingstablein the bottomlayer(Fig.8a:dashedandcontinuouslinesoverlapinthe bottomlayer).Althoughthewatercontentintheupperlayerislow inthisscenario,thethreephenotypesareabletoextractitatthe beginning of theperiod, as theyhave a lot of roots there. The phenotype P3 has more ability to extract the soil water from

Fig.5.3-dimensionalvisualisationofsoilwatercontentasinfluencedbyreferencehydraulicarchitectureofthethreephenotypesafter6.5daysfortheSWtopscenario.See correspondingvideosinsupplementarymaterialS1andS2forreferenceandincreasedhydraulicproperties,respectively.

Fig.6. AverageactualandcumulativetranspirationofthethreephenotypesinSWbot(A)andSWtop(B)scenarios.Red:phenotype1;green:phenotype2andblue: phenotype3.Thepotentialtranspirationisrepresentedbytheblacksolidline.(Forinterpretationofthereferencestocolourinthisfigurelegend,thereaderisreferredtothe webversionofthisarticle.)

deeperlayerbelow80cmfromthebeginningoftheperiodon.On the opposite, phenotype P1 extracts soil water less deep and suffersfromstrongerstress(seeFig.7).

Whenwaterislocatedintheupperlayer,P1andP2areableto takeupmorewaterfromthathorizonascomparedtoP3(Fig.8b). AsP3cannotcompensatethisloweruptakeintheupperhorizon bya muchhigheruptakein thedrierbottomhorizon,itsuffers fromearlierstress.

Fig.8cshows thewater changes over thewholesimulation period for case SWbot (continuous lines) and SWtop (dashed lines). Although the sink terms are very different between phenotypes,thisisnotreflectedinthesoilwatercontentchanges. Indeedwatercontentchangesnotonlyinfunctionofthesinkterm

Sbutalsoduetothewaterpressuredistributioninthesoilwhich generatewaterflow.Thisisparticularlyclearneartheinterface betweenthewetanddryzones,wherewaterchangesoccurdueto waterandthusmatricpotentialdifferences.

Whenwecomparethesinktotherootlengthdensityprofiles (Fig. 8d), we hardly see any direct correspondences for any phenotypes.This is due tothe fact that water is preferentially extractedwherethewaterisavailable.Inaddition,therootlength densityprofileonlypartiallyreflectsthedistributionoftheroot

abilitytoextractwater.Thehydraulicarchitecturei.e.howtheroot abilitytoextractwaterisdistributedintothesoil,combinedwith thewateravailabilitycontroltheuptake(Javauxetal.,2013).

Tosummarize,weobservedthat(1)P1whichhasmorerootsin theupperlayerisveryefficientin theSWtopcase,buthaslow abilitytodealwitha drierupperlayer;(2)P3,whichhasmore deeperrootsoutperformsforSWbot;(3)P2transpiresasmuchas P1forSWtopandasmuchasP3forSWtop.However,itsequivalent soilwaterpotentialisalwaysmorenegativethanthetwoother phenotypes.

3.2.In_fluenceofroothydraulicproperties

Itwasshowninsection3.1thatrootarchitecturedetermines theextractionpattern.Inthissection,weinvestigatehowdistinct root hydraulic properties influence waterextraction and stress onset.Byincreasingtheradiallocalconductanceofthelaterals(H case) and comparing the performance of the 3 genotypes as compared to their initialconductance values (R case), we can assesstheimpactofthehydraulicpropertiesonrootwateruptake. The root equivalent conductance Krs (see Eq. (8)) is a key

parameterwhichcharacterizesthehydraulicarchitecture,i.e.the impactoftherootsystemarchitectureandofthedistributionof the root segment hydraulic properties. As the local hydraulic propertiesdependtotherootorder(mainorlateral)andtotheage oftherootsegments(seeTable2andFig.4d),eachphenotypehas adifferentKrs.ValuesofthemeanplantequivalentconductanceKrs

for the six cases are given in Table 2. Phenotypes P1 and P2 typically have a relatively similar Krs, as they have a similar

proportion of root segment age and order. We observe the following ranking: Krs(P3R)<Krs(P1R)<Krs(P2R)<Krs(P3H)<Krs

(P2H)<Krs(P1H).Multiplyingtheradialconductivityofthelaterals

by10increasestheKrsbyafactor2.8,2.7and1.8forP1,P2andP3,

respectively, as root segment age and order differ between phenotypes.

Thechangeofwatercontentisvisualizedinthesupplementary materialVideoS2forthehigherconductance(P1H,P2HandP3H)

and theSWBotscenario.Ascompared toP1R,P2RandP3R(see

VideoS1),theextractionpatternsarereinforced.Table4showsthe amount of transpiration after 7 days for the two hydrological regimes,thethreephenotypesandthetwoKrs.HigherKrsalways

increases the amount of extracted water. Under the SWtop

Fig. 7.Equivalent total soil water pressure as a function of the cumulative transpirationforSWbot(solidlines)andSWtop(dashedlines).Red:P1,green:P2 andblue:P3.(Forinterpretationofthereferencestocolourinthisfigurelegend,the readerisreferredtothewebversionofthisarticle.)

Fig.8.1-DsinktermprofileunderscenarioSWbot(A)andSWtop(B)after0.5(solidlines)and6.5(dashedlines)daysandcorrespondingwaterchanges(C)androotlength densities(D).Red:P1,green:P2andblue:P3.(Forinterpretationofthereferencestocolourinthisfigurelegend,thereaderisreferredtothewebversionofthisarticle.)

scenario, we do not observe any stress (100% of the Tpot is

extracted)forP1HandP2H,whileP3Hsuffersfromaslightstress.

For SWtop, the different root system architectures generate a actualtranspiration difference of 12% between phenotypes. By increasing the conductance of the laterals, there is almost no impactoftherootsystemarchitectureanymore.ForSWBot,stress stilloccursforallphenotypeswithhigherKrs.However,differences

betweenrootarchitecturegenerateonly5_–8%differenceofactual transpiration while a difference in Krs increases the actual

transpirationby20–30%.

In thefollowing,wefocusonthescenariowithpredominant subsoilwaterdependenceSWbot,andonthetworootphenotypes P2and P3 withadaptedrootdistribution forsuchhydrological conditions.

Fig.9comparesthetranspirationdynamicsofP2andP3with referenceandincreasedrootradialconductivities for a10days period. When the local radial conductivity of a plant root is increased, its capacity to extract water is improved (i.e. Krs

increases and roots pose less resistance to water uptake and movementinsidetherootsystem),andthustranspirationishigher foragivenpotentialdifferencebetweensoilandroot(seeEq.(9)). Weobservethattherankingofcumulativetranspirationover10 daysfollowstherankingoftheKrsexplainedherebefore.

WhilethetwophenotypesbehaverathersimilarintheSWbot scenario when the reference hydraulic properties are used (denotedaP2RandP3R),thereisa moredistinctdifferentiation

when considering an increased Krs (denoted as P2H and P3H).

Indeed,P2HissuperiorintranspirationcomparedtoP3Hoverthe

10daysofsimulation.StillP2Halsoshowsastrongerdecreasein

transpirationratecomparedtoP3H,whichwouldresultinhigher

stressoverprolongeddryperiods.Indeed,after10days,P3Hgetsa

higherdailytranspirationratethanP2H.Ingeneral,whateverits Krs,P3remainsmorestableoverthesimulationperiod,andalways

hasahighertranspirationratethanP2attheendofthesimulation period.

Fig.10givesanotherperspectiveonthecomparisonbetween both phenotypes. It shows the instantaneous stress fraction

(Tact/Tpot)asafunctionofthefractionofthewaterextractedfrom

thesoil(calledhereaftersoilwaterdepletionD)definedas:

D_ðt_Þ¼100

u

ini

u

ðtÞ

u

ini

u

r

(10) with

u

ini,

u

r,

u

ðtÞ,theinitial,residualandattimetwatercontent

ofthesoil,respectively.Theinstantaneousstressfractionreflects thereductionintranspirationandthus,thestomatalclosureata giventimet.Aplantwithhigherstressfractionkeepsitsstomata opensothatcarbonacquisitionisnotdecreasedandthussuffers less fromwater shortage.In Fig.10, weobservethat thewater depletionishigherforphenotypeswithhigherrootconductance

Krs.Wealsoseethatforagivenamountofextractedwater,thehigh Krsphenotypes (P2H and P3H) experience less stress. It clearly

illustrates that the water availability for plants is not only a questionofsoiltypebutalsoofrootconductance.P2Hforinstance

isabletoextractthepotentialtranspirationrateatthebeginningof theperiodwithoutreduction,duetoitshighKrs.Ifwecomparethis

withFig.9,weseethatP2Hisabletoextractmorewateroverfirst

partof thesimulation period and thus hasa strongertrend to depleteavailablewater.P3Honthecontraryhasasustainedwater

extraction over longer times. At the end of the periods P3 phenotypeshavealwayshighercumulatedwaterextractedwitha higherwaterpotentialthanP2phenotypes,i.e.abetterresistance toprolongeddroughtperiod.

Thiscorrespondstotwodifferentstrategiesfortheconsidered period:P2Htakesasmuchwateraspossibleatthebeginningbut

reducesmorestronglyitstranspirationstream,while P3Hhasa

moreconservativebehaviour,keepingaconstanttranspirationrate withtime.Notethatthereisnodifferenceinthewayhowstress onset is represented or parameterised betweenscenarios. This differenceisonlyduetoadifferentroothydraulicarchitecture,i.e. P2HhasahigherKrsthanP3Hwhichallowsmorewateruptakeat

thebeginningbutmorestressattheendofthesimulationtime.

4.Discussion

Agriculturehastoachieveamoreefficientuseofwatertocope withfutureneedsoffoodproductionandcompetitionbetween differentfreshwaterusers(Rockströmetal.,2007).Thiscanbe achieved by reducing losses via soil management change (e.g. mulchcoverage)andmoreefficientwateracquisitionbyimproved crops(e.g.Passioura,1977).Rootarchitectureandfunctioningare keycroptraitsinrain-fedcroppingsystemswhereyielddepends on optimum use of site-specific water availability during the growingseason.

Twomainchallengestobreedingforefficientrootsystemsso farare: (i)selection ofan appropriateroottargettrait, and (ii) ensuringthatthis traiteffectivelyconveysimprovedcropwater supply.Vadezetal.(2008)demonstratedthatstructural knowl-edgeofrootsystemsaloneisnotsufficienttounderstanddifferent wateruptakecapacityamongchickpeacultivars.Ourstudyclearly sustains thisempirical observation:although thereisa relation between the distribution of water availability and root axes allocationinthesoilprofile,rootfunctionalityasexpressedbyroot equivalentconductanceappearedaskeyvariabletoinfersuperior wateruptakeofagivenphenotype.Amainfindingofourstudyis that root length density distribution alone is not sufficient to describe root water uptake from soil. Root systems consist of dynamicpopulationsofrootsofdifferenttypesandage,withage dependent root axial conductances and radial conductivities (Draye et al., 2010).As in Doussanet al. (2006) our model is basedoncombiningrootarchitectural,rootsystemhydraulicand soilhydraulicpropertiesincludingthepossibilityofcompensation andredistribution.Inourstudy,thedifferenceinwateracquisition inducedbydifferentarchitecturalroottraits(the3phenotypes)

Fig.9.ActualandcumulativetranspirationchangeforP2withreference(light green,P2R)andincreased(darkgreen,P2H)rootradialconductivityandP3with

reference(lightblue,P3R)andincreased(darkblue,P3H)rootradialconductivityfor

the SWbotscenario. The black solid line is the potential transpiration. (For interpretationofthereferencestocolourinthisfigurelegend,thereaderisreferred tothewebversionofthisarticle.)

Table4

Cumulativetranspiration[mm]andpercentageofthetotalpotentialtranspiration effectivelytranspiredaftersevendaysforeachscenario.

P1 P2 P3

R H R H R H

SWtop 29.5/79.1 37.3/100 28.9/77.5 37.3/100 25.2/67.5 36/96.5 SWbot 21.9/58.7 32.5/87.1 23.8/63.8 34.6/92.7 23.3/62.5 29.7/79.6

wasmuchsmallerthantheincreaseinducedbyincreasingradial hydraulicconductivityoflateralrootsbyafactor10(Table4).This demonstrates that rootarchitectural traits strictosensu are not sufficienttoexplainwateruptakefromsoilbyplantroots,butroot architecture and related age distribution of root segments is important for overall conductance. This is in line with the conclusionsofVadez(2014).

Withinthedehydrationavoidancetype ofdroughtresistance strategies,Levit(1980) distinguishedbetweenwatersaversand waterspenders.Ourstudyshowedthatroottraitscanconferboth, watersavingandwaterspendingonashortperiod.TheP3root phenotypewasawatersaver.Concerningrootsystemarchitecture (distribution)P3hadcomparativelyhighestallocationofthesink todeeperlayersand comparativelyless sink strengthin upper layers(Fig.8).Wheneverupperlayerscontributedessentiallyto water supply, P3 thus had lowest transpiration.However with increasingdepletionP3couldsustainuptakefromdeeperpartsof theprofileoverlongertimes(Figs.9and10).Theprolongeduptake fromthedeeperlayerisrelatedtothelowersinkstrengthleading toalessintensedepletion.Theotherphenotypeshadamorewater spending behaviour with quick initial depletion and stronger decreaseoftranspirationovertime.Foroverallcropperformance the importance of high short term water extraction vs. low sustained uptake depends on the drought scenario. If only intermittent dry spells have to be buffered, a water spending depletionrootphenotypeismoreefficientassuchabehaviourwill keepstomatamoreopen.Incaseoflongerdryperiodshowevera rootphenotypeconferringwatersavingwillimprovecropwater supply. Here we do not consider potential competitive effects betweenplantwateruptakeandtranspirationlossesfromupper layers. Generally water saving is only effective for stored soil moistureindeeperlayersnotpronetoevaporationlosses.

Traditionally,wateruptakesimulationmainlyconsideredroot distribution,withmorerecentarchitecturemodelsgivingabetter insightintothe3Dstructureofrootsystems(Drayeetal.,2010). Morerecentlyafocuswasonintegratingrootfunctionality into architecture models. While some cropping system models like APSIM (Keating et al., 2003) used an empirical parameter for functionality,moremechanisticapproachesstrivetoconsiderroot hydraulicarchitectureassuch(e.g.Sperryetal.,1998).Ourresults showed that differentiation between phenotypes P2 and P3 became more evident when considering root conductance (Table 4). Under a high conductance scenario, P2 showed a substantialincreaseininitialwateruptakewithvaluesnearthe potential transpiration, followed bya quickdecrease. Thus the waterspendingbehaviourwasaccentuated.ForP3therewasalso an increase in the transpiration level, still the extent was less comparedtoP2and thisrootingphenotypemaintainedamore

stable transpirationlevel evenathigher roothydraulic conduc-tance.ThestrongerdifferentiationbetweenP2andP3inthehigh conductancescenariowasduetotheagedependenceofthisroot functionaltrait.AsP3containedyoungerrootsegmentsindeeper layerswithstillloweraxialconductance,thebulkincreaseinroot conductance(Krscf.Table2)islessimportant.Thisisinlinewith

the findings on the role of root conductance for transpiration resumedbyComasetal.(2013)whostatedthatgenerallyhighly conductivelargediameterxylemvesselsarerelatedtohighlevels of(unstressed)transpiration,whilelowerdiametervesselsinduce watersaving.

ThedifferentiationbetweenP2andP3atthehighconductance scenario also indicates that still there was significant uptake capacity from the upper soil compartment. The substantially higherinitialtranspirationofP2wasmainlyaresultofenhanced uptakeforupperlayer.Asrevealedbythesinkdistribution(Fig.8), thehigherrootlengthdensityintheuppercompartmentresulted insubstantialproportionofwaterextractedfortheupperpartof theprofileparticularlyduringthefirstdays.Thesinkdistribution revealsthatwiththeadvanceofdepletionovertime,upperlayer extractionwasincreasinglysourcelimited,whiletowardslower layerssinkstrengthwaslimitedbythelowerrootingdensity,i.e.it wasmoresinklimited.Thesinkstrengthintheupper compart-ment was further increased in the highconductance scenario, leadingtoanefficientandquickexploitationofextractablewater resources(notshown).Inthelowerlayerssinkstrengthwasnot only limited by root distribution but further decreased in proportiontotheupperlayerbythelowerconductanceofyoung segments. Following Fitter's terminology (Fitter, 2002), root system architecture thus determines the overall exploration capacityofthesoilprofileviasynchronizationofwateravailability anddepthdistributionofrootsegments(source-sink synchroni-zation), while rootfunctionality (partiallyreflected in theroot equivalent conductance) defines its capacity to exploit the availablewater,supportingthespendingvs.savingbehaviour.

In ordertosustainyield underdrought conditions,breeders needtoblendtogetherallknowledgeondroughttolerance-related traitsandtheirphenotypicexpression(Cattivellietal.,2008).It remainsdifficulttoassesstheoveralleffectoftraitscontributingto droughttolerance,becauseseveraltraitscanplayroles,andthese traits are likely to interact with one another and with the environment.

5.Conclusions

Wesimulatedtwocontrastinghydraulicregimestoanalysethe performanceofrootphenotypeswithsurfacenearrootallocation (P1) vs. steeper rootallocation (P2 and P3), where P2 and P3

Fig.10.Reductionoftheactualtopotentialtranspirationratioforatendayslongsimulationasafunctionofthesoilwaterdepletioninthesoil(in%).BluelinesareforP3and greenlinesforP2.Darkcoloursstandforrootsystemswithanincreasedradialconductivityandlightcoloursforreferencelateralconductivities,botharefortheSWtop scenario.Theinitialclassificationoftherootsystemsisdeterminedbythevalueoftherootequivalentconductance(recalledontheright).(Forinterpretationofthereferences tocolourinthisfigurelegend,thereaderisreferredtothewebversionofthisarticle.)

correspondtodeepandsteepphenotypeswithhighlateralgrowth forP3.Asexpected,superiorityofa givenrootarchitecturewas dependentonthewaterregime.Forthesoilconditionsusedhere, our simulations showed that a deep and steep phenotype is beneficialonlyinsituationswherecropwatersupplydependson subsoilmoisturewhile surface-near allocation ofroots is more preferentialwhencropscanrelyonhighin-seasonrainfall.This correspondstofindingsfromvegetationecologyandecohydrology (e.g.SchenkandJackson,2002;Pretietal.,2010).

Although the root systems of the three virtual phenotypes consideredinthisstudyhavethesamevolume,theybehavequite differentlyintermsofwateruptakefromsoil.

In general, the same amount of carbon spent can create different root system architectures with different hydraulic propertiesthatwillaffectoverallwateruptakebehaviour.

Inparticular,therootlengthdensityprofileisnotsufficientto characterizerootsystemwateruptakeefficiency.Inthissimulation casestudywekepttheoverallamountofcarbonspentconstant andcomparedtheeffectwhenthecarbonwasspentintomoreor less deep and steep root system architectures. However, this resultsinthefactthatwedidnotmodelthecheapaspectofthe ideotypeofLynch(2013),whichcouldalsoaffecttheconclusionsof thisstudyregardingrootsystemwateruptakeefficiency.

Regardingthehydrologicalconditions,phenotypeP3thathad fewer andlonger lateralswas better in asituationthat can be found in climateswithadrysummerandhighimportanceofsubsoilwater:it hasamoreconservativebehaviouronalongerterm.Forplantswith comparablerootingdepth,theoverallrootsystemconductanceKrsis

akeyparametertoexplaintranspirationdynamics.

Theplantrootsystemswecreatedweregeneric,althoughthe variabilityofparameterswaschosenincorrespondencewiththe genotypicvariationsofmaizerootsystemsanalysedintheDROPS projectfordroughttolerantyieldingplants.Wedemonstratedhow rootarchitecture and hydraulicproperties can inducedifferent behaviour,alsoasafunctionoftheenvironmentconsidered,and thusoneshouldbecarefulwhiledesigninganideotypebasedon rootarchitecturaltraitsalone.Beyondtherootarchitectureitself, theagedistributionandrelatedroothydraulicpropertiesneedto be considered. These results could feed into cropping system modelstoseetheeffectoftheseprocessesoncropyield.

Acknowledgments

This work is a contribution of the Transregio Collaborative Research Center 32, Patterns in Soil–Vegetation–Atmosphere Systems:Monitoring,ModellingandDataAssimilation,whichis fundedbytheGermanResearchAssociation,DFG.Thisworkhas alsobeenfundedinpartbytheprojectDROPS(DROughttolerant yielding PlantS: http://www.drops-project.eu), which received funding from the European Communitys Seventh Framework Programmeunderthegrantagreementno.FP7-244374.F.M.is supported by the Fonds National de la Recherche Scientifique (FNRS)ofBelgiumasaresearchfellow.D.L.isrecipientofanAPART

– fellowship of the Austrian Academy of Sciences at the Computational Science Center. We acknowledge the Austrian ScienceFund(FWF)throughgrantno.V220–N13(A.S.).

AppendixA.Supplementarydata

Supplementarydataassociatedwiththisarticlecanbefound,in theonlineversion,athttp://dx.doi.org/10.1016/j.fcr.2014.05.009.

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