LETTER Size and functional diversity of microbe populations control plant persistence and long-term soil carbon accumulation

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1 LETTER Ecology Letters, (2005) 8: xxx xxx do: /j x Sze and functonal dversty of mcrobe populatons control plant persstence and long-term sol carbon accumulaton Sébasten Fontane 1 * and Sébasten Barot 2 1 Unté d Agronome, INRA de Clermont-Ferrand, 234 Avenue du Brézet, Clermont- Ferrand, France 2 Laboratore d Ecologe des Sols tropcaux, IRD de Bondy, 39 Avenue H. Varagnat, Bondy, France *Correspondence: E-mal: fontane@clermont.nra.fr Abstract Sol organc matter (SOM) models are based on the equaton dc/ )kc whch states that the decomposton rate of a partcular carbon (C) pool s proportonal to the sze of the pool and the decomposton constant k. However, ths equaton does not adequately descrbe the decomposton of recalctrant SOM compounds. We present an alternatve theory of SOM dynamcs n whch SOM decay rate s controlled by the sze and the dversty of mcrobe populatons and by the supply of energy-rch ltter compounds. We show that the SOM pool does not necessarly reach equlbrum and may ncrease contnuously, whch explans how SOM can accumulate over thousands of years. However, the smulated SOM accumulaton nvolves the sequestraton of avalable nutrents. How can plants persst? Ths queston s explored wth two models that couple the C cycle wth a lmtng nutrent. The frst model consders a sngle type of mcrobe whereas the second ncludes two functonal types n competton for energy and nutrent acquston. The condton for plant persstence s the presence of these two competng mcrobal types. Keywords Carbon cyclng, carbon storage, carbon : ntrogen couplng, mcrobal dynamcs, mcrobal functonal dversty, mneralzaton, nutrent mpact, plant persstence, prmng effect, sol ecosystem functonng. Ecology Letters (2005) 8: xxx xxx INTRODUCTION Sol organc matter (SOM) represents the major carbon reservor of the bosphere atmosphere system and the man nutrent source for plant growth (Falkowsk et al. 2000). Consequently, predctng carbon (C) and ntrogen (N) cyclng through SOM s crucal n order to predct global changes and to allow for the adopton of alternatve agrcultural practces that enable a decrease n the use of mneral fertlzers. Modellng SOM dynamcs s not a novelty n sol scence and many models already exst (Jenny 1941; McGll 1996). However, whlst these models provde accurate smulatons of SOM dynamcs for a varety of land uses (Smth et al. 1997), some emprcal results on longterm SOM dynamcs n natural ecosystems remans unexplaned. For example, t s generally thought that the sol snk capacty s lmted and that old non-dsturbed sols should have reached equlbrum n terms of ther C balance (Lal 2004). Paradoxcally, there has been a steady C accumulaton n the sols of many ecosystems over mllenna (Syers et al. 1970; Schlesnger 1990). Moreover, the mean age of SOM s of the order of decades at sol surface (> 0.15 m) whereas t may be thousands of years old n deeper sol horzons (< 0.5 m) (Martel & Paul 1974; Rumpel et al. 2002). The only way to explan ths result usng current models would be to consder an extreme change n the chemcal composton of SOM along sol profles. However, to date no analyss of the chemcal and physcal composton of SOM along sol profles reveals such an extreme change (Rumpel et al. 2002; Krull & Skjemstad 2003). These ntrgung results stress the need for a better knowledge of the mechansms nvolved n SOM mneralzaton. Sol organc matter s the result of the long-term accumulaton n sols of bochemcally recalctrant C compounds and more or less decomposable compounds that are physcally sequestered by sol mnerals (Torn et al. 1997; Jastrow & Mller 1998). In artfcal culture, the addton of energy-rch substrates enables some mcrobes to

2 2 S. Fontane and S. Barot actvely degrade these recalctrant C compounds wth ther extracellular enzymes (Blondeau 1989). However, energyrch substrates are scarce n natural sol. As a result, the decomposton of SOM should be slow because the acquston of energy from such substrates s low and cannot sustan mcrobal growth (Paul & Clark 1989). Ths lack of mcrobal growth probably explans why mcrobal C does not exceed 1 2% of the total sol C (Paul & Clark 1989). Gven ths energy lmtaton n sols, fresh organc matter (FOM) lke plant ltter may act as a source of energy-rch substrates and ncrease the rate of SOM mneralzaton (Löhns 1926). Ths acceleraton of SOM mneralzaton by the supply of FOM, the so-called Ôprmng effect of organc matterõ (sensu Bngeman et al. 1953), has been dffcult to demonstrate expermentally untl recently (Wu et al. 1993; Fontane et al. 2004a,b). Moreover, the mechansms nvolved n the prmng effect are not fully understood (Kuzyakov et al ; Fontane et al. 2003). The supply of FOM s thought to stmulate SOM mneralzaton through a general stmulaton of mcrobal actvtes. The delvery of energy-rch compounds such as glucose or fructose, however, has no effect on SOM mneralzaton although t strongly stmulates mcrobal growth and respraton (Dalenberg & Jager 1989; Wu et al. 1993). Ths lack of predctve understandng explans why current models do not nclude the prmng effect (McGll 1996). However, the prmng effect has mportant consequences on SOM dynamcs. The supply of FOM can ncrease the mneralzaton of SOM by % dependng on the FOM characterstcs, the addton rate and the sol mneral nutrent status (Wu et al. 1993; Cheng et al. 2003; Fontane et al. 2004b). Increased rates of SOM mneralzaton persst n sol for several months after the complete decomposton of FOM, whch leads wth tme to mportant C losses (Fontane et al. 2004a). Such prmng may even nduce a negatve C balance,.e. the supply of C decreases the total sol C content (Fontane et al. 2004b). Consequently, model predctons may dffer radcally f the prmng effect s taken nto account. Recent advances n our understandng of the mechansms nvolved n the prmng effect provde gudelnes for modellng ths phenomena. These studes provde evdence that the prmng effect depends both on the supply of energy to decomposers, and also on competton between mcrobal functonal types (Fontane et al. 2003, 2004a,b). The supply of FOM not only stmulates the decomposers of SOM, but also stmulates FOM-specalzed decomposers. These FOM decomposers, commonly classfed as r-strategsts, grow quckly and specfcally consume FOM (e.g. Lemogne et al. 1951; Panka 1970). Thus, there are two mcrobal functonal types that compete for FOM, one degradng exclusvely FOM (the r-strategy FOM decomposers) and the other, whle beng able to breakdown FOM, nevertheless manly lves on SOM (the K-strategy SOM decomposers). Based on ths competton for resources, t should be possble to predct the mpact of FOM and sol mneral nutrents on the ntensty of the prmng effect (Fontane et al. 2003). In ths paper, we explore how ncludng the prmng effect n current SOM models could result n qualtatvely dfferent predctons about C and N cyclng. To ths end, we present a theory of SOM dynamcs n whch SOM decay rate s controlled by the sze and dversty of mcrobe populatons and by the supply of FOM. Although some current models already separate mcrobal bomass nto two or more functonal types these bomasses are mostly treated as organc matter pools and are not consdered to control the SOM decay (Jenknson & Rayner 1977; McGll 1996). Our approach uses a seres of mathematcal models of ncreasng complexty to fnd the mnmal set of mechansms requred to account for emprcal evdence of the prmng effect, long-term SOM dynamcs and plant mcrobe coexstence n ecosystems. We frst present two smple C-based models ncludng a sngle type of prmary decomposers (the SOM decomposers): a decomposton model descrbng the dynamcs of the decomposton-mcrobal growth system (model 1); a model of SOM dynamcs that further ncludes SOM synthess (model 2). We show that these models can predct the lack of SOM decomposton n deep sol and the steady accumulaton of SOM n ecosystems. However, the smulated SOM accumulaton nvolves the sequestraton of nutrents, whch s lkely to lead to a nutrent shortage threatenng plant persstence. Ths beng the case, how can plants persst? Ths queston was explored wth two stochometrcally explct models that couple the C cycle (descrbed prevously) wth a lmtng nutrent. We use N as an example of a lmtng nutrent for plants but our models may be applcable to other nutrents such as phosphorus 3 (e.g. Harrngton et al. 2001). The models do not explctly represent the plant compartment but we state that plant persstence mples that the N nput to sol owng to plant FOM losses (plant ltters and excretons) must be compensated by an equvalent output of N from the sol mneral pool. Otherwse, plants could not compensate ther N loss and would dsappear (Tlman 1990). The frst C N model (model 3) consders a sngle type of decomposers whereas the fnal model ncludes two functonal types of decomposers: the SOM decomposers and the FOM decomposers (model 4). We analyse these models and show that the condton for plant persstence s the presence of these two mcrobal types. THE MODELS Defntons of varables and parameters are summarzed n Table 1.

3 1 Modellng long-term SOM dynamcs 3 Table 1 Varables and parameters of the four models Symbol Defnton Dmenson Model 1 C s Carbon stock n sol organc matter (SOM) Quantty of carbon C ds Carbon stock n SOM decomposers Quantty of carbon A Decomposers consumpton rate of SOM Tme )1 r Fracton of decomposer bomass released as CO 2 Tme )1 Fresh organc matter (FOM) carbon flux (Quantty of carbon) (tme) )1 Idem for model 2, and s Decomposers producton rate of SOM Tme )1 Idem for model 3, and C f Carbon stock n FOM Quantty of carbon a Ntrogen : carbon rato n SOM and n decomposers Dmensonless b Ntrogen : carbon rato n FOM Dmensonless k FOM decomposton rate under substrate lmtaton Tme )1 Rate of mneral N dffuson n sol Tme )1 U d Carbon flux assocated wth the decomposton of FOM by SOM decomposers (Quantty of carbon) (tme) )1 U IMS Ntrogen mmoblzaton-mneralzaton flux nduced by SOM decomposers (Quantty of ntrogen) (tme) )1 U Ntrogen that flows nto the ecosystem (Quantty of ntrogen) (tme) )1 U o Ntrogen that flows out of the ecosystem (Quantty of ntrogen) (tme) )1 U up Ntrogen flux assocated wth the ntrogen uptake by the plant cover (Quantty of ntrogen) (tme) )1 Idem for model 4, except k s deleted, and C df Carbon stock n FOM decomposers Quantty of carbon y SOM-decomposer consumpton rate of FOM under substrate lmtaton Tme )1 u FOM-decomposer consumpton rate of FOM under substrate lmtaton Tme )1 U f Carbon flux assocated wth the decomposton of FOM by FOM decomposers (Quantty of carbon) (tme) )1 U IMf Ntrogen mmoblzaton mneralzaton flux nduced by FOM decomposers (Quantty of carbon) (tme) )1 The model of SOM decomposton: model 1 Tradtonal SOM models are based on the frst-order knetcs dc/ )kc whch states that the decomposton rate of a partcular C pool s proportonal to the sze of the pool and the decomposton constant k (McGll 1996). Although ths formalsm seems relevant for easly degradable ltter compounds t s not well suted to descrbe the decomposton of recalctrant SOM compounds because n ths latter case the decomposton rate s lmted by the quantty of ÔenzymesÕ and not by the quantty of ÔsubstratesÕ. Indeed, a substantal amount of SOM s avalable n sols but the low qualty of ths organc matter restrcts mcrobal growth and enzymatc actvtes (Paul & Clark 1989, but see also Schmel & Wentraub 2003). Ths lmtaton by the amount of ÔenzymesÕ s confrmed by experments whch ndcates a hgh acceleraton of SOM mneralzaton after addton of FOM (Wu et al. 1993; Fontane et al. 2004a,b). As SOM decomposton s lmted by the amount of ÔenzymesÕ, the overproducton of enzymes by stmulated decomposers accelerates SOM decomposton. Based on ths lmtaton by the amount of ÔenzymesÕ, we constructed the smplest model of SOM decomposton (Fg. 1a). Sol organc C (C s ) s degraded by the decomposers (C ds ) that are suppled by a flux of FOM from the non-modelled plant compartment ( ). Decomposers respre and de, whch releases CO 2 (r). The rate of SOM decomposton s assumed to be proportonal to decomposer bomass. Thus, the supply of FOM ncreases the decomposer bomass and the rate of SOM decomposton, whch s the prmng effect. The model equatons read as follows: dc s AC ds ; ð1þ dc ds ða rþc ds þ ; ð2þ where A s the rate of SOM consumpton by the decomposers. The model of SOM dynamcs: model 2 Recalctrant compounds of plant and mcrobal orgn are released n sol by sol mcrobes (Jastrow & Mller 1998). These compounds accumulate n sol, whch leads to the formaton of SOM n the long term. SOM may have plant or mcrobal orgns but ths dstncton does not change the

4 4 S. Fontane and S. Barot Fgure 1 Flow dagram of the decomposton model (model 1), the sol organc matter dynamcs model (model 2) and the carbon and ntrogen coupled model (model 3). The three models assume one sngle type of decomposer. The arrows represent the carbon (contnuous arrows) and ntrogen (dashed arrows) flows between compartments. behavour of the model. We gnore ths complcaton and assume that the producton rate of SOM (s) s proportonal to the decomposer bomass. The model equatons read as follows (Fg. 1b): dc s ðs AÞC ds ; ð3þ dc ds ða r sþc ds þ ; where s + r s the turnover rate of decomposers. The C N model of SOM dynamcs wth a sngle type of decomposer: model 3 ð4þ As SOM contans N (Hmes 1997), SOM accumulaton n sol nvolves the sequestraton of N that s usually scarce n sols. Ths could decrease N avalablty for plants, threaten plant persstence n ecosystems and also alter the functonng of decomposers. Indeed, the C : N rato of FOM (plant ltter) s larger than that of decomposers (Ågren & Bosatta 1996). Both because of ths msmatch and because of decomposer respraton, the mantenance of decomposer C : N rato can lead ether to the uptake of mneral N n sol soluton by the decomposers (the mmoblzaton process) or to the release of mneral N (the mneralzaton process) (Ågren & Bosatta 1996). In the frst case, N avalablty n sols can be too low to allow the potental growth of decomposers: decomposers are N-lmted and FOM decomposton s reduced (Recous et al. 1995). Thus, stocks and fluxes n sols depend on mass-balance constran for C and N (Elser et al. 1996; Daufresne & Loreau 2001). Here, we explore how takng nto account the co-lmtaton of mcrobes by ether C or N n a stochometrc (Elser et al. 1996) verson of the prevous model changes the predctons about SOM dynamcs. We also test whether ths thrd model allows plant persstence n ecosystems,.e. whether N nput to sol through FOM can be compensated for by an equvalent output of N from the sol mneral pool. The model s made up of three carbon compartments coupled wth three ntrogen compartments wth constant C : N ratos, plus a compartment for sol mneral N (Fg. 1c). For the readablty of equatons, we express the C : N ratos as N : C ratos. In comparson wth the prevous model, the FOM compartment s taken nto account as FOM s not necessarly degraded by the decomposers and may accumulate when mneral N s scarce. The bomass of decomposers and the SOM pool are assumed to have the same and constant N : C rato (a) (Stevenson 1982; Hmes 1997; Martens et al. 2003). In fact, the N : C rato of decomposers s slghtly hgher than that of SOM but ths assumpton does not change the general behavour of the model and smplfes the readablty of equatons. The N : C rato of FOM (b) s constant and lower than that of decomposers (a). Uptake and release of mneral N from the decomposers are assumed to be controlled only by decomposer homeostass alone. Inputs and outputs of mneral N nto the system are assumed to be constant. U and U o represent the amount of N that flows nto (atmospherc N deposton, symbotc N fxaton) and out of (N leachng, dentrfcaton) the ecosystem, respectvely, and U up represents the N uptake by the plant cover. Because of the strct C and N couplng n the compartments and fluxes, the dynamc equatons for the model can be reduced to four ndependent varables, the stocks of ether C or N n the decomposers, FOM, SOM and the mneral N pool. As our frst two models are C based, we have chosen the C stocks to measure the organc pools: dc s dc f ðs AÞC ds ; U d ; ð3þ ð5þ

5 1 Modellng long-term SOM dynamcs 5 dc ds ða s rþc ds þ U d ; ð6þ dn U U o U up þ U IMs ; ð7þ where C f, U d and U IMs, respectvely, are the amount of C contaned n the FOM compartment, the FOM-carbon decomposton flux, and the N mmoblzaton mneralzaton flux nduced by the mantenance of the C : N rato of SOM decomposers. The mmoblzaton mneralzaton flux U IMs can be determned as the dfference between the organc N avalable for the decomposers and the total N requred for the mantenance of the decomposer C : N rato (Fg. 1c): U IMs aac ds þ bu d asc ds aðac ds þ U d sc ds rc ds Þ; U IMs arc ds þðb aþu d : ð8þ The flux U IMS s negatve when the decomposers mmoblze N and postve when the decomposers mneralze N. In contrast to SOM, energy-rch FOM compounds sustan mcrobal growth and are quckly decomposed when N s not lmtng so that FOM decomposton and decomposer growth are both lmted by the amount of ÔsubstrateÕ (Paul & Clark 1989). Such C lmtaton probably explans why the dc/ )kc functon adequately descrbes the decomposton of FOM. Thus, the decomposers can be ether carbon- or ntrogen-lmted. Under C lmtaton, the decomposton flux U d s expressed by the tradtonal functon, kc f, where k s the rate of FOM decomposton under substrate lmtaton (N n excess). Under N lmtaton, the decomposton flux U d s lmted by the mmoblzaton flux. In ths case, the mmoblzaton flux U IMS )N, where s the rate of mneral N dffuson n sol. Thus, accordng to eqn 8 the decomposton flux U d can be expressed as N þ arc ds a b when SOM decomposers are N-lmted. Lebg s law of the mnmum, expressed n ts smplest way (Grover 1997), determnes whether SOM decomposers are C- or N-lmted: U d Mn N þ arc ds ; kc f a b : ð9þ The C N model of SOM dynamcs, two decomposer types: model 4 Because the prevous model does not allow plant-decomposer coexstence (see the Results secton), a second type of decomposer has been added (Fg. 2). Two populatons of mcrobes are thus competng for FOM and mneral N, one degradng exclusvely FOM (FOM decomposers) and the other degradng FOM and SOM (SOM decomposers) (Fontane et al. 2003, 2004a,b). In all other respects, FOM decomposers are smlar to SOM decomposers n terms of functonng: the two decomposer types have the same N : C rato, a, rate of CO 2 producton, r, rate of SOM producton, s. The model equatons read as follows: dc s dc f dc ds dc df ðs AÞC ds þ sc df ; U d U f ; ða s rþc ds þ U d ; U f ðs þ rþc df ; dn U U o U up þ U IMS þ U IMf ; wth U IMS arc ds þðb aþu d ; U IMf arc df þðb aþu f ; ð10þ ð11þ ð6þ ð12þ ð13þ ð14þ where C df s the C of FOM decomposers, U f the FOMcarbon decomposton flux and U IMf the N mmoblzaton mneralzaton flux nduced by FOM decomposers. Lebg s law of the mnmum determnes whether the two decomposer types are C- or N-lmted: U d Mn N þ arc ds ; yc f a b U f Mn N þ arc df a b ; uc f ; ; ð15þ where y s the rate of FOM consumpton by SOM decomposers and u the rate of FOM consumpton by FOM decomposers under substrate lmtaton (N n excess). Thus, y + u corresponds to the total rate of FOM decomposton under substrate lmtaton (k n the prevous model 3). RESULTS The systems of dfferental equatons defnng the four models were solved to determne the sze of the dfferent compartments at equlbrum. Some compartments actually reach equlbrum, others ncrease or decrease accordng to the constant rates that can be computed.

6 6 S. Fontane and S. Barot Fgure 2 Flow dagram of the carbon and ntrogen model of sol organc matter dynamcs, two decomposer types (model 4). Model 1 The decomposer bomass at equlbrum s obtaned by settng eqn 2 to 0 and dc s ðs AÞCds l U ðs AÞ s þ r A : ð19þ Cds r A : ð16þ In ths case, the rate of SOM decomposton can be determned as dcs ACds A r A : ð17þ The equlbrum value of decomposer bomass must be postve, whch mples A < r (eqn 16). Ths means that decomposers attan equlbrum only f the consumpton of SOM by the decomposers does not compensate for ther turnover rate. If ths condton s not fulflled, the bomass of decomposers and SOM decomposton rate contnuously ncrease untl SOM exhauston. Moreover, as decomposers cannot use SOM as ther sole source of energy, the longterm mantenance of decomposers and SOM decomposton hnge on the supply of FOM (eqns 16 and 17). Wthout a flux of FOM the decomposer bomass drops to 0 and SOM mneralzaton stops. Such a lack of decomposton s known to occur n deep sol horzons despte the avalablty of SOM (Martel & Paul 1974; Rumpel et al. 2002) and has been shown for several sols ncubated for 20 years wthout FOM (Wadman & de Hann 1997). Model 2 At equlbrum (eqn 3) C ds s þ r A ð18þ As n the prevous model, the long-term mantenance of SOM decomposton depends on the supply of FOM (eqn 18). The SOM pool does not reach equlbrum unless s A or 0 (eqn 19). In ths specfc case, the SOM pool at equlbrum ðcs Þ depends on the ntal condtons used. In general although, the SOM pool contnuously ncreases or decreases dependng on whether s ) A s postve or negatve. The values of s and A may depend on many factors affectng mcrobe functonng (temperature, sol mosture and mneralogy) but the energy content of FOM s lkely to be the most mportant factor. For example, FOM wth a hgh lgnn content should have low A value relatve to s. In any case, f decomposers are suppled wth FOM ( > 0) and f the producton of recalctrant SOM compounds s hgher than the consumpton of these compounds by the decomposers (s ) A > 0), the SOM pool ncreases constantly wthout reachng equlbrum. Ths s consstent wth the steady C accumulaton n sols of many ecosystems over mllenna (Syers et al. 1970; Schlesnger 1990). Model 3 Here, we test whether the model allows for plant persstence n ecosystems, that s, whether the N nput to sol va FOM s compensated for by an equvalent output of N from the sol mneral pool (b ) U up 0). When decomposers are C-lmted, the bomass of decomposers (C ds ) and the FOM pool (C f ) reach equlbrum

7 1 Modellng long-term SOM dynamcs 7 Cds s þ r A C f k : ð20þ At ths equlbrum, changes n the SOM pool and the mneral N pool follow constant rates: dc s ðs AÞC ds ðs AÞ s þ r A ; dn U U o U up þb aðs AÞ s þr A : ð21þ Takng the condton of plant persstence (b ) U up 0) nto account, the change n mneral N pool can be determned as dn U U o aðs AÞ s þ r A : ð22þ As n the prevous model, the SOM pool does not reach equlbrum unless s A or 0 (eqn 21). It s also clear that any change n the SOM compartment affects the mneral N compartment because of sequestraton of N n SOM (eqns 21 and 22). If we consder n eqns 21 and 22 that the SOM compartment contnuously ncreases (s > A and > 0) and that the net N supply to the ecosystem (U ) U o ) s very low (Vtousek & Howarth 1991), then the N mneral pool decreases constantly. Thus, when decomposers are C-lmted, a constant accumulaton of SOM leads to the exhauston of sol mneral N and to plant dsappearance. When decomposers are lmted by N, the bomass of decomposers (C ds ) and the mneral N pool (N) reach the equlbrum Cds N aðs AÞ bðs þ r AÞ N U : ð23þ U o U up At ths equlbrum SOM and FOM dynamcs are determned by the followng constant rates dc s U U o U up aðs AÞ bðs þ r AÞ ; dc f U U o U up ðsþr AÞ aðs AÞ bðsþr AÞ : ð24þ Here SOM accumulaton depends on mcrobal parameters and on the amount of mneral N that flows nto and out of the sol (eqn 24). When there s a net mneral N nput nto sol (U ) U o ) U up > 0), SOM accumulates leadng to N sequestraton. When mneral N s scarce (U ) U o ) U up 0), SOM accumulaton and the underlyng N sequestraton cease. In ths case, the SOM pool reaches equlbrum (eqn 24). Note that n ths case the FOM pool does not reach the equlbrum and ncreases contnuously (unless 0) owng to a lack of decomposton. N * > 0 requres U ) U o ) U up > 0 (eqn 23). Ths s the condton n whch the N-lmted decomposers mmoblze mneral N and survve. However, ths s not realstc because net N supply to ecosystems s usually very small relatve to the quantty of N requred by vegetaton (U )U o U up ) (Vtousek & Howarth 1991). Consequently, the exstence of a plant cover (U up > 0) leads to the exhauston of sol mneral N and fnally to the dsappearance of the vegetaton. We conclude that the model cannot account for plant persstence, rrespectve of the nutrtonal state consdered for the decomposers (ether C- or N-lmted). When decomposers are lmted by C, SOM accumulates despte the avalablty of N leadng to a N defct n the sol. When decomposers are lmted by N, SOM accumulaton depends on the avalablty of mneral N. However, by defnton, N-lmted decomposers mmoblze mneral N only. Ths mples that plant N requrements must be met by net N nputs nto a gven ecosystem, whch s not a realstc assumpton. These results show that t s not possble to account for the emprcal evdence of SOM accumulaton and plant-decomposer coexstence by consderng a sngle decomposer type. Model 4 Usng ths model we test whether the ncluson of addtonal functonal types of decomposers allows for plant-decomposer coexstence. Each of the two decomposer types can be ether C- or N-lmted. Thus, four scenaros must be consdered for the analytcal studes (Tables 2 and 3). The two decomposer types are carbon-lmted: case 1 Although two decomposer types are taken nto account, the outcome n ths case s qualtatvely smlar to that of the model wth one decomposer type lmted by C: whether the SOM pool decrease or ncrease depends on FOM-carbon flux and mcrobal parameters, and not on the avalablty of mneral N (Table 3). The smulated SOM accumulaton nduces a steady decrease n N avalablty owng to ts sequestraton n SOM. As the net N supply to ecosystems s usually low (U» U o ) the steady decrease n mneral N wll fnally lead to the exhauston of sol mneral N. The two decomposer types are ntrogen-lmted: case 2 Agan n ths case the result s qualtatvely the same as wth one decomposer type lmted by N: the change n SOM depends on mcrobal parameters and on the amount of mneral N that flows nto and out of the sol, whereas the N mneral pool can reach a steady state (Table 3). However, the system perssts f, and only f, the net N supply to the

8 8 S. Fontane and S. Barot Table 2 Non-trval steady states for the four scenaros of model 4 Decomposer lmtatons FOM decomposers lmted by C SOM decomposers lmted by C FOM decomposers lmted by N SOM decomposers lmted by N FOM decomposers lmted by C SOM decomposers lmted by N FOM decomposers lmted by N SOM decomposers lmted by C ecosystem brngs more N than s absorbed by the plant cover (U ) U o > U up ), whch s unrealstc (Table 2). The SOM decomposers are N-lmted and the FOM decomposers are C-lmted: case 3 As SOM decomposers are lmted by N, an ncrease n N supply (a hgher U for example) should ncrease SOM decomposer bomass. In the present case, an ncrease n N supply leads to a decrease n the bomass of SOM decomposers unless s + r < 0, whch s not bologcally possble. Thus, the combnaton of parameters resultng n ths case should not arse n nature. The SOM decomposers are C-lmted and the FOM decomposers are N-lmted: case 4 Once the plant persstence condton (b ) U up 0) s taken nto account n eqn. (Tables 2 and 3) any change n Equlbrum values Cf Ul y þ u Cdf u ðy þ uþðs þ rþ Cds y ðs þ r AÞðy þ uþ Cdf N as bðs þ rþ Cds N aðs AÞ bðs þ r AÞ N U U o U up 2 Cf ðs þ rþ Cdf u h ðs þ r AÞ U U o U up þ b þ aða sþ h Ara ðs þ rþ ðu U o U up þ b Þþas Ul Cds s þ r Ara C df N C df aðs AÞ bðs þ r AÞ Cds Cf ðs þ r AÞ Cds y h ðs þ r AÞ U U o U up þ b þ aða sþ h Ara ðs þ rþ ðu U o U up þ b Þþas Ul Cds s þ r Ara N as bðs þ rþ Cdf s þ r A the SOM pool depends on the net N balance for the ecosystem alone. Net N nput to the ecosystem (U ) U o > 0) ncreases the bomass of FOM decomposers that are N-lmted (Table 2). As SOM decomposers are lmted by energy, an ncrease n the bomass of FOM decomposers and n ther uptake of FOM leads to a decrease n the bomass of SOM decomposers and, n turn, to a decrease n the rate of SOM mneralzaton. As a result of these changes, the SOM pool ncreases wthout reachng equlbrum (Table 3). When there s net N output from an ecosystem, the bomass of FOM decomposers decreases whereas the bomass of SOM decomposers ncreases, resultng n an ncrease n the rate of SOM mneralzaton. As a result, the SOM pool decreases. These results demonstrate the exstence of a chan of nteractons between the avalablty of N, the relatve abundance of the two decomposer types, the SOM mneralzaton rate and fnally s þ r A

9 1 Modellng long-term SOM dynamcs 9 Table 3 Sol mneral N status and sol C dynamcs for the four scenaros of the model 4 once the decomposers reach equlbrum Decomposer lmtatons Sol mneral N status at steady state of decomposers Sol C dynamc at steady state of decomposers h h yðs AÞ yðs AÞ s þ r A þ su s þ r Ul y þ u dcs s þ r A þ su s þ r U Uo Uup þ bul a Ul y þ u dn FOM decomposers lmted by C SOM decomposers lmted by C h ðu Uo aðs AÞ bðs þ r AÞ þ as bðs þ rþ UupÞ A s s dcs U Uo Uup 2 N FOM decomposers lmted by N SOM decomposers lmted by N U Uo Uup þ bul a dcs aðs AÞ bðs þ r AÞ C ds N FOM decomposers lmted by C SOM decomposers lmted by N U Uo Uup þ bul a dcs as bðs þ rþ C df N FOM decomposers lmted by N SOM decomposers lmted by C the change n the SOM pool. Such lnkages allow for SOM accumulaton to be regulated by the amount of N avalable n sol, whch explans why the mneral N pool reaches an equlbrum (Table 3). The system perssts at steady state when t reaches equatons (Table 2) wth b ) U up 0 (plant persstence condton) and postve values for C f *, C df *, C ds *, N*. C * f > 0 requres s þ r A > 0: ð25þ Thus, the rate of SOM consumpton by SOM decomposers must be lower than ther turnover rate. As shown n model 1, ths condton means that the long-term mantenance of SOM mneralzaton depends on the supply of FOM. N* > 0 requres as bðs þ rþ > 0; ð26þ whch ndcates that the N : C rato of FOM must be suffcently lower n value than that of the decomposer bomass(b a). If ths condton s fulflled, then the populaton growth of FOM decomposers depends on the avalablty of mneral N. Indeed, the N mmoblzaton mneralzaton flux ðu IMf Þ arcdf þðb aþ ð U f Þ ½bðs þ rþ asšcdf s negatve n ths case, whch ndcates that FOM decomposers mmoblze N. Most ncubatons of plant ltter and exudates nduce net N mmoblzaton (Recous et al. 1995; Mary et al. 1996), whch suggests that FOM decomposers commonly depend on mneral N. Ths s supported by experments showng the mportance of gross N mmoblzaton flux n sols (Hart et al. 1994; Mary et al. 1996). Thus, condton (26) seems realstc. Takng nto account the condton of plant persstence (b ) U up 0), Cdf > 0 requres U o U < aða sþ s þ r A : ð27þ The term on the rght refers to the N that flows out of the SOM pool and goes to the mneral pool (Fg. 3, A > s)when the equlbrum bomass of SOM decomposers reaches ts maxmal value ( /s + r ) A). At ths equlbrum pont, FOM decomposers are excluded by a lack of N and full FOM flux s absorbed by SOM decomposers. Thus, the system perssts at steady state f the net N output from an ecosystem (U o ) U ) remans lower than the mneral N producton through SOM mneralzaton. As the mneral N producton through SOM mneralzaton determned by sotopc dluton s commonly larger than the N balance for the ecosystem (Vtousek & Howarth 1991; Hart et al. 1994; Mary et al. 1996), condton (27) s lkely to occur n sols. Cds > 0 requres, U U o < as s þ r : ð28þ

10 10 S. Fontane and S. Barot The term on the rght represents the N that flows out of the avalable pool and goes to the SOM pool (Fg. 3) when the equlbrum bomass of FOM decomposers reaches ts maxmal value ( /s + r). Thus, the system perssts at a steady state f the net N supply to the ecosystem (U ) U o ) remans lower than the mneral N sequestraton through SOM formaton. As ndcated above, the amount of N nvolved n the SOM mneralzaton-formaton turnover s commonly larger than the N balance for the ecosystem (Vtousek & Howarth 1991; Hart et al. 1994; Mary et al. 1996). Thus, condton (28) s lkely to occur n sols. In ths case, the model meets wth condtons of feasblty (Daufresne & Loreau 2001) and stablty (the Routh-Hurwth crtera for local stablty, May 1974) (calculatons not shown). Frst, these results show that t s possble to account for the emprcal evdence of the plant-decomposer coexstence by consderng two major decomposer functonal types,.e. FOM decomposers and SOM decomposers, and ther nteractons wth N. Second, they show that plants and decomposers are able to coexst when SOM decomposers are C-lmted and FOM decomposers are N-lmted (case 4). Thrd, they show that the mechansm of plant persstence s a chan of nteractons between the avalablty of N, the relatve abundance of the two decomposer types, the SOM mneralzaton rate and fnally the change n SOM pool. When mneral N s abundant, SOM mneralzaton s low and the SOM pool ncreases. When mneral N becomes scarce, SOM mneralzaton accelerates and the SOM pool decreases. Ths acceleraton of SOM mneralzaton releases mneral N that becomes avalable for plants. Fnally, our results show that SOM accumulaton depends on the N balance for the ecosystem untl the net N nput becomes saturatng. In ths latter case, FOM decomposers become C-lmted and SOM accumulaton s lmted by FOM-carbon fluxes (results not shown). DISCUSSION Most SOM models assume that SOM decay only depends on the SOM pool and dsregard the roles of the sze and the dversty of mcrobal populatons, that s, the presence of several mcrobal types and ther nteractons. However, experments hghlghtng the mportance of prmng effects of organc matter ndcate that the rate of SOM mneralzaton depends on the sze of SOM decomposer populatons and on the competton for energy and nutrent acquston between several mcrobal functonal types (Fontane et al. 2003; Schmel & Wentraub 2003). Here, we show that models n whch SOM decay s controlled by the sze and the dversty of mcrobes populatons result n qualtatvely dfferent predctons on C and N cyclng and may explan some emprcal results on SOM dynamcs. Three novel predctons (presented below) emerge from our models. Dependence of SOM decomposers (and mneralzaton) on FOM supply Our four models of ncreasng complexty smulate the prmng effect: the delvery of FOM to sol mcrobes ncreases the sze of SOM decomposer populaton and, n turn, the rate of SOM mneralzaton. They also predct that the long-term mantenance of SOM decomposers reles on the supply of FOM. Ths ndcates that wthout FOM supply, decomposers slowly dsappear or become dormant and SOM mneralzaton ceases. Such a predcton explans how the lack of ltter supply n deep sol horzons could lead to a lack of SOM mneralzaton. Ths reconcles the apparently contradctory results of SOM radocarbon datng (assocated wth the tradtonal decomposton equaton dc/ )kc), whch suggest an extreme change n the decomposablty of SOM along sol profles, and those of drect measurements of the composton of SOM, whch do not suggest such a change (Martel & Paul 1974; Rumpel et al. 2002). The C n deep sol horzons could also persst over long-tme scales because ths C s physcally bound to sol mnerals and exsts n forms that decomposers cannot access (Torn et al. 1997). However, our predcton can be tested n the laboratory: f our assumpton s rght, then the supply of FOM to a sol sampled at depth should promote decomposer actvty and mneralzaton of ancent sol C. Such an experment should take care to preserve the physcal structure of the sol. Non-lmted capacty of sols to accumulate SOM Current models generally predct that the SOM pool of old sols have attaned equlbrum. Such predctons result from the use of the tradtonal decomposton equaton to depct SOM mneralzaton. If sol C mneralzaton depends on the sol C pool, then sol C mneralzaton ncreases wth the ncreasng sol C content wth tme untl the C output equals the C nput ndcatng that SOM has attaned equlbrum (Hénn & Dupus 1945). However, when mneralzaton s modelled by an equaton based on the sze of decomposer populatons, the mneralzaton of recalctrant sol C does not ncrease wth the sol C pool. In ths case, the C pool does not necessarly reach equlbrum and may contnuously ncrease (the predcton of models 2, 3 and 4). Ths predcton s consstent wth the steady C accumulaton n sols of many ecosystems for perods of even > years (Syers et al. 1970; Schlesnger 1990). Lmtaton of long-term SOM accumulaton by avalable N Another predcton of our theory s that the accumulaton of SOM n sols depends on the avalablty of N. If one assumes that SOM accumulaton and the underlyng N

11 1 Modellng long-term SOM dynamcs 11 sequestraton occurs rrespectve of mneral N avalablty, then our model 3 shows that ecosystems are very lkely to collapse owng to a N defct for plants. It s obvous that plants and mcrobes coexst n most ecosystems. Ths coexstence s only possble f there s a feedback mechansm controllng the sequestraton of nutrent. Our model 4 shows that such a mechansm could result from a chan of nteractons between the avalablty of N, the relatve abundance of populatons of FOM and SOM decomposers, and fnally the change n the SOM pool. When mneral N s abundant, the model predcts a low rate of SOM mneralzaton and an ncreasng SOM pool. When mneral N becomes scarce n the sol, the model predcts a relatve ncrease n the populatons of SOM decomposers, an acceleraton of SOM mneralzaton and no accumulaton of SOM. Such lnkages are supported by recent experments. Small ncreases n N avalablty change the mcrobal communty structure (Waldrop et al. 2004), decrease the producton of some enzymes nvolved n the degradaton of complex organc matters (Carrero et al. 2000), decrease the SOM mneralzaton rate (Hagedorn et al. 2003), and lead to an ncrease n sol C content (Fontane et al. 2004b). We emphasze that lmtaton of SOM accumulaton by N apples to N-lmted ecosystems and does not concern fertlzed agro systems. Lmtatons of the models Some of the assumptons of the model mght seem unrealstc. A key assumpton s that the nput of FOM to the sol s contnuous. Although ths assumpton seems reasonable n the case of natural sols where the plant cover s mantaned over tme, t does not hold true n the case of cultvated sols. In cultvated sols, the supply of FOM s dscontnuous and sols can be mantaned wthout vegetaton over long perods durng whch sol N s mneralzed and leached. Such dynamc aspects cannot be studed by an analyss at equlbrum. A second key assumpton of our models s that the rate of SOM mneralzaton only depends on the sze of decomposer populatons. In fact, SOM avalablty could also lmt SOM decay, at least n sols extremely poor n organc matter. Future models should take nto consderaton both the SOM pool sze and the mcrobe populaton szes, and ther results should be compared wth expermental data. CONCLUSIONS Despte ts smplcty, our model 4 has potental mplcatons for broader scale processes. Terrestral ecosystems sgnfcantly buffer global warmng by sequesterng a quarter of anthropogenc emssons of CO 2 (0.8 Pg C year )1 ) of whch half results from the accumulaton of refractory SOM substances n sols (0.4 Pg C year )1 ) (Schlesnger 1990; Houghton 2003). The future capacty of terrestral ecosystems to act as a C snk depends on the sol snk potental and the factors controllng sol C accumulaton. Our results combned wth others (Syers et al. 1970; Schlesnger 1990) suggest that the sol snk s potentally unlmted and that the sequestraton of refractory SOM may contnue for mllenna. However, the possble ncrease n C uptake by vegetaton under elevated CO 2 should not ncrease the current SOM sequestraton rate. Indeed, a decrease n sol mneral nutrents s expected as a consequence of a hgher nutrent sequestraton n SOM and a hgher prmary producton (Díaz et al. 1993). Our model 4 predcts that such nutrent defcts wll lead to an ncrease n SOM decomposer abundance and to a lack of SOM accumulaton, whch n turn mantans nutrent avalablty for plants. Fnally, our model predcts that C storage n terrestral ecosystems depends on the ablty of ecosystems to sequester more nutrents. We progressvely made our model more complex n order to fnd the mnmal set of mechansms requred to account for major ecosystem functons. 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