Soil organic matter decomposition driven by microbial growth:

A simple model for a complex network of interactions

Cathy Neill*, Jacques Gignoux

Ecole Normale Supeerieure, Laboratoire d’ecologie, CNRS UMR 7625, 46 rue d’Ulm 75230 Paris cedex 05, France

Received 30 March 2005; received in revised form 5 July 2005; accepted 20 July 2005

Available online 24 August 2005

Abstract

Priming effects are expressions of complex interactions within soil microbial communities. Thus, we aimed at building a microbial

population growth model which could deal with different substrates, resources and populations. Our model divides the decomposition/growth

process at the population level in two stages, mimicking mechanisms taking place at molecular and cellular scales: (1) the first stage is a

reversible process whereby microbial biomass capture their substrate to form a complex within definite proportions; (2) the second stage is

the irreversible rate-limiting utilization of substrate per se. It is supposed to be a first order process with respect to the quantity of complex.

We put these assumptions into equations using an analogy with chemical reactions at equilibrium. We show that this model (1) provides a

mathematical formalism that bridges the gap between first order decay of substrates and Monod kinetics; (2) sets constraints on the possible

combinations of microbial functional traits, yielding microbial strategies in agreement with observations; (3) allows to model both positive

and negative priming effects, and more generally complex interactions between the various components of a soil system. This model is

designed to be used as a kernel in any soil organic matter model.

q 2005 Elsevier Ltd. All rights reserved.

Keywords: Monod kinetics; First order kinetics; Stoichiometry; Colimitation; Multiple limitation; Maintenance; Priming effects

1. Introduction

First order kinetics have long been the mainstay in soil

organic matter models (McGill, 1996) because they are

often good approximations of mass losses in litter bags.

However, litter decomposition takes place in soils where,

through microbial action, it is liable to interact with native

soil organic matter decomposition. These interactions have

been recently experimentally demonstrated using isotope

tracing (for instance Wu et al., 1993; Fontaine et al., 2004b).

In unlabeled soils, any change in unlabeled CO2 respiration

after the addition of a labeled substrate has been termed a

priming effect (Kuzyakov et al., 2000). There is an

increasing number a studies which suggest that priming

effects are ubiquitous, can be of quantitative importance

(Kuzyakov et al., 2000; Fontaine et al., 2004a; Hamer and

Marschner, 2005) and are very variable in intensity and in

0038-0717/$ - see front matter q 2005 Elsevier Ltd. All rights reserved.

doi:10.1016/j.soilbio.2005.07.007

* Corresponding author. Tel.:C33 144 32 38 78; fax:C33 144 32 38 85.

E-mail address: neill@biologie.ens.fr (C. Neill).

direction (positive or negative, see also Hamer and

Marschner, 2002). It seems that priming effects cannot be

accounted for with linear effects and even that their

interpretation may need to take into account antagonistic

effects specific of different microbial functional groups

(Bell et al., 2003; Fontaine et al., 2003; 2004b; Hamer and

Marschner, 2005).

Priming effects are perhaps the most conspicuous reason

why one should want to see soil organic matter models

based on a more mechanistic, microbially-driven treatment

of decomposition, as already advocated by McGill (1996).

But, because decomposition is driven by microbial growth,

features such as microbial stoichiometric and maintenance

requirements also have important consequences on soil

organic matter dynamics. Recent models have introduced a

number of microbial constraints (Gignoux et al., 2001;

Schimel and Weintraub, 2003), but these attempts were not

without parameterization troubles, especially for mainten-

ance rates (Gignoux et al., 2001). Actually, it turns out that it

is not so easy to introduce microbial growth as modeled

by microbiologists in soil organic matter models.

First, just as first order kinetics have been the mainstay

in soil organic matter models, Monod model has been

Soil Biology & Biochemistry 38 (2006) 803–811

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Table 1

Summary of the model parameters and variables

Symbol Meaning

B Microbial biomass concentration

S Substrate concentration

X Complex formed by biomass and substrate

n Stoichiometric coefficient of the substrate in the complex

m First order constant of stage 2 in the model

h Carbon to nitrogen ratio of microbial biomass (mole basis)

Yc Carbon yield: number of units of b formed per mole of carbon

uptaken

Ycmax Growth carbon yield: carbon yield if maintenance is set to zero

Yn Nitrogen yield: number of moles of nitrogen required to form

one unit of biomass

G Instantaneous specific growth rate of microbes on a given

substrate

D Instantaneous specific decay rate of substrate by a given

microbial population

mmax Maximum specific growth rate of microbes

kmax Maximum first order decay rate of substrate

K Affinity of a given microbial population for a given substrate

mt Turnover rate coefficient of biomass

mx Maintenance energy coefficient of biomass

C. Neill, J. Gignoux / Soil Biology & Biochemistry 38 (2006) 803–811804

the mainstay in microbiology (Kovarova-kovar and Egli,

1998). Unfortunately, these two models are incompatible

with each other’s hidden assumptions. Monod model

assumes that the microbial specific growth rate is ultimately

limited, whereas the first order decay rate of the substrate is

not. Indeed, writing that a biomass increment follows a

Monod curve: db=dtZmbðs=KCsÞ means that the first order

substrate consumption rate (1/s)(ds/dt) can increase infi-

nitely as biomass increases. First order kinetics with respect

to the substrate yield just the opposite: if the substrate

concentration is increased, the biomass could potentially

grow infinitely fast. Therefore, these two models seem to be

totally different in essence. Second, later microbial growth

models in microbiology have mainly focused on detailed

intracellular processes (Koch, 1997; Kovarova-kovar and

Egli, 1998), and as such are not suitable for soil modeling.

Third, most microbial growth models have been designed

for suspended cultures growing on soluble substrates,

whereas, in soils, insoluble substrates are predominant and

might lead to different behaviors.

Therefore, the aim of this work was to build a model at the

population or at the community level able to reconcile the

microbiologists’ insights with the soil organic matter

decomposition process. It is not a soil organic matter model

in itself, but is intended to be used as amicrobial growth based

kernel in any soil organic matter model. For that purpose, we

kept it as simple as possible. It is based on a two-stage

formulation of decomposition/growth, leading to two key

assumptions regarding these stages. We give three qualitative

applications of the model that makes it a potentially useful

model. First, we show that the model does bridge the gap

between first order decay and Monod kinetics. Second, we

show that the model yields predictions about microbial

physiology consistent with experimental evidence: this may

help to refine microbial strategies. Finally, we show that the

two simple assumptions of the model make complex

interactions between substrates and microbial populations

possible. In particular, we illustrate the ability of the model to

predict positive as well as negative priming effects.

2. Model description

2.1. One population, one substrate

Notations of variables and parameters are listed in

Table 1. We will first consider one microbial population B

and a single substrate S. We will denote abundances by

small letters. We will express abundances in units of moles

of carbon per kg of soil (C-moles). The model assumes that

decomposition is driven by microbial growth, therefore:

Kds

dtf

db

dt

The model splits the decomposition/growth process into

two stages. The first one is a stage where microbial biomass

must capture enough resources before subsequent proces-

sing. When microbes have collected a piece of substrate, we

will say that they form a complex together. The second stage

is the subsequent utilization of complexed substrate to yield

new biomass.

Specifically, the model is based on two hypotheses.

Hypothesis 1. The first stage is reversible and each unit of

biomass must capture a definite number of units of substrate

before entering stage 2. This definite number, denoted by

the stoichiometric coefficient n, sets when resources are

in sufficient amount for being processed through stage 2.

At any time, we note x the quantity of biomass which has

formed a complex with a quantity nx of substrate. We will

call x the complexed fraction of biomass and bKx the free

fraction. Likewise, nx will be called the complexed fraction

of substrate and sKnx its free fraction.

Hypothesis 2. The second stage is irreversible and rate-

limiting of the whole process. It is a first order process with

respect to x, and its first order constant will be denoted by m.

Concretely speaking, substrates are either soluble or

insoluble. The solubilization step is generally the irrevers-

ible, rate-limiting step of decomposition and growth on

insoluble substrates (Lynd et al., 2002). Then, complexing

an insoluble substrate simply means that microbial cells will

get adsorbed on or attached to their substrate, such as

bacteria on cellulose. Detachment may occur so that it is a

reversible process. In contrast, for a soluble substrate which

can be readily uptaken inside the cell, capturing it is

presumably equivalent to absorbing it into the cell.

Excretion of the substrate as is or as slightly transformed

metabolites is the opposite process. This mechanism is

known to happen and is called ‘overflow metabolism’

(Russell and Cook, 1995). The irreversible, rate-limiting

Fig. 1. Solution of colimitation equation with K/N and YcZ1 (top) and

KZ1 and YcZ1 (bottom).

C. Neill, J. Gignoux / Soil Biology & Biochemistry 38 (2006) 803–811 805

step is presumably the utilization of intracellular molecules

of substrate into metabolic pathways for biosynthesis. As a

result, the complexed state of the substrate is a small

metabolite.

Then, the model gives biomass increments through:

db

dtZmx (1)

If all the biomass has complexed enough substrate, xZb,

and microbes are exponentially growing at specific rate m.

Conversely, if all the substrate is being complexed by

biomass, then xZ(s/v), and, assuming for the moment that

all complexed substrate is ultimately consumed, we have:

ds

dtZKmnx ZKmns (2)

Then, decomposition is first order with respect to the

substrate abundance. But, the model allows for all possible

values of x between those two extreme cases, which leads to

deviations from exponential increase (for biomass) or decay

(for the substrate). We can sum up the model for the

decomposition(growth process of a single population on a

single substrate through writing:

BCnS4X/2BCW (3)

where W stands for waste (CO2, NH4 and organic wastes).

The stoichiometric coefficient v is supposed to depend only

on intensive properties of both biomass and substrate, not on

abundances. Defining h as the constant carbon to nitrogen

ratio of microbial biomass, Yc and Yn as the carbon and

nitrogen yields of microbial population B with respect to

substrate S (i.e. the number of moles of carbon and nitrogen

necessary to build one C-mole of biomass), n as the nitrogen

concentration of the substrate (carbon concentration is one

since substrate abundance is expressed is C-moles), the

stoichimetric coefficient n can be computed in order to fulfill

the stoichiometric requirements of microbes:

nZMax1

Yc

;1

hYnn

� �(4)

From this, if the carbon to nitrogen ratio of the substrate

exceeds the threshold element ratio of microbes, hYn/Yc, it is

the amount of nitrogen which sets v and there will be excess

carbon. We assume that it will be respired through energy

spilling metabolic pathways (Russell and Cook, 1995).

Conversely, if carbon is limiting, excess nitrogen will be

mineralized.

There exist various possible formulations for computing

x, knowing b and s. We will assume that the first stage

reaches its thermodynamic equilibrium because the second

one is a slow process. We use a simplified version of the

mass action law. To the left hand side of the equation, we

put the product of the free fractions because only those are

liable to meet and increase the complexed fraction. To the

right hand side of the equation we put the quantity of

complexed fraction divided by an equilibrium constant, or

affinity, K. This yields:

ðbKxÞðsKnxÞZx

K(5)

K has a dimension of 1/C-moles. We dropped the exponents

usually found in mass action laws because consistency

requires that the solution x of Eq. (5) should not depend on

the unit which was arbitrarily chosen to express our state

variables. The formulation above is invariant with respect to

changes in units.

Eq. (5) is a second order equation, whose solution is

analytically straightforward and has been noted in other

contexts (Koch, 1997; Baird and Emsley, 1999; Lynd et al.,

2002). It is a simple equation for expressing that x is

colimited by b and s (Fig. 1).

2.2. Several populations, several substrates

The model can be generalized to the case where there are

several microbial populations, (Bi)i%n, and substrates,

(Sj)j%p. In this case, we write one Eq. (3) for every possible

interaction between the considered entities. For instance, if

we consider only pairwise interactions, we write:

Bi CnijSj4Xij/2Bi CWij

C. Neill, J. Gignoux / Soil Biology & Biochemistry 38 (2006) 803–811806

and we introduce the affinities Kij and the first order rate

constants mij Mass conservation and mass action laws yield

a system of coupled equations whose unknowns are the xij:

biKX

j

xij

!sjK

Xi

nijxij

!Z

xij

Kij

(6)

where it is apparent that each population competes with

every other for common substrates and that substrates also

‘compete’ with each other for being complexed by any

given population.

We can also consider reactions involving more than one

substrate. The line of reasoning is the same, the only

difficulty here lying in the calculation of stoichiometric

coefficients. For instance, let us consider a possible reaction

between biomass B on the one hand, and substrates Sj and Sk

on the other. We propose that we set stoichiometric

coefficients so that they satisfy the two constraints:

Ycðnj CnkÞR1 hYnðnjnj CnknkÞR1

which express that there must be enough carbon and

nitrogen in the complex to build one C-mole of biomass. A

solution (nj, nk) with equality in both constraints exists only

if the two substrates are such that one has a carbon to

nitrogen ratio higher than the threshold element ratio of the

population whereas the second substrate has a carbon to

nitrogen ratio lower than this threshold.

3. Applications

3.1. Bridging the gap between microbial kinetics

and decomposition kinetics

First, we will consider pure microbial cultures on single

substrates. In the case where the affinity K/N, the value of

x tends towards the smallest of b and ns, leading to first order

kinetics with respect to either b or s. If K is finite, x departs

from its maximum value and the model predicts deviations

from first order kinetics. Specifically, we can consider three

important cases:

– When bOO(s/n), i.e. substrate is limiting,

approximating bKx with b in Eq. (5) leads to

Table 2

Kinetic parameters for microbial cellulose utilization. Specific decomposition rat

Organism Substrate, cultivation mode, t

Clostridium cellulolyticum, anaerobic MN301, continuous, 34 8C

Clostridium thermocellum, anaerobic Avicel, continuous, 60 8C

Fibrobacter succinogenes, anaerobic Sigmacell 20, continous, 39 8

Ruminococcus albus, anaerobic Avicel, continuous, n.a.

Ruminococcus flavefaciens, anaerobic Sigmacell 20, continuous, 39

Trichoderma reesei, aerobic Ball milled cellulose, continu

a Here we reported the maximum observed in the original paper (Peitersen, 19

a reverse Michaelis-Menten formalism: xZ ðbsÞ=

ðð1=KÞCnbÞ.

– When s/nOOb, i.e. biomass is limiting, approxi-

mating sKnx with s in Eq. (5) leads to Monod

kinetics: xZ ðbsÞ=ðð1=KÞCsÞ.

– When the substrate is soluble, and if we assume

that the complexed substrate is intracellular as

mentioned earlier, then the residual measurable

concentration of substrate, sobs, (in, for instance,

the soil solution) is sKnx. Substituting for sobs, in

Eq. (5), we get Monod kinetics again, with respect

to sobs: xZ ðbsobsÞ=ðð1=KÞCsobsÞ.

These three particular cases confer to the model a solid,

well-documented basis, on a large spectrum of values for b

and s. In addition, the model extends decomposition

formalisms and microbial kinetics, and bridges the gap

between them. In light of the model, each of these

formalisms can be seen as valid approximations only at

opposite ends of the range spanned by the amounts of

biomass and substrate: this is no surprise that Monod

kinetics and first order kinetics cannot be applied at the

same time. Besides, the model formalism features a

continuous colimitation between b and s, without any

need to implement threshold values. Therefore, the model

appears as a very natural extension and generalization of

well-known formalisms.

It also brings an important supplementary constraint.

From Eqs. (1) and (2), it follows that m, the first order rate

constant of the second stage is at the same time the

maximum value of two specific rates: the instantaneous

specific decay rate, dZKð1=sÞðds=dtÞ, and the instantaneous

specific growth rate,gZ ð1=bÞðdb=dtÞ (note that here specific

does not refer to the same denominator). We examined data

from continuous cultures of aerobic and anaerobic strains on

cellulose to test this (Table 2, from Lynd et al., 2002).

Within any given experiment, the maximum of g assessed as

the maximum sustainable dilution rate and the mean value

of d calculated from linear regressions over all dilution rates

are quite close to each other.

Usually, decomposition models assign to any substrate a

maximum specific decay rate, say kmax Conversely, let us

introduce the absolute maximum specific growth rate, mmax,

of a given microbial population (where absolute means that

es of cellulose are not necessarily maximum ones.

emperature Maximum net specific

growth rate (hK1)

Specific decay

rate d (hK1)

0.09 0.05

0.17 0.16

C 0.076 0.07

0.095 0.05

8C 0.1 0.08

ous, 30 8C 0.08a 0.1

77), contrary to Lynd et al who reported an extrapolated value.

C. Neill, J. Gignoux / Soil Biology & Biochemistry 38 (2006) 803–811 807

the value is taken over all ossibly observed specific growth

rates, whatever the substrate). What are the relationships

between m, mmax and kmax? m must satisfy m%mmax and

m%kmax. If mZmmax the rate-limiting step is independent of

the nature of the substrate sustaining growth; then it must be

a late step of biomass synthesis. Conversely, if mZkmax, the

rate-limiting step of the substrate consumption is indepen-

dent of the microbial population actually growing on it. So it

must be an early step of substrate degradation. Since, the

rate-limiting step either pertains to the degradation process

of substrate into metabolites or to the process of biomass

synthesis from metabolites, we conclude that mZMin(mmax,

kmax). The model predicts that any given microbial

population may have different maximum specific growth

rates m depending on the substrate it grows on, which is

commonly observed in continuous cultures.

Furthermore, if kmax%mmax, as is presumably the case for

insoluble substrates, the model predicts that mZkmax.

Microbial populations growing on similar insoluble sub-

strates at similar temperatures should display similar

maximum specific growth rates. Data from Table 2 support

this conclusion. Note that the strains differ in their mmax: for

instance the reported mmax for Clostridium cellulolyticum is

0.17 hK1 at 34 8C on cellobiose (Guedon et al., 1999),

whereas Fibrobacter succinogenes can grow as fast as

0.38 hK1 at 39 8C on ball-milled filter paper (Lynd et al.,

2002). Finally, one might be surprised at the fact that

anaerobic and aerobic bacteria may grow at similar specific

rates, despite the fact that the former have three times lower

yields than the latter on cellulose. It is true that anaerobic

bacteria will consume three times as much cellulose as

aerobic ones at similar dilution rates. But, the prediction on

the maximum m of g and d is a different one and does not

depend on yields.

3.2. Maintenance and microbial strategies

Here, we will still consider a single microbial population

B growing on a substrate S. We will examine the effects of

maintenance respiration (which we distinguish from

biomass turnover), as forecast by the model.

We define exogenous maintenance as an exogenous

substrate consumption, which is respired to provide energy

for maintenance related functions; endogenous maintenance

means that maintenance related functions are carried out

using energy derived from recycling of preexisting biomass.

It requires an autolytic mechanism.

In the model, endogenous maintenance does not have any

effect upon decomposition/growth other than decreasing

microbial biomass. But exogenous maintenance has entirely

different consequences. For a microbial population B with

an exogenous maintenance, some of the carbon contained in

the complexed substrate must be assigned to maintenance.

Let Ycmax denote the growth yield, i.e. the yield that would

be observed had B have no maintenance requirements.

From mass conservation we must have:

nxRx

Ycmax

Cmxb (7)

where mx stands for the maintenance coefficient. Hypothesis

1 tells us that, should too many substrate be complexed by b,

it could be released, as is or as an intermediate metabolite.

But, it sets a definite maximum to the amount of substrate

that can be complexed by one unit of biomass. As a result,

the model predicts that there is a lower limit to the

complexed fraction of biomass, which enables growth.

Rearranging Eq. (7) yields:

x

bR

1

m

mx

ðnK1=YcmaxÞ

This minimum fraction is inversely proportional to the

maximum specific growth rate, m, so exogenous mainten-

ance must have been selected only for those microbes

which are able to grow fast (high mmax)on labile substrates

(high kmax). Otherwise, it would more than frequently

impede growth. Therefore, the model suggests that

exogenous maintenance should be associated with r

strategists, and endogenous maintenance with K strate-

gists. It is presumably among slow growing Basidiomy-

cetes or Ascomycetes that K strategists are to be found.

These fungi constantly grow and forage for food

throughout the soil. This seems only possible with some

endogenous maintenance. Fungi are known to be able to

autolyse their older hyphae and reallocate nutrients over

long distances, to the tip of growing hyphae (Jennings and

Lysek, 1999). In contrast, most bacteria do not autolyse

(Koch, 1997) and display an exogenous maintenance

(Russell and Cook, 1995).

The model also predicts that neither growth nor

maintenance will take place below a threshold amount of

complexed biomass. This implies that maintenance energy

ensures growth related functions, which may be cut down

when no growth is possible. Reported important mainten-

ance functions in bacteria are indeed growth related: wall

lysis so that the cell volume may expand (Mitchell and

Moyle, 1956), ions fluxes to maintain the membranne

potential, which many bacteria let decrease as soon as

exogenous substrates are depleted (Russell and Cook,

1995). Also, Button (1985) showed that there was a

threshold for substrate uptake in seawater. According to

Russell and Cook (1995), in bacteria, ‘maintenance should

be used only to define growth when most of the cells in the

population are capable of growing’. When no growth is

possible, bacterial cells can display a quiescent but neither

sporulated nor encysted state (Koch, 1997). In this state,

they can slowly catabolize small energy reserves, a process

which has been termed endogenous metabolism but which

should not be confused with endogenous maintenance. Its

rate is much lower than that of maintenance energy and it

‘should be defined as a state when no net growth is

possible’ (Russell and Cook, 1995). Thus, in bacteria,

Table 3

Parameters values for the simulation of priming effects

Parameter symbol Values

b 0.04 C-mol kgK1, soil

mmax 0.04 hK1

mt 0.001 hK1

mx 0.25

Yc 0.4

s1 0.8 C-mol kgK1 soil

kmax1 0.01 hK1

Ks1 0.05

s2 0.04 C-mol kgK1

kmax2 0.05/0.01/0-005 hK1

Ks2 1000

C. Neill, J. Gignoux / Soil Biology & Biochemistry 38 (2006) 803–811808

maintenance appears to be a truly growth related function

and, just as growth, requires a minimum amount of

exogenous substrate.

We can also see that the stoichiometric coefficient v

should be as large as possible to lower the amount of

complexed biomass required to trigger activity. From Eq.

(4), Yc should be as small as possible. So the microbial

threshold element ratio is shifted up by exogenous

maintenance whereas that of microbes with an endogenous

maintenance should be comparatively lower. This is

consistent with (1) an adaptation of r strategists as

consumers of nitrogen depleted substrates and fungal K

strategists as consumers of nitrogen-rich humus; (2) a

compensation of r strategists (bacteria and sugar fungi)

having a nitrogen-rich biomass (h%6) when fungal K

strategists display higher carbon to nitrogen ratios

(10%h%15).

3.3. Modeling priming effects

We will now consider a system with one microbial

population B and two substrates S1 and S2. S1 is the native

substrate of population B until S2 is added to the system. S2is labeled so that one can track the origin of the CO2 respired

by B. Any change in S1 mineralization by B after addition of

S2 has been termed a ‘priming effect’, where we allow for

positive as well as negative effects. We will assume that B

has an endogenous maintenance.

Now, the model predicts that before the addition of S2, a

certain amount of b, say x1, will be complexed to S1. If the

affinity K1 of B for S1 is finite, then x1 will be smaller than b

and s1/v1. Because the first stage is reversible (Hypothesis

1), B can dissociate from S1 upon addition of S2, especially

if B has a high affinity K2 for S2 or if S2 is added in

substantial amounts. This will result in a negative priming

effect. But, the addition of S2 will presumably enhance

microbial growth, and the newly formed biomass may in

turn complex again with S1, especially if all S2 is already

being complexed or when S2 becomes exhausted. Since, x1did not reach its maximum value before S2 addition, an

increase in b may result in a higher x1 than what was initially

the case. Then the model will predict a positive priming

effect.

We can illustrate the behavior of the model numerically.

We considered a single fungal population whose character-

istics were those of slow growing K strategists (Baath, 2001;

Henn et al., 2002, see Table 3). Quantities were set

according to Fontaine et al. (2004b), except for mineral

nitrogen, considered as non-limiting. Note that due to poor

affinity, the initial specific decay rate of organic matter

approximated 2!10K5 hK1 (half life: 4 a). Because

microbes had a mmax of 0.04 hK1, more labile substrates

than cellulose, i.e. kmaxR0.05 hK1, would not be decom-

posed by them at higher rates than mmax.

We computed the dynamics of these experiments using

the following system of ordinary differential equations:

db

dtZm1x1 Cm2x2Kmtb (8)

ds1dt

ZKm1

x1yc

C ð1KmxÞmtb (9)

ds2dt

ZKm2

x2yc

(10)

dw

dtZ

ð1KycÞ

ycðm1x1 Cm2x2ÞCmxmtb (11)

where w stands for the respired CO2. The concentrations x1and x2 were determined from the system 6 after

linearization. Linearization was a good approximation and

allowed a straightforward numerical computation. We

plotted the fraction of CO2 respired from either substrates

(Fig. 2). All substrates induce a negative priming effect at

first. The more recalcitrant the substrate, the longer lasting

the negative priming. When a substrate is exhausted, the

microbes shift to native organic matter, thus inducing a

positive priming effect.

A number of studies have conclusively shown the

existence of positive and negative priming effects in soils,

whether by adding carboneous or nitrogenous substrates

(reviewed by Kuzyakov et al., 2000). The hypotheses listed

in Kuzyakov et al. (2000) correspond to the mechanisms

predicted by the model, i.e. preferential substrate utilization

for negative primings and biomass increase for positive

ones. The results of our simulation find some support in the

experiments of Hamer and Marschner (2002, 2005) who

found that catechol, a phenolic compound, was more liable

to induce negative priming effects on lignin, peat and soils

than more labile substrates. The quantitative importance of

priming effects in natural systems not only depends on the

quality of incoming substrates but also on the time scale

considered and on the frequency of substrate inflow. From

our simulation, we may conjecture that with a periodic

inflow of S2 of 14 days or so, S1 mineralization will be

dramatically altered in the long term compared to a situation

where no interaction is taken into account. Note, though,

that here we have considered only one microbial population

Fig. 2. Unlabeled soil respiration rates and microbial biomass after addition

of a labeled substrate. Labeled respiration rates are not shown as they

featured classical single peaked curves. The solid line represents the control

treatment (no addition). Other lines feature variables after addition of three

types of substrates: substrate 21 has kmaxZ0.05 hK1; substrate 22 has kmax

0.01 hK1; and substrate 23 has kmaxZ0.005 hK1.

C. Neill, J. Gignoux / Soil Biology & Biochemistry 38 (2006) 803–811 809

and that antagonistic effects of the quality and of the

frequency of incoming substrates on the resulting priming

are to be expected, especially if one considers microbial

competition (Fontaine et al., 2003).

4. Discussion

4.1. Comparison with other microbial growth models

Although Monod kinetics have remained the mainstay in

microbial physiology and ecology, a number of attempts

have been made to carry out more detailed and mechanistic

models. Some models have tried to solve for growth fluxes

by considering the whole set of enzymatic reactions along

the metabolic chain (Metabolic control analysis, Kacser and

Burns, 1973). This approach cannot be reasonably extended

to a population or community level. Others have focused on

the analysis of just the initial steps bringing substrates into

the metabolism of the cell, leading to a two-stage uptake

formulation: reversible uptake followed by irreversible

enzymatic utilization. Independent derivation of the same

second order equation giving the uptake flux of one cell

were made by different workers (reviewed by Koch, 1997),

and this equation is essentially the same as the solution of

Eq. (5), except that it has been used at the cellular level:

instead of using the total quantity of biomass, they have

used the total quantity of substrate carriers present at the

surface of the cell, and no stoichiometric coefficient were

introduced. These models proved more accurate than the

Monod model (Koch, 1997). Our model really follows the

same line of reasoning, but we applied the corresponding

mechanisms at the population level, and we extended it to

insoluble substrates, and other substrates where the rate-

limiting step is located uphill uptake along the chain.

Therefore, the first reversible step is not necessarily uptake.

But it is most important that it be reversible, because this

feature allows growth regulation by microbes.

The two-stage mechanism hypothesized here also

resembles that of a single enzymatic reaction, but our

model differs from the concept of Synthesizing Unit of

Kooijman (2000). Kooijman considers that intermediate

states are at steady-state and do not build up, so he

advocates for the use of fluxes rather than states. We

consider states rather than fluxes because we assumed that

the intermediate state just before the rate-limiting step does

build up. Furthermore, he also argues that enzymes do not

dissociate with their substrates, whereas it is a key

assumption of our model. Logically then, the mathematical

formulations of the two models are quite different.

4.2. Comparison with other soil organic matter

model kernels

Although first order kinetics have remained the mainstay

in soil organic matter models, some important aspects of

microbial physiology and growth have progressively been

included in recent models. The first one is microbial

stoichiometry. Thresholds have been introduced to decide

whether carbon or nitrogen, or possibly another nutrient,

was limiting for organic matter decomposition. But usually

these thresholds do not alter the decay rates of soil organic

matter pools, they only limit microbial growth through

reduced substrate utilization efficiency (Franko, 1996; Li,

1996; Molina, 1996; Schimel and Weintraub, 2003 but see

Gignoux et al., 2001). Our model also introduces such a

threshold in Eq. (4), but the substrate C to N ratio not only

affect substrate utilization efficiencies but also their decay

rates, since an increase in n will decrease the quantity of

complex, hence the specific decay rate d. Also the fate of

excess nutrients differs between models. This is an

important issue given that it might represent a significant

flux. Excess nitrogen is usually mineralized, not stored. We

assumed the same for excess carbon because bacteria have

limited ability for storage and accumulation of intracellular

C. Neill, J. Gignoux / Soil Biology & Biochemistry 38 (2006) 803–811810

metabolites could even be poisonous for them (Russell and

Cook, 1995; Koch, 1997). An increasing number of studies

have pointed out that excess energy was spilled through

futile cycles (reviewed by Russell and Cook, 1995).

A second feature of microbially mediated decomposition

is maintenance. In light of the model and given the current

debate regarding the relative functional importance of r

versus K strategists, or bacteria versus fungi, maintenance

type may be of particular relevance. To date, there seems to

be an important bias regarding maintenance. First, to our

knowledge, all models or experimental settings consider

only one possible maintenance type, either exo-or endogen-

ous. We think that this might be a serious shortcoming if the

two actually occur at the same time in any soil. Second,

modeling works are biased towards endogenous mainten-

ance and experimental settings towards exogenous main-

tenance. Very few of the models we have examined

explicitly assume that maintenance is exogenous or is a

growth related process (Gignoux et al., 2001; Schimel and

Weintraub, 2003). On the contrary, many models account

for maintenance as a constant fraction of biomass turnover

(Powlson et al., 1996). This amounts to assume an

endogenous maintenance, although it is not always stated

so (authors sometimes refer to cannibalism process by other

microbes). This bias may be due to the fact that endogenous

maintenance is far simpler to implement in a model. In

contrast, experimental settings usually consider that

maintenance is exogenous, may be because fast-growing

bacteria have been much more studied than slow growing

fungi. For instance, the fact that Anderson and Domsch

(1985) sought to measure maintenance rates through

glucose amendment, and also that this led to a technique

for measuring and analyzing microbial biomass (Anderson

and Domsch, 1978; Stenstrom et al., 2001) is of

significance.

Several studies have shown that in some cases, the

primed CO2 came from native microbial biomass. Earlier

hypotheses were that this apparent priming was due to an

enhancement in microbial turnover or death and their

subsequent mineralization (Dalenberg and Jager, 1989; Wu

et al., 1993). Then later authors have suggested that it was

due to endogenous metabolism in bacteria (De Nobili et al.,

2001; Bell et al., 2003). We suggest that it might as well be

the consequence of an increase in fungal biomass, hence an

increase in their endogenous maintenance respiration. This

is all the more plausible that continuously foraging fungi

could indeed be those that stay alert all the time in soils and

could preempt scarce resources from perhaps not dormant,

but certainly more demanding bacteria.

Finally, as for biomass-dependence of decomposition

itself, none of the models we have been able to examine so

far (1) departs from an irreversible process which is an

increasing function of biomass; (2) introduces the sup-

plementary constraint mZMin(mmax, kmax) The latter

constraint is a not so intuitive prediction of our model.

But, in practice, when it comes to model the decomposition

of recalcitrant substrates, it amounts to taking mZkmax.

However, it might be important to consider when one

studies microbial competition for the decomposition and

uptake of a labile substrate. The former feature of other

models is what, in our view, makes them unable to model

negative priming effects, not to mention a continuous

transition between positive and negative priming effects, as

a function of all the abundances of all the substrates and the

microbial populations considered in a given soil system.

4.3. Conclusion

Our model rests on two assumptions from which result a

series of qualitative predictions that find some experimental

support in the literature. There exist various possible

mathematical formulations of the model but it is its

description of the mechanisms involved in the decom-

position/growth processes that matters. As such, the model

can be applied as a kernel in any decomposition model

which provides some implementation of other aspects not

addressed here such as organic matter compartmentaliza-

tion, fate of microbial turnover, change in quality as

decomposition proceeds.In a forthcoming paper, we test the model against data

from cellulose continuous cultures (Neill and Gignoux,

2005). Current work is being carried on to parameterize and

test the model on data from priming effects experiments.

Acknowledgements

We thank Sebastien Barot, Mehdi Cherif, Sebastien

Fontaine, Gerard Lacroix and two anonymous reviewers for

helpful comments on an earlier version of the manuscript.

This work was supported by the French government,

ministry of Research as a part of the Continental Biosphere

National Program (PNBC), and from the GlobalSav project,

funded by the ‘ACI Ecologie quantitative’.

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