Abstract We have developed a spatially explicit

model of plant root and soil bacteria interactions in

the rhizosphere in order to formalise and study the

microbial loop hypothesis that postulates that

plants can stimulate the release of mineral N from

the soil organic matter by providing low molecular

weight C molecules to C-limited microorganisms

able to liberate into the soil enzymes that degrade

the organic matter. The model is based on a

mechanistic description of diffusion of solutes in

the soil, nutrient uptake by plants, bacterial

activity and bacterial predation. Modelled soil

bacterial populations grow, mediate transforma-

tions among several forms of nitrogen (mineral

and organic) and compete for nitrogen with plants.

Our objectives were to see if we could simulate the

stimulation of turnover of the microbial loop by

exudates and to study the effects of diffusion of C

and N in the rhizosphere on these different pro-

cesses. The model qualitatively mimics most of the

characteristics of the microbial loop hypothesis. In

particular, (1) plant exudates increase the growth

of bacteria in the soil and (2) increase the degra-

dation of soil organic matter and N mineralisation.

(3) The increased bacterial biomass induces an

increase in predator biomass and, as a result, (4)

plant mineral N uptake is increased threefold

compared with scenarios without exudation.

However, the temporal dynamics simulated by the

model are much slower than observed dynamics

(the increase in uptake appears after a few

months). Taking into consideration the diffusion

of C and N containing molecules in soil has large

effects on the spatial structure of the bacterial and

predator biomass. However, the average biomass

of bacteria and predators, N mineralisation and

plant N uptake were not affected by these prop-

erties. The model provides a quantitative and

mechanistic explanation of how plants could ben-

efit from liberating low molecular organic matter

and the subsequent stimulation of the microbial

loop and increases N mineralisation.

Keywords Plant–bacteria interactions ÆExudates Æ Microbial loop hypothesis Æ Barber–

Cushman model Æ Competition Æ Mutualism ÆNitrogen Æ Carbon

Introduction

The nitrogen (N) cycle in the soil depends on

complex interactions between plants, soil

X. Raynaud Æ J.-C. Lata Æ P. W. LeadleyEcologie, Systematique et Evolution, UMR 8079 Bat.362, Universite Paris-Sud XI, F-91405 Orsay Cedex,France

X. Raynaud (&)Biogeochimie et Ecologie des Milieux Continentaux,Ecole Normale Superieure, 46, rue d’Ulm, F-75230Paris Cedex 05, Francee-mail: xavier.raynaud@ens.fr

Plant Soil

DOI 10.1007/s11104-006-9003-9

123

ORIGINAL PAPER

Soil microbial loop and nutrient uptake by plants: a testusing a coupled C:N model of plant–microbial interactions

Xavier Raynaud Æ Jean-Christophe Lata ÆPaul W. Leadley

Received: 16 December 2005 / Accepted: 3 April 2006� Springer Science+Business Media B.V. 2006

organisms and soil physical and chemical prop-

erties. In the rhizosphere, the N cycle is intimately

linked to the carbon (C) cycle during the miner-

alisation and immobilisation processes (Fig. 1;

Mary et al. 1996). Therefore, C and N are fun-

damental elements driving the interactions be-

tween plants and microorganisms in soils, and

mineralisation/immobilisation processes can be

complex because they depend on a wide variety

of biotic interactions including competition,

mutualism and predation (Hodge et al. 2000;

Kuzyakov et al. 2003; Paterson 2003).

Both plants and microorganisms compete for

N because they both absorb N from soil mineral

pools (NHþ4 and NO�3 ) (Verhagen et al. 1995;

Kaye and Hart 1997; Hodge et al. 2000; Korsaeth

et al. 2001), and microorganisms and some plants

can absorb small organic compounds containing

N (Barak et al. 1990; Jones and Hodge 1999).

However, the exact nature of the competitive

interactions between plants and microorganisms

for N remains unclear (Kaye and Hart 1997;

Hodge et al. 2000). Plant and ammonifying bac-

teria also maintain a mutualist relationship.

Plants provide most of the soil C in terrestrial

ecosystems through litter production and het-

erotrophic soil microorganisms depend on this

source of C for their growth. In particular, an

important source of C for these microorganisms

is thought to be the low molecular weight

organic molecules that are liberated by roots into

the soil (Grayston et al. 1996; Hodge et al. 1998;

Owen and Jones 2001; Kuzyakov et al. 2003). In

return, most plants require N released by deg-

radation of the soil organic matter by microor-

ganisms. In addition to these relationships, the

consumption of soil microorganisms by their

predators may be responsible for the release of C

N

C

Ext

race

llula

r

NO3NH +4

Ammonifiers

N

C

Nitrifiers

N

C C

N

Other microbes

Plant

N

C

AmmonifiersAmino acid uptake

CO 2

2Respiration or CO uptake

CO uptake (autotrophy)2

Organic MatterCohorts

Soil Organic Matter degradationthrough the excretion of extra cellular enzymes by ammonifiers

uptakeammonium

Plant respiration

Plant absorption

Ammonifiersnitrate uptake

Am

mon

ifica

tion

Pla

nt a

bsor

ptio

n

Res

pira

tion

uptake

uptake

amm

onium uptake

Nitrifiers

Am

mon

ifier

s

Nitrifiers respiration

Plant exudation and litter

Ammonifiers

Nitr

ifica

tion

amm

onifi

catio

nE

nzym

e

Ammonium

Nitrate

Fig. 1 Coupling of the N and C cycle in the rhizosphere. Gains and losses of nutrients like atmospheric deposition,fertilisation or leaching are not represented on this figure. Dotted lines are fluxes that are not simulated in our model

Plant Soil

123

and N from the soil bacterial population

(Clarholm 1985a).

These interactions have been qualitatively

formalized in the soil microbial loop hypothesis.

The soil microbial loop, which refers to the

cycling of N and C between soil and microbial

pools, has been suggested to be a driver of the

dynamics of nutrients and microbial biomass in

the soil (Clarholm 1985a, b, 1989; Ingham et al.

1986a, b; Verhagen et al. 1994, 1995; Paterson

2003; Bonkowski 2004). This hypothesis postu-

lates that some organisms like plants, earth-

worms, etc (sometimes referred to as ecological

engineers; van Breemen and Finzi 1998) can

stimulate the release of mineral N from the soil

organic matter by providing low-molecular weight

C molecules to C-limited microorganisms. In a

conceptual model of plant–soil organism interac-

tions, Clarholm (1985b) distinguished four dif-

ferent steps: (1) the liberation of low molecular

weight organic molecules by roots increases the

growth rate of soil bacterial populations near

roots, (2) growth of the bacterial population leads

to increased soil organic matter degradation and

increased microbial demand for mineral N, (3)

higher bacterial activity leads to increased pre-

dation rates on bacterial population near the root

and, finally (4) N liberated through predation can

be taken up by plant roots or by other microor-

ganisms. In this scenario, the release of mineral N

is stimulated due to higher recycling rates of N in

the microbial loop and, in particular, by higher

rates of mineralisation. Therefore, increased N

mineralisation is due to the liberation of enzymes

by active microorganisms that degrade the

organic matter (Nannipieri et al. 1983) and higher

predation rates on these microorganisms

(Clarholm 1985a, 1989; Ingham et al. 1986a).

The four steps of the microbial loop conceptual

model correspond to a division of plant–microbial

interactions in time. The presence of the root (or

any other ecological engineer) is necessary to

initiate the system, but this hypothesis does not

deal explicitly with the heterogeneity of solutes

around the root. Indeed, the soil is a low diffusive

medium and movements of solutes depend on

diffusive properties of the solute itself (Nye and

Tinker 1977; Tinker and Nye 2000) and of the soil

water content. Roots are localised in the soil and

their activity (uptake of nutrients, exudation...)

creates heterogeneity in several characteristics of

the soil like the concentrations of solutes, soil

water content, etc (Kuchenbuch and Jungk 1982;

Barber and Silberbush 1984; Kuzyakov et al.

2003). Therefore, bacteria are often more

numerous near the roots than at greater distances

due to the enrichment in low molecular weight

molecules of the soil near roots (Papavizas and

Davey 1961; Dijkstra et al. 1987). Solute gradi-

ents around the roots potentially play an impor-

tant role in the dynamics of plant–microbial

interactions. Nitrogen concentrations around

roots are generally lower than at greater distances

(Tinker and Nye 2000). In contrast, due to root

exudation, carbon concentrations are higher near

the root than at greater distances (Kuzyakov

et al. 2003). Because N and C gradients go in

opposite ways with distance from the root surface,

bacteria could be N limited near the root whereas

they could be C limited at greater distances. Some

experiments have already shown that some par-

ticular species of bacteria could be N limited in

the rhizosphere (Jenson and Nybroe 1999).

However, it is not clear whether most bacteria on

the rhizoplane are N limited due to intense

competition with root and with other bacteria, or

if it is only the case for a few bacterial species.

Models of interactions between plants and soil

microorganism have already provided interesting

insights such as: the stoichiometry of N and C

could play an important role in the long-term

stability of the interactions between plant and

decomposers (Daufresne and Loreau 2001), the

balance between mineralisation and immobilisa-

tion processes depends on the available mineral

N in the soil (Korsaeth et al. 2001) or NHþ4concentrations are determined both by the het-

erotrophic mineralisation flux and the nitrifying

activity (Riha et al. 1986). A model developed

by Harte and Kinzig (1993) showed that the

interactions between plant and bacteria could be

extremely complex and that plants could reduce

the N mineralisation flux by having high mineral

N uptake rates, leading to N limitation of bac-

teria. However, to our knowledge, the microbial

loop hypothesis as put forward by Clarholm

(1985b) and others has never been formalised at

the spatial scale at which it has been proposed to

Plant Soil

123

occur, i.e., at the scale of an individual growing

root.

Our first objective was to formalise the

microbial loop hypothesis using a spatialised

model that simulates plant–microbial interactions

in the rhizosphere. We then used this model to

quantitatively explore the four components of the

Clarholm conceptual model. In particular, we

addressed the following questions: (1) To what

extent and under what conditions might exudates

increase bacterial populations around the root?

(2) If such increases occur, to what extent might

they lead to greater ammonification rates? (3)

What mechanisms might control the dynamics of

predation? (4) Under what conditions might

plants increase their acquisition of N by liberating

exudates into the soil? Lastly, we also used the

model to study the potential importance of the

development of nutrient gradients in the rhizo-

sphere on the spatial distribution of bacteria and

the resulting effects on the processes described in

the Clarholm model.

Model development

Full equations for the rhizosphere model are gi-

ven in the Appendix. We only present below se-

lected details of these equations. Symbols written

using roman characters represent chemical ele-

ments (N, NHþ4 . . .). Biomass pools for bacteria

and predators and parameters are written in

italics. Brackets indicate solute concentrations.

Rhizosphere model

The structure of the model and the parameters

describing the soil and roots are similar to Lead-

ley et al. (1997) model. Definitions, symbols, units

and values of the parameters used in the model

can be found in Table 5 or 6 in the Appendix.

Soil structure

The rhizosphere model is derived from a Barber–

Cushman type model (Barber and Silberbush

1984). The soil is modelled as a set of parallel and

vertical soil cylinders of a fixed height,

surrounding a single absorbing root. Each soil

cylinder is divided in several concentric subcyl-

inders to simulate diffusive fluxes through the soil

(see Leadley et al. 1997, for details) and the

model estimates the nutrient uptake of an aver-

age root. The model simulates simultaneously

diffusive fluxes of ammonium, nitrate, organic

matter and exoenzymes through the soil subcyl-

inders. Every chemical element in the model can

be buffered by the soil exchange capacity (Barber

and Silberbush 1984; Lahdesmaki and Piispanen

1992; Guggenberger and Kaiser 2003).

Organic matter is divided into three classes of

decreasing degradability noted 1 to 3. Each class i

is represented by an average molecule containing

C and N. The C:N ratio of this average molecule

(C:Niorg) is allowed to change during the simula-

tions depending on the soil bacterial and plant

activity. Each class i can be degraded by bacterial

activity into class of lower complexity (details

below). The first class is the only one that can be

directly absorbed by soil bacteria; the other clas-

ses need to be decomposed into the first class

through the activity of exoenzymes in order to be

available to bacteria. The first class is assumed to

be low molecular weight, water-soluble organic

matter which is a readily available substrate for

soil microorganisms (Gregoritch et al. 2003;

Kalbitz et al. 2003).

Root model

The root is assumed to enter in the soil at a cer-

tain date after the beginning of the simulation.

The root grows down into the soil at the rate gP

(constant, cm/s). We distinguish two zones on the

root defined by their length on the root and by the

distance between the apex and the beginning of

the zone: one corresponds to the exudation zone

and the second is where nutrients are taken up.

These zones can overlap on the root. As the soil

has a fixed height, the root apex exits the mod-

elled soil volume after some time. In very long

simulations, we assume that the constant growth

of the modelled root can be assimilated to dif-

ferent roots passing through this soil cylinder.

Plants take up NHþ4 and NO�3 following a

Michaelis–Menten equation (Høgh-Jensen et al.

1997; Adamowicz and Le Bot 1999). Exudation of

organic molecules from the root exudation zone is

Plant Soil

123

modelled as the result of a passive leakage of

organic matter using Fick’s law. Active reab-

sorption of organic molecules by the root is

modelled using Michaelis–Menten equation

(Jones and Darrah 1992; Darrah 1996). The root

exudes soluble organic compounds of class 1.

Bacterial model

General principles

Our model simulates the growth of two soil bac-

terial populations, one ammonifying, the other

nitrifying. For both populations, we distinguish

general characteristics of bacteria (such as nutri-

ent uptake, cell death...) and others specific to the

particular processes of ammonification or nitrifi-

cation. Ammonifiers are heterotrophic for C and

can immobilise or ammonify soil organic matter.

The balance between immobilisation and ammo-

nification depends on bacterial needs in C and N

and the availability of C and N in organic or

mineral forms. In contrast, nitrifiers are auto-

trophic for C through nitrification. We have

considered a single ammonifying group because

the model focuses on the mineralisation process

and not on the importance of bacterial diversity in

this process. We also grouped ammonium oxi-

disers and nitrite oxidisers into one single popu-

lation that nitrify ammonium to nitrate as there is

a high positive relationship between these two

groups (Gee et al. 1990; Grundmann and

Debouzie 2000). For both populations, bacterial

biomass N and C (BN and BC, mmol) is the sum of

all internal bacteria compartments containing N

and C (Eq. 1):

BN ¼ NorginþNHþ4in

þNO�3inþNRSN

BC ¼ CorginþNRSC

ð1Þ

The different N and C pools defined in the

model are given in Table 1.

In the following equations, bacterial pools are

described by the letter B when equations deal

with any of the bacterial type, and by the letters A

and N, when they are specific to the ammonifying

or nitrifying population, respectively. Equation

for C organic matter are given only when they

differ to the product of a C:N ratio with the

nitrogen dynamics.

General characteristics of simulated bacterial

populations

We assume that a change in the bacterial pool N

or C is the sum of uptake minus losses. The

general equations for changes in bacterial popu-

lation are given in Eqs. (2) and (3) (some of the

fluxes can be zero, depending on the bacterial

population):

Table 1 N- and C-poolssimulated by the bacterialmodel. Units are mmol

Pool Symbol

Bacterial populationTotal N and C biomass BN, BC

Organic N and C in bacteria except NRSN or NRSC Norgin;Corgin

C and N in enzymatic system reducing nitrate NRSN, NRSC

Intra-cellular ammonium NHþ4in

Intra-cellular nitrate NO�3in

Mineral soil poolsSoil solution ammonium NHþ4out

Soil solution nitrate NO�3out

Soil carbon dioxide CO2

Soil organic poolsOrganic matter pools. i is the class of organic matter.

The smaller is i, the more biologically accessible is theorganic compound

Niorgout

;Ciorgout

Enzymes degrading the organic matter EN, EC

Predator populationPopulation size of predator PN

Plant Soil

123

Changes in bacterial pool N

¼ UptakeðNHþ4 Þ þUptakeðNO�3 ÞþUptakeðNorgÞ � PredationN � ExoenzymeN

� TurnoverN ð2Þ

Changes in bacterial pool C

¼ UptakeðCorgÞ þUptakeðCO2Þ � PredationC

� ExoenzymeC � TurnoverC ð3Þ

As the model takes into account some intra-

cellular nutrient concentrations and some fluxes

across the bacterial membrane, it is necessary to

calculate the volume of the cell representing the

population and the surface exposed to the exter-

nal medium. We used parameters from Pseudo-

monas fluorescens to define the relationships

between bacterial N and cell volume (Prescott

et al. 1999). Using values from Clarholm (1985b)

and Prescott et al. (1999), we found a propor-

tionality coefficient between the N content of the

microbial biomass and the cell volume of

VB ¼ 3:96 cm3 �mmol�1BN

. Similarly, we used a

coefficient of SB ¼ 8:08� 104 cm2 �mmol�1BN

mak-

ing correspondence between the cell surface and

N content of the biomass.

Tables 2 and 3 describe the different parame-

ters used for calculating nutrient fluxes between

pools. For each parameter given in Table 2 (glo-

bal parameters), values can be different for every

population simulated in the model. Pool sizes of

bacterial populations were converted from cell

counts using an average C concentration per cell

of 80.8 · 10–15 gC/cell (Taylor et al. 2002).

Common material fluxes for every bacterial

populations

Ammonium uptake and assimilation Ammonium

uptake is modelled as the sum of two uptake sys-

tems, one active (HATS) and the other passive

(LATS). The active system is modelled by a

Michaelis–Menten equation and the passive sys-

tem by Fick’s law using intra-cellular and extra-

cellular concentrations. The resulting relationship

is given in Eq. 4 where UBðNHþ4 Þ is the uptake rate

of ammonium by bacteria (mmolNHþ4� s�1),

UmaxðNHþ4 Þ and KMðNHþ4 Þ are respectively the

maximum uptake rate (mmolNHþ4�mmolBN

� s�1)

and the half saturation constant of the Michaelis–

Menten kinetic (mmolNHþ4� cm�3), ½NHþ4 �out and

½NHþ4 �in are respectively the extra-cellular

and intra-cellular ammonium concentration

(mmol Æ cm–3), PermðNHþ4 Þ is the membrane per-

meability (cm2 Æ s–1) and BN is the bacterial N

biomass (mmol).

UBðNHþ4 Þ¼BN

UmaxðNHþ4 Þ

NHþ4� �

out

NHþ4� �

outþKMðNHþ4 Þ

þPermðNHþ4 ÞSB NHþ4� �

out

�� NHþ4� �

in

�!ð4Þ

We assume that ammonium assimilation

depends on bacterial biomass (quantities of en-

zymes are correlated with bacterial biomass).

Assimilation of ammonium (AB, mmol Æ s–1) is

described by a Michaelis–Menten equation

(parameters Amax (NHþ4 ), mmolNHþ4�mmolB � s�1

and KaðNHþ4 Þ, mmolNHþ4� cm�3) and depends on

the intra-cellular ammonium concentration (Eq. 5).

ABðNHþ4 Þ¼BN �AmaxðNHþ4 Þ½NHþ4 �in

½NHþ4 �inþKaðNHþ4 Þð5Þ

Nitrate uptake and assimilation Nitrate assimi-

lation is energetically less interesting than

ammonium assimilation because it needs to be

converted to ammonium before it is assimilated

into biomass. Therefore, nitrate uptake only oc-

curs when ammonium concentrations are insuffi-

cient to maintain the bacterial biomass (Betlach

et al. 1981; Merrick and Edwards 1995; Meier-

Wagner et al. 2001). If bacteria need N, nitrate

uptake equations follows a Michaelis–Menten

relationship as stated by Eq. 6, otherwise,

UBðNO�3 Þ ¼ 0.

UBðNO�3 Þ¼BN �UmaxðNO�3 Þ½NO�3 �out

½NO�3 �outþKMðNO�3 Þð6Þ

Reduction of intracellular nitrate to ammo-

nium is a necessary step in nitrate assimilation

(Merrick and Edwards 1995). As there can be

Plant Soil

123

great variations in intra-cellular nitrate concen-

tration, the reduction of nitrate is assumed to be

regulated by an enzymatic system (Nitrate

Reduction System—NRS) that is synthesised at

the rate synthNRS (mmolNRS �mmol�1BN� s�1) from

the pool BN only when nitrate concentration

becomes greater to a minimum value MinðNO�3 Þ(mmolNO�3

� cm�3) (Eq. 7). However, this enzy-

matic systems returns to the organic biomass pool

at the rate lNRS (mmolNRS Æ s–1) in the pool BN.

This enzymatic system is made of C and N and is

characterised by a constant ratio C:NNRS.

Table 2 Symbols, units and common values of generic parameters of the bacterial model

Parameter Symbol Value Unit

General parametersCell volume per unit N-biomass VB 3.96b,e cm3 �mmol�1

BN

Soil-cell exchange surface per unit N-biomass SB 8.08 · 104 b,e cm2 �mmol�1BN

Ammonium uptake (UBðNHþ4 Þ)Permeability coefficient of ammonium

through bacterial membranePermðNHþ4 Þ1.0 · 10–6 cm2 � s�1

Maximal rate of active absorption of ammonium UmaxðNHþ4 ÞA : 5.0 · 10–5 f; N : 2.0 · 10–3 c mmolNHþ4�mmol�1

BN� s�1

Half-saturation constant of active ammoniumuptake kinetic

KMðNHþ4 Þ A : 1.5 · 10–5 d,f; N : 7.0 · 10–5 c,d,g,h mmolNHþ4� cm�3

Ammonium assimilation (AB)Maximal rate of ammonium assimilation AmaxðNHþ4 Þ 2.0 · 10–7 mmolNHþ

4�mmolBN

� s�1

Half-saturation constant of ammoniumassimilation kinetic

KaðNHþ4 Þ 1.0 · 10–7 mmolNHþ4� cm�3

Nitrate absorption (UBðNO�3 Þ)Maximum rate of nitrate uptake UmaxðNO�3 Þ 2.0 · 10–3 a mmolNO�3

�mmol�1BN� s�1

Half-saturation constant of nitrateuptake kinetic

KMðNO�3 Þ 5.0 · 10–3 a mmolNO�3cm�3

Enzymatic system for the reduction of nitrateMinimum intra-cellular concentration for

the synthesis of the systemMin (NO�3 ) 1.0 · 10–7 mmolNO�

3� cm�3

Synthesis rate of the enzymatic system synthNRS 1.0 · 10–7 mmolNRS �mmol�1BN� s�1

Maximum rate of nitrate reductionper unit enzyme

Redmax 2.0 · 10–7 mmolNO�3�mmol�1

NRS � s�1

Half saturation constant of the reduction kinetic KR 1.0 · 10–7 mmolNO�3� cm�3

Degradation rate of the enzymatic system lNRS 1.0 · 10–6 mmolNRSÆ s–1

C:N ratio of the enzymatic system C:NNRS 20 Unit-lessRespiration and excretionCarbon respiration rate lB (CO2) 1.0 · 10–8 mmolCO2

�mmolBC� s�1

Ammonium excretion rate lB ( NHþ4 ) 0 mmolNHþ4�mmolBN

� s�1

Nitrate excretion rate lB ( NO�3 ) 0 mmolNO�3�mmolBN

� s�1

Light organic carbon excretion rate lB ( Corgi) 0 mmolCorg �mmolBC� s�1

Light organic nitrogen excretion rate lB ( Norgi) 0 mmolNorg �mmolBN� s�1

Predation parametersMaximum predation coefficient PredmaxB 2.0 · 10–6 mmolBN

� cm�3

Size of the bacterial populationprotected from predation

Bprotect

N1 · 10–7 mmolBN

� cm�3

Half saturation constant of predation KP,B 1 · 10–7 mmolBN� cm�3

Predator death rate lP 5 · 10–7 mmolNorg �mmolP � s�1

Predation efficiency of predator effB13

aUnit-less

Lost biomass in NHþ4 or NO�3 pool qB;NHþ4

13

aUnit-less

Lost biomass in organic matter pools qB;Norgi

PqB;Norgi ¼ 1

3

aUnit-less

Multiple values in parenthesis correspond to coefficients for various classes of organic matter. B represents any of thesimulated bacterial populations, A and N correspond to ammonifiers and nitrifiers, respectively. When there is multiplecitation for a value, we give the mean value between citationsaBetlach et al. (1981); bClarholm (1985b); cRiha et al. (1986); dVerhagen et al. (1995); ePrescott et al. (1999); fMeier-Wagner et al. (2001); gAlleman and Preston, unpublished data and hKoops and Pommerening-Roser (2001)

Plant Soil

123

if ½NO�3 �in �MinðNO�3 ÞdNRSBN

dt¼ BN � synthNRS � lNRS

�NRSBN

dNRSBC

dt¼ C:NNRS �

dNRSBN

dt

8>>>>><>>>>>:

ð7Þ

if ½NO�3 �in\ MinðNO�3 ÞdNRSBN

dt¼ �lNRS �NRSBN

dNRSBC

dt¼ C:NNRS �

dNRSBN

dt

8>><>>:

Nitrate is reduced to ammonium which is

added to the intra-cellular ammonium pool. The

reduction reaction is modelled using a Michaelis–

Menten equation (parameters Redmax; mmolNO�3�

mmolNRS � s�1 and KR; mmolNO�3� cm�3) as

described by Eq. (8).

RedBðNO�3 Þ ¼ Redmax �NRSN �½NO�3 �in

½NO3�in þKR

ð8Þ

Table 3 Symbols, units and common values of specific parameters for ammonifiers and nitrifiers

Parameter Symbol Value Unit

Specific parameters for ammonifiers (AN)Pool size

Nitrogen in organic bacterial pool AN 5 · 10–7 mmol Æ cm–3

C:N ratio C:NA 3.42* mmolC �mmol�1N

Absorption of organic matterMaximum uptake rate per unit biomass Umax (N1

org) 1.5 · 10–6 b,c,d mmol �mmol�1AN� s�1

Half-saturation constant for the uptake kinetic KM (N1org) 1 · 10–5 b,d mmolN1

org� cm�3

Extracellular enzyme synthesisSynthesis rate of the enzymatic system synthE 1.0 · 10–9 mmol �mmol�1

AN� s�1

C:N ratio of the enzymatic system C:NE 20 unit lessDegradation rate of the enzymatic system lE 1.0 · 10–6 mmolE � s�1

Organic matter degradationDegradation rate of organic matter class iper unit enzyme

k(i) (0.05, 0.05, 0.005) mmolNiorg�mmol�1

E � s�1

Simplification rate of organic matter class i a(i) (0.01, 0.01, 0.001) mmolNiorg�mmol�1 � s�1

Mineralisation rate of organic matter class i m(i) (0.005, 0.05, 0.005) mmolNiorg�mmol�1 � s�1

Half saturation constant of the degradingenzyme for each organic matter class

KM(E,i) (5 · 10–12, 5 · 10–12, 5 · 10–12) mmolNiorg� cm�3

Specific parameters nitrifiers (NN)Pool size

Nitrogen in amino acid pool NN 5 · 10–7 mmol Æ cm–3

C:N ratio C:NN 3.42* mmol�1C �mmol�1

N

Reducing powerMaximum rate of ammonium oxidation Redoxmax 2.0 · 10–7 mmolNHþ

4�mmol�1

NN� s�1

Half-saturation constant of the reduction kinetic Kred 1.0 · 10–7 mmolNHþ4� cm�3

CO2 fixationStoichiometry coefficient g 1a mmolCO2

�mmol�1NHþ

4

Multiple values in parenthesis correspond to coefficients for various classes of organic matter. A and N correspond toammonifiers and nitrifiers, respectively*A C:N ratio of 3.42 mmolC Æ mmol–1

N equals to 4.0 gC Æ g–1N

aPelmont (1993); bJones and Hodge (1999); c Vinolas et al. (2001); and dBuesing and Gessner (2003)

N and C turn-over Each bacterial population

has specific maintenance losses for carbon diox-

ide, ammonium, nitrate and soluble organic

compounds. These losses are excreted into the

soil at rates lBðCO2Þ; lBðNHþ4 Þ; lBðNOþ3 Þ;lBðN1

orgÞ; lBðC1orgÞ (mmol �mmol�1

B � s�1). For

example, lB(CO2) represents the basal respira-

tion rate per unit biomass of bacteria. We used

two independent excretion rates for organic

compounds so that we can modulate the C:N ratio

of the excreted products.

Plant Soil

123

Population C:N maintenance Each bacterial

population is characterised by a constant C:N

ratio (C:NB). Since the assimilation and excretion

or respiration of C and N are parametrised

independently, the correction to maintain the C:N

ratio constant is made through excretion of the

surplus of N or C into the soil. We used the

conditional system (Eq. 9) to determine whether

the population has a surplus of C or N. In these

equations, qBNand qBC

are the quantities excreted

in N and C respectively, for maintaining the C:N

ratio. In the case where N is the growth limiting

factor, nitrate is taken up following Eq. 6 before

correcting their C:N ratio.

ifdBC

dBN\C:NB :

qBN¼ dBN � dBC=C:NB

qBC¼ 0

( ð9Þ

ifdBC

dBNþUBðNO�3 Þ\C:NB :

UBðNO�3 Þ¼dBC=C:NB�dBN

qBN¼0

qBC¼0

8>><>>:

ifdBC

dBN þUBðNO�3 Þ� C:NB :

UBðNO�3 Þ ¼ BN �UmaxðNO�3 Þ

�NO�3� �

out

NO�3� �

outþKM NO�3

� �qBN¼ 0

qBC¼ dBC � dBN þUBðNO�3 Þ

� �C:NB

8>>>>>>>><>>>>>>>>:

qBNis excreted in the external medium as NHþ4

and qBCas CO2.

Predation Predation can be a major factor con-

trolling N mineralisation (Clarholm 1985b;

Bonkowski 2004). The model simulates predation

of bacteria by amoeba or ciliates by considering a

generalist predator community that feeds on all

bacteria in the model. The C:N ratio of predators

is assumed to be equal to the bacterial C:N.

Depending on the type of bacteria, parameters

values can be different. Predation is based on a

Lotka–Volterra type relationship, but we use a

saturating function of predation (expressed by the

parameter BprotectN ) to simulate a part of the bac-

terial population that can be protected from

predation by living in soil pores smaller than the

predator size (Wright et al. 1995). The predation

flux (PredB, mmol Æ s–1) in the model is therefore

calculated as

PredB ¼ PredmaxB � PN �BN � B

protectN

� �BN � B

protectN

� �þKP;B

ð10Þ

The quantity PredB (mmol) is removed from the

bacterial pool and is either immobilised in pre-

dators or distributed among the different nutrient

pools following the Eqs. (11) and (12) where dPdt

represents the quantity immobilised in predator

and MBðXÞ is the quantity distributed in pool X

(X is one of NHþ4 ;NO�3 ;Niorg, Clarholm 1985b).

Other parameters are described in Table 2.

dP

dt¼ effB � PredB

MBðNHþ4 Þ ¼ ð1� effBÞ � qB;NHþ4� PredB

MBðNO�3 Þ ¼ ð1� effBÞ � qB;NO�3� PredB

ð11Þ

In the case of organic materials, the equations

are almost identical except that the C corre-

sponding to the mineral N fraction is added to the

first organic class (Eq. 12).

if i¼ 1ðrhizoplaneÞMBðN1

orgÞ¼ ð1�effBÞ �qB;N1org�PredB

MBðC1orgÞ¼C:NB � ð1�effBÞ �qB;N1

org

��PredBþMB;NHþ

4þMB;NO�3

�

8>>>>><>>>>>:

ð12Þ

if i > 1 ðsoilÞMBðN1

orgÞ ¼ ð1� effBÞ � qB;N1org� PredB

MBðC1orgÞ ¼ C:NB � ð1� effBÞ � qB;N1

org� PredB

8<:

Each distribution coefficient qB,X is linked

through the Eq. (13), where n represents the total

number of organic matter classes.

Plant Soil

123

qB;NHþ4þ qB;NO�3

þXn

i¼1

qB;Niorg¼ 1 ð13Þ

Specific fluxes for ammonifying bacteria (AN)

Ammonifying bacteria differ from other bacteria

due to their heterotrophy and their ability to

excrete enzymes that can degrade the soil organic

matter.

Heterotrophy Ammonifiers absorb labile organic

matter and use the C for making biomass. The

absorption equation (Eq. 14) is a Michaelis–

Menten type equation using the N concentration

of low molecular weight organic matter (N1orgout

).

Jones and Hodge (1999) described bacterial amino

acid uptake kinetics by the sum of a passive

(LATS) and an active uptake system (HATS).

However, in contrast to the uptake of ammonium

and nitrate, we neglected the passive absorption

because Jones and Hodge (1999) found that LATS

contributed significantly to uptake only for con-

centrations that are much higher than those typi-

cally found in soils. Uptake is based on the N

fraction of the organic matter, the C fraction is

absorbed with respect to the C:N ratio of the or-

ganic matter (C:N1org).

UAðN1orgÞ ¼ AN �UmaxðN1

orgÞ �N1

org

h iout

N1org

h ioutþKM N1

org

� �ð14Þ

These fluxes correspond to both uptake and

assimilation of organic matter and are directly

added to the organic bacterial pool of AN.

Degradation of soil organic matter Ammonify-

ing bacteria excrete enzymes that degrade the soil

organic matter to simpler components like amino

acids. These enzymes are synthesised at the rate

synthE (mmol �mmol�1AN� s�1) and have a C:N

ratio C:NE. The variation of N in the enzyme pool

(dEN/dt) is described by Eq. (15), the variation in

C is simply C:NE � dEN=dt.

dEN

dt¼ AN � synthE � lE � EN ð15Þ

These enzymes can degrade organic matter

from all three classes. We assumed that N flux

degraded from organic matter of class i separates

into 3 parts: one goes into class i–1, another into

class 1 and another into the NHþ4 pool. Equations

describing this degradation are:

DiðNiorgÞ ¼ kðiÞ � EN �Ni

org=ðKMðEÞ þ ENÞ ð16Þ

SiðNiorgÞ ¼ aðiÞ �DiðNi

orgÞ

SiðNHþ4 Þ ¼ mðiÞ � SiðNiorgÞ

Changes in C are similar equations corrected

with respect to the C:N ratio of the corre-

sponding class of organic matter without con-

sidering the SiðNHþ4 Þ flux. DiðNiorgÞ is the rate of

degradation of the organic matter of class i

which depends both on the concentration in

organic matter and in enzymes. k(i) is the max-

imum rate of degradation of compounds from

class i. SiðNiorgÞ is the part of the degradation

that does not enter pool i–1 and SiðNHþ4 Þ is the

flux of N that enters the NHþ4 pool. Therefore,

the quantity of N entering the first organic

matter pool is SiðNiorgÞ � SiðNHþ4 Þ. a(i) describes

the part of the degradation flux that does not

enter the i–1 class and m(i) the part of the

SiðNiorgÞ flux that is mineralized to NHþ4 . In all

cases, the greater is i, the smaller are the values

of k(i), a(i) and m(i).

Specific fluxes for nitrifying bacteria (NN)

When considered as a single group, nitrifying

bacteria (i.e. ammonium oxidisers + nitrite oxi-

disers) use soil CO2 to build up the C fraction of

their biomass through the oxidation of ammo-

nium into nitrate. We divided this process into

two parts: the creation of some reducing power

inside the cell and the fixation of CO2 using this

reducing power.

Creation of the reducing power The reducing

power follows a Michaelis–Menten type equation

Plant Soil

123

depending on the bacterial biomass and the intra-

cellular ammonium concentration (Eq. 17).

Coefficient Redoxmax describes the maximum

rate of ammonium oxidation per unit biomass

(mmolNHþ4�mmolNN

� s�1) and coefficient Kred

(mmolNHþ4� cm�3) is the half saturation constant

of the Michaelis–Menten kinetic. The nitrate

produced through this reaction is assumed to be

excreted in the external medium.

Redox ¼ Redoxmax �NN �NHþ4� �

in

NHþ4� �

inþKred

ð17Þ

Carbon dioxide fixation Based on the calculated

reducing power Redox, we used a stoichiometry

coefficient g (mmolCO2�mmol�1

NHþ4) giving the

number of mole of fixed C for each mole of oxi-

dised ammonium (Eq. 18). The flux AssimN(CO2)

is supposed to be directly assimilated into the

bacterial biomass.

AssimNðCO2Þ ¼ g�Redox ð18Þ

Model analysis

Parameterisation

Various literature sources were used to para-

meterise the model. Sources for bacteria param-

eters are given, when available in Tables 2 and 3.

Plant and soil parameters are given in Appendix

B, Tables 5 and 6. Exudation rates were

calculated to simulate a C flux of 2.0 · 10–9–2.0 ·10–6 mmolC cm�2

root s–1 (Jones and Darrah 1995;

Jones and Hodge 1999; Farrar and Jones 2000;

Gahoonia et al. 2000). Most plant parameters

come from data measured on grasses.

Numerical solution

The model is solved using the forward Euler

method on a PC. Because errors associated with

the forward Euler method are very sensitive to

the choice of time step and pixel size we have

used double precision declarations in the Fortran

program, a relatively small sub-cylinder size and

have been careful to run the model at several time

steps to ensure that the numerical solution was

accurate. In most cases we have used a time step

of 1 s.

Analysis scenarios

The main analysis of the model follows different

scenarios presented in Table 4. These scenarios

were intended to study (1) the impact of exudation

by roots on the transformation of N in the soil and

its uptake by roots and (2) the consequences of the

development of C and N gradients on these pro-

cesses. For every scenario, parameter values were

identical except those concerning the exudation

flux or the spatialisation. In the model, space is

represented by the number of cylinders around the

root. Theoretically for the same soil volume, the

more cylinders surround the root, the more accu-

rate the model is for describing nutrient gradients.

Influence of space was tested by running the model

with one (non-spatialised scenario) or 20 cylinders

(spatialised scenario) for the same soil volume. We

tested the effects of the reabsorption of exudates

by plants by comparing simulations where plants

were not allowed to take up exudates, with two

simulations using different values of reabsorption

rates by roots (10–9 and 10–8 mmol Æ cm–2 Æ s–1).

Sensitivity analysis

In order to better understand the behaviour of the

model, we also studied the sensitivity of its

outputs through a sensitivity analysis where all

the relevant model parameters were indepen-

Table 4 Scenarios used for the analysis of the plant–bacteria interaction model

Scenario Exudation Spatialisation

E+S+ Y YE+S– Y NE–S+ N YE–S– N NNP No plant

Exudation refers to the exudation of high C:N moleculesby plants. Spatialisation refers to the number of soil sub-cylinders defined in the model: not spatialised, 1 cylinder;spatialised, 20 subcylinders. Scenario NP is similar to E–S–except that there are no uptake of ammonium by plants

Plant Soil

123

dantly divided or multiplied by 2 and 10. Because

the effects of the spatialization on most output

variables average values (plant net N uptake,

average bacterial biomass in the whole soil cyl-

inder...), were limited, the sensitivity analysis was

made based on the E+S– scenario. We studied in

the sensitivity analysis a 2-fold and 10-fold change

of the values of each parameter (167 parameters

in total when considering 3 organic matter clas-

ses).

Results

Population dynamics of bacteria is influenced

by the presence of roots

The analysis of the model suggests that the lib-

eration of C from roots can substantially modify

the spatial structure of bacterial communities

(Fig. 2). In all of the scenarios with exudation,

ammonifying biomass is about 100 times larger

than in scenarios without. In addition, the E+S+

scenario shows that the size of the ammonifying

biomass depends on the proximity to the root.

With the exudation rates that we used for these

simulations, the ammonifying biomass is about

10% higher in the first soil cylinder (close to the

root) than in the last one. Interestingly, ammo-

nifying biomass in the E+S– scenario is similar to

the average biomass in the E+S+ scenario, which

suggests that even though diffusive constraints in

the soil can create gradients in microbial popu-

lation size or nutrient concentrations, it does not

affect the total biomass of ammonifiers when

integrated over the entire soil cylinder. There-

fore, spatialisation has minor effects on the

average concentrations in the model and in all of

the graphics, scenarios E+S+ and E+S–, as well as

E–S+ and E–S–, always overlap. Scenarios with-

out exudation generate much lower biomass val-

ues, and the scenario E–S+ does not show any

with exudation without exudation no plant

0 50 100 150 200 250 300 350

0.0e

+00

1.0e

–05

Het

erot

roph

s (m

mol

N/c

m3 so

il)

0 50 100 150 200 250 300 350

0.0e

+00

1.0e

–05

0 50 100 150 200 250 300 350

0.0e

+00

1.0e

–05

Mean1st CylinderLast CylinderNot Spatialized

0 50 100 150 200 250 300 350

0e+

002e

–07

4e–0

7

Nitr

ifier

s (m

mol

N/c

m3 so

il)

0 50 100 150 200 250 300 350

0e+

002e

–07

4e–0

7

0 50 100 150 200 250 300 350

0e+

002e

–07

4e–0

7

0 50 100 150 200 250 300 350

0e+

004e

–07

8e–0

7

Time (days)

Pre

dato

rs (

mm

olN

/cm

3 soil)

0 50 100 150 200 250 300 350

0e+

004e

–07

8e–0

7

Time (days)

0 50 100 150 200 250 300 350

0e+

004e

–07

8e–0

7

Time (days)

Fig. 2 Evolution of the ammonifying (up), nitrifying(middle) and predator (bottom) population size with timein scenarios with exudation (left)/ without exudation

(centre) and without plant (right). The root enters the soilat day 50 and exudation occurs from days 50 to 53

Plant Soil

123

differences between cylinders, which suggests that

the system without exudates is C-limited by

existing SOM regardless of where the bacteria are

situated in the soil.

In contrast to ammonifiers, nitrifying biomass

is lower under exudation due to higher competi-

tion with ammonifiers but does not show any

gradient in the E+S+ scenario. Population growth

is maximal in the ‘No Plant’ case due to a higher

availability of ammonium.

Predators play an important role in the model

in regulating bacterial populations. Figure 2

shows a typical Lotka–Volterra pattern of preda-

tion between predators and ammonifying bacte-

ria. In the spatialised scenarios, patterns in the

predator biomass are qualitatively similar to those

of the bacterial biomass with the highest biomass

found in the cylinders close to the roots (Fig. 2).

The release of C in the soil increases mineral

N availability

The increased activity and growth of bacteria

following the C flush in the rhizosphere (Fig. 2) is

followed by an increase of the degradation of soil

organic matter and the predation on the bacterial

community. All of these processes increase the

transformation of N in the rhizosphere which

leads to an increased NHþ4 and NO�3 availability

in the system. Therefore, the average NHþ4 con-

centration has a short peak in the scenarios with

exudation (Fig. 3). However, there is a large time

lag between the entry of the root into the soil and

the higher NHþ4 concentrations. This time lag

results from an initial period of strong net im-

mobilisation followed by N release as a result of

predation.

As nitrifier biomass in the ‘no plant’ scenario is

much higher than in any other studied scenario,

this leads to higher nitrification rates and, there-

fore, higher nitrate concentration simulated by

the model.

Plants may improve their N uptake by loosing C

Our simulations also suggest that the losses of C

by roots could be beneficial to plants in terms of

N uptake (Fig. 4). Figure 4 shows that plants ex-

udating C can take up more N than non-exudat-

ing ones. This is because they have access to N

pool which is made available by the microbial

loop. Despite favouring larger bacterial commu-

nities near the rhizoplane, the C flux from the

roots to the soil can greatly improve plant N up-

take in the long term through the increase of the

N turnover in the rhizosphere. N uptake by plants

in the two scenarios with exudation (E+S+ and

E+S– scenarios) is three times higher than in the

scenarios without exudation.

Sensitivity of model parameters

Figure 5 shows the sensitivity of some of the plant

net N uptake to changes in parameter values. Data

were plotted only if a change in the parameter

0 50 100 150 200 250 300 350

0e+

004e

–06

8e–0

6

Time (days)

Ave

rage

NH

4+ C

onc.

(m

mol

/cm

soil

3)

0 50 100 150 200 250 300 3500.0e

+00

1.0e

–06

2.0e

–06

Time (days)

Ave

rage

NO

3 C

onc.

(m

mol

/cm

soil

3)

−

Fig. 3 Evolution of the average concentration in NHþ4(left) and NO�3 (right) in the soil cylinder with time. Theroot enters the soil at day 50. Exudation occurs from days50 to 53. Solid line: exudation and spatialised (E+S+);short dashed line: exudation, but not spatialised (E+S–);

dotted line: no exudation, but spatialised (E–S+); dashed-dot line: no exudation and not spatialised (E–S–); longdashed line: no plant (NP) short dashed line is hiddenbehind solid line.

Plant Soil

123

value induced more than a 5% change in the

studied variable. This was the case for 14 parame-

ters out of 164. In some cases (such as lP, effA or

PredmaxN), values modelled with parameters di-

vided or multiplied by 10 do not surround the zero

percent change line (for example, plant N uptake is

always lower whether we multiply or divide any of

the predation parameters by 2). This is because

changes in these parameters heavily modify the

dynamics of microbial growth such that equilib-

rium was not reached after 1 year of simulation. In

other cases (such as NN, [P]...), the change of

parameter values led to numerical errors so that we

could not plot the resulting change on plant N up-

take. Compared to our scenario without exudation,

plant N uptake was always higher with exudation,

suggesting that exudates improves over-minerali-

sation over a wide range of parameter space.

Given our default parameters, plant net N up-

take is only sensitive to a small number of param-

eters with the N concentration in the different

organic matter classes having the greatest effects.

Initial values of the different bacterial populations

also alter the plant N uptake, suggesting that

competition occurs between plants and soil

microorganisms for the uptake of mineral N.

Ammonifier and nitrifier biomass is sensitive to

changes in a larger number parameters (not

shown), in particular to parameters describing

population growth such as uptake capacities or

predation.

Discussion

Based on our model structure and parameters, we

can mimic some key aspects of Clarholm (1985b)

conceptual model including the effects of exu-

dates on (i) bacterial populations, (ii) organic

matter mineralisation, (iii) bacterial predation

and (iv) plant N nutrition.

Bacterial populations are influenced

by exudates

Observations of microbial populations in the

rhizosphere show strong gradients in population

size as a function of the distance from the root

surface for a variety of plant species (Dijkstra

et al. 1987; Paul and Clark 1989; Chen et al.

2002). Microbial biomass or numbers are gener-

ally 2–10 times higher next to the rhizoplane than

in bulk soil, with the steepest gradients between 0

and 5 mm from the root surface. These gradients

in microbial biomass are strongly correlated with

changes in labile organic C concentrations (Chen

et al. 2002).

In the model, the C gradient created by diffu-

sion processes in the spatialised scenario allowed

the development of greater bacterial populations

against the rhizoplane. Using moderate values of

exudation rates, the biomass against the rhizo-

plane was about 10% greater than in the last soil

subcylinder which is smaller than observed

0 50 100 150 200 250 300 350

–4e–

06–2

e–06

0e+

00

Time (days)

N ta

ken

up b

y pl

ant (

mm

ol)

Fig. 4 Evolution of cumulative plant N in the soil cylinderwith time. The root enters the soil at day 50. Exudationoccurs from days 50 to 53. Solid line: exudation andspatialised (E+S+); short dashed line: exudation, but not

spatialized (E+S–); dotted line: no exudation, but spatial-ized (E–S+); dashed-dot line: no exudation and notspatialized (E–S–); long dashed line: no plant (NP) shortdashed line is hidden behind solid line.

Plant Soil

123

gradients. However, root exudation has an influ-

ence on the whole soil cylinder, due to the dif-

fusive ability of exudates. Indeed, modelled

bacterial biomass near the rhizoplane (1st cylin-

der) in scenario with exudation (scenarios E+S+

and E+S–) was on average 50 times greater than

without exudation (scenarios E–S+, E–S– and

NP). The scenario with exudation but not spa-

tialised also show increased biomass, showing that

exudation itself is a factor of increasing biomass

in the model.

Exudates increase soil organic matter

degradation

Liljeroth et al. (1994) have shown that rhizode-

position can lead to a substantial increase in soil

organic matter degradation. In addition, adding

fresh organic material to soils often leads to in-

creased degradation of soil organic matter, which

has often been referred to as the ‘‘priming effect’’

(Fontaine et al. 2003). Some ecosystem level

observations have also been viewed as evidence

of increased N mineralisation under conditions of

increased rhizodeposition (e.g., Hamilton and

Frank 2001). However, there is a great deal of

debate over the importance of the ‘‘priming

effect’’ and the mechanisms that control it

(Fontaine et al. 2003).

Bacterial populations in the model excrete

enzymes that degrade soil organic matter. Thus,

increases in the bacterial biomass in the scenarios

with exudation lead to higher releases of

enzymes. Since the enzymes are assumed to at-

tack all classes of organic material there is an

increased degradation of the soil organic matter

and an associated increase in ammonification.

Our simulations are coherent with observed

effects of rhizodeposition and additions of fresh

organic matter on the degradation of soil organic

matter; however, the mechanisms are based on

several strong hypotheses. In particular, we as-

sume that we can group all ammonifying bacteria

into a single functional group, that they excrete

% change

PermP(Norg1)

b(E)

[Norg2]

[Norg3]

AN

ImaxA(Norg1)

synthe

E

a(1)

[P]

effA

NN

PredmaxN

P

400 200 0 200 400

µ

µ

Fig. 5 Sensitivity of net plant N uptake to changes inparameter values. Data were plotted only if they inducedmore than a 5% change compared to the standardparameter value. Circles represent the change whenparameters were multiplied or divided by two, triangleswhen parameters were multiplied or divided by ten. Solidsymbols give the value of output when the parameter wasmultiplied by 2 or 10, the open symbol when the parameterwas divided by 2 or 10. The vertical line represents the

zero percent change line. In some cases values modelledwith parameters divided or multiplied by 10 do notsurround the zero percent change line because changesheavily modify the dynamics of microbial growth such thatequilibrium was not reached after 1 year of simulation. Inother cases the change of parameter led to numericalerrors so that we could not plot the resulting change onplant N uptake

Plant Soil

123

one enzyme type that degrades all classes of

organic matter, and that soil organic matter can

be grouped into three classes. Soil organic matter

degradation is much more complex in natural

systems due to the broad range of organic matter

types and the potential specificity of enzymes that

degrade soil organic matter (Fontaine et al.

2003). The rate and the importance of degrada-

tion of soil organic matter may therefore depend

on the microbial diversity in the soil (Loreau

2001).

Exudates lead to mineral N release through

increased predation

Interactions between soil bacteria and predator

also seem to be an important determinant of the

turn-over rate of nutrients in the soil. Lotka–

Volterra dynamics in the soil between soil bac-

teria and predators have been suggested (Killham

1994) and our model suggests that an increase in

C availability can increase these dynamics.

Experimental data suggest that predators play

an important role in regulating soil bacteria and

fungi populations and the release of N from these

organisms (Clarholm 1981; Ingham et al. 1986b;

Jones et al. 1998; Rønn et al. 2002). Clarholm

(1981) used watering or precipitation events

which induced sharp increases in bacterial popu-

lations in order to investigate the effects of bac-

terial grazers on bacterial population dynamics in

the field and in pots. These observations and

experiments show ‘‘Lotka–Volterra’’ type preda-

tor–prey dynamics with a sharp peak in the prey

population (bacteria) after ca. 2 days followed by

a decline in the prey population associated with a

sharp peak in the predator (amoebae) popula-

tions at about 5 days. These dynamics are

accentuated in the presence of plants due to

higher microbial biomass in the soil before

watering or rain events. We have only partially

succeeded in reproducing these kinds of preda-

tor–prey dynamics. The introduction of the

exuding root into the system increases bacterial

biomass, but the subsequent increase in predator

population which occurs gradually over several

hundred days is much slower than observed by

Clarholm (1981). It is not clear if this is a problem

with the predator component of the model, or due

to differences between watering and root exu-

dates in controlling both bacterial and predator

populations but the fact that the predator com-

ponent of the model is not limited by a superior

predator (in contrast with Clarholm (1981)

experiments where the soil food web is main-

tained) may explain these differences. The tem-

poral dynamics of N mineralisation (and the

important gain in uptake by plants) is also sur-

prisingly quite slow in our simulations. This could

be due to the slow dynamics of predators. How-

ever, Trinsoutrot et al. (2000), while studying the

dynamics of low N organic residues still observed

a net immobilization of N in an agricultural soil

after 168 days of experiment. Although we

believe that organic residues are different from

exudates, these results suggest that N dynamics

can be rather slow in soils.

Several experiments have already shown that

elevated atmospheric CO2 increased root rhizo-

deposits (Williams et al. 2000). Our results sug-

gest that the increase of rhizodeposits availability

leads to an increase of soil organic matter min-

eralisation. Changes in atmospheric CO2 con-

centrations might have some impacts in the short

term on N turnover in soils due to an increase of

available C to the bacterial biomass. Experiments

have already provided evidences that elevated

CO2 increases bacterial or predator biomass

(Jones et al. 1998; Williams et al. 2000; Rønn

et al. 2002, 2003). Therefore, increased CO2

might lead to an increase in soil organic matter

degradation.

Plants can benefit of an increase in mineral N

uptake from exudates

It has been suggested that plants can increase

their access to N locked up in soil organic matter

by stimulating turnover in the microbial loop

through root exudation, and this hypothesis has

been formulated and examined at the several

scales ranging from the rhizosphere (Coleman

et al. 1984; Clarholm 1985b) to the whole eco-

system (Hamilton and Frank 2001). The key final

assumption in the Clarholm conceptual model is

that the N liberated by the increased turnover in

the microbial loop can be taken up by plants in

the face of competition by soil microorganisms

Plant Soil

123

for this N. All our simulations suggest that exu-

dation can lead to an overall increase in mineral

N uptake by roots due to an increase of soil or-

ganic matter degradation and turnover in the

microbial loop. The increased uptake is similar in

the spatialised and not spatialised scenarios.

Jones and Darrah (1993) have suggested that

liberation of organic compounds into the soil is

the result of the leakage of molecules through

the opened phloem vessels at the root tip

(protophloem) and that plant re-absorbed these

organic compounds to limit their C losses.

Other suggested that the re-uptake could be a

means to limit bacterial growth in the immedi-

ate vicinity of roots, and therefore to decrease

the N competition with these microorganisms

(Jones and Hodge 1999; Owen and Jones 2001).

In some of our simulations, uptake of organic

compounds by roots only slightly limits the

growth of bacterial populations in the rhizo-

sphere, and did not lead to a significant increase

in the uptake of N by plants (data not shown).

However, we found that if plant uptake capacity

for organic N is too high, the resulting compe-

tition between plants and bacteria for organic

matter limits bacterial growth and organic

matter degradation, thereby reducing plant N

uptake. Root exudation may therefore provide

advantages to plants by increasing the N avail-

ability in the rhizosphere.

Root-induced over mineralisation

and ecosystem functioning

The model simulates the transformations of N in

a small volume of soil after the addition of exu-

dates by a root. In this small volume of soil, the

model suggests that the flux of N is net immo-

bilisation in bacterial biomass soon after the

addition of C carbon then net mineralisation

some days after. This suggests that, at the scale of

roots and at a given time, N fluxes vary in space

from net immobilisation to net mineralisation,

depending on the dynamics of the soil trophic

web, which is highly dependant on the availability

of C and N. Moreover, the model suggests that N

fluxes also vary in time at a given location in the

soil.

Model limitations and conclusions

Due to its complex structure, several parameters

values are lacking. This attempt of modelling the

microbial loop in soils was also aimed at identifying

areas where experimental data is cruelly lacking. In

particular, the description of the microbial com-

munity (e.g., number of different bacterial groups,

predation component, etc) or the structure of the

organic matter is very crude and experimental data

could greatly improve our knowledge on popula-

tion dynamics of bacteria in soils or organic matter

transformations. However, we believe that the

approach we have undertaken in this work is

important to better understand the relationships

between soil biology and nutrient turn-over.

Larger scale models of ecosystem functioning

have not considered the potential effects of the

soil microbial loop on plant competition for

nutrients. Our model has been developed at the

scale of roots and its behaviour suggests that the

effects of the microbial loop on nutrient cycling

occur at this scale. In plant communities with

relatively high root densities, this small scale

behaviour should result in a net over-mineralising

effect of the input of exudates to the soil.

Finally, our results show that models devel-

oped at the scale at which processes occur are

necessary to get a better understanding of their

importance at larger scale.

Acknowledgements We gratefully thank three anony-mous referees and the editor for valuable comments on aprior version of this manuscript. Computer source code ofthe model is available from X. Raynaud upon requests.

Appendix A: Pool variations equations

Symbols are the same that were given in the text.

UptPðNHþ4 Þ and UptPðNO�3 Þ represent respec-

tively ammonium and nitrate uptake rate by plant

(see Leadley et al. 1997, for details). ExðNiorgÞ and

ExðCiorgÞ are the rate of exudation of organic

matter from class i by plant. All these plant

variables only occur in the first soil cylinder

(against the rhizoplane) and are equal to 0 in the

other cylinders. For simplicity sake, variations of

concentrations of NHþ4 ;NO�3 and organic N or C

Plant Soil

123

between cylinders due to diffusion and mass

fluxes are expressed by the factor Fc(X). Details

on calculating Fc factor between cylinders are

given in Leadley et al. (1997).

Subscript A represents a parameter for total

biomass of ammonifying bacteria, N for total

biomass of nitrifying bacteria and B for the total

biomass of every bacterial population (i.e. A+N).

Ammonifying bacteria

Organic N in biomass

dNorgin AN

dt¼ AssimAðNHþ4 Þ þUptAðN1

orgÞ

� dNRSAN

dt� qAN

� PredA

�AN synthE þ lAðNHþ4 Þ�þlAðNO�3 Þ þ lAðN1

org�

dNorgin AC

dt¼ UptAðC1

orgÞ �dNRSAC

dt� qAC

� C:NA � PredA �AC C:NE � synthEð

þlAðCO2Þ þ lAðC1orgÞ�

Intra-cellular ammonium

dNHþ4in

dt¼ UptAðNHþ4 Þ þRedAðNO�3 Þ

�AssimAðNHþ4 Þ

Intra-cellular nitrate

dNO�3in

dt¼ UptAðNO�3 Þ �RedAðNO�3 Þ

Nitrate reduction enzymatic system

Relation is given in Eq. (7).

Nitrifying bacteria

Organic N in biomass

dNorgin NN

dt¼ AssimNðNHþ4 Þ �

dNRSNN

dt� qNN

� PredN �NN lNðNHþ4 Þ�

þlNðNO�3 Þ þ lNðN1orgÞ�

dNorgin NC

dt¼ AssimNðCO2Þ �

dNRSNC

dt� qNC

� C:NN � PredN

�NC lNðCO2Þ þ lNðC1orgÞ

� �

Intra-cellular ammonium

dNHþ4in

dt¼ UptNðNHþ4 Þ þRedNðNO�3 Þ

�AssimNðNHþ4 Þ �Redox

Intra-cellular nitrate

dNO�3in

dt¼ UptNðNO�3 Þ �RedNðNO�3 Þ

Nitrate reduction enzymatic system

Relation is given in Eq. (7).

Mineral soil products

Soil solution ammonium

dNHþ4dt

¼ ANlAðNHþ4 Þ þNNlNðNHþ4 Þ

þMBðNHþ4 Þ þ qAN�UptBðNHþ4 Þ

�UptPðNHþ4 Þ þ FcðNHþ4 Þ

Plant Soil

123

Soil solution nitrate

dNO�3dt

¼ ANlAðNO�3 Þ þNNlNðNO�3 Þ þRedox

þMBðNO�3 Þ þ qNN�UBðNO�3 Þ

�UptPðNO�3 Þ þ FcðNO�3 Þ

Soil carbon dioxide

dCO2

dt¼ BN � lBðCO2Þ þ qBC

�AssimNðCO2Þ

Soil organic matter

Organic matter (n classes)

The equation given here is general. Functions that

has not been defined in the text like those con-

cerning organic compounds larger than n, are

assumed to be zero.

If i>1, variations in the organic pools are ex-

pressed as:

dNiorg

dt¼ExðNi

orgÞþANlAðNiorgÞþNNlNðNi

orgÞ

þlEENþMBðNiorgÞþFcðNi

orgÞ�DiðNiorgÞ

þDiþ1ðNiþ1org Þ�Siþ1ðNiþ1

org Þ

dCiorg

dt¼ ExðCi

orgÞ þANlAðCiorgÞ þNNlNðCi

orgÞ

þ C:NElEEN þMBðCiorgÞ þ FcðCi

orgÞ�DiðCi

orgÞ þDiþ1ðCiþ1org Þ � Siþ1ðCiþ1

org Þ

If i=1, the equation is :

dN1org

dt¼ ExðN1

orgÞ �UptAðN1orgÞ þANlAðN1

orgÞ

þNNlNðN1orgÞ þ lEEN þMBðN1

orgÞ

þ FcðN1orgÞ � S1ðNHþ4 Þ þ

Xn

j¼1

SjðNjorgÞ

dC1org

dt¼ ExðC1

orgÞ �UptAðC1orgÞ þANlAðC1

orgÞ

þNNlNðC1orgÞ þ C:NElEEN þMBðC1

orgÞ

þ FcðC1orgÞ þ

Xn

j¼1

SjðCjorgÞ

External enzymes

Variations for this pool are given in Eq. (15).

Appendix B: Plant and soil parameters

Plant parameters are given in Table 5, soil

parameters are given in Table 6.

Table 5 Symbols, units and common values of plant parameters

Parameter Symbol Value Reference

Root radius rP 0.06 mm Williams and Yanai (1996) andHøgh-Jensen et al. (1997)

Root elongation gP 3.3 · 10–5 cm–1 Æ s–1 Farrar and Jones (2000)Length between apex and exudation zone BE 0Length of exudation zone LE 8.5 cmLength between apex and absorption zone BA 0Length of absorption zone LA ¥Ammonium maximal absorption capacity ImaxP (NHþ4 ) 1 · 10–9 mmol � cm�2 � s�1 Høgh-Jensen et al. (1997)Half saturation constant for ammonium

uptakeKMP (NHþ4 ) 1 · 10–4 mmol � cm�3 Høgh-Jensen et al. (1997)

Nitrate maximal absorption capacity ImaxP (NO�3 ) 1 · 10–9 mmol � cm�2 � s�1 Høgh-Jensen et al. (1997)Half saturation constant for nitrate uptake KMP (NO�3 ) 1 · 10–4 mmol � cm�3 Høgh-Jensen et al. (1997)

Membrane permeability of organic molecules PermP (Niorg) (1 · 10–7, 0, 0) cm�2 � s�1 Estimated from Nielsen

et al. (1994)C:N of exudates C:Ni

org (80,40,10)Maximal rate of uptake of organic molecules ImaxP (Ni

org) (0, 0, 0)

Half saturation constant for Norg uptake KM P (Niorg) (10–4, 10–4, 10–4)

Multiple values in parenthesis correspond to coefficients for classes of organic matter

Plant Soil

123

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