Priming effect and microbial diversity in ecosystem functioning and response to global change: a modeling approach using the SYMPHONY model

Integration of the priming effect (PE) in ecosystem models is crucial to better predict the consequences of global change on ecosystem carbon (C) dynamics and its feedbacks on climate. Over the last decade, many attempts have been made to model PE in soil. However, PE has not yet been incorporated into any ecosystem models. Here, we build plant/soil models to explore how PE and microbial diversity influence soil/plant interactions and ecosystem C and nitrogen (N) dynamics in response to global change (elevated CO2 and atmospheric N depositions). Our results show that plant persistence, soil organic matter (SOM) accumulation, and low N leaching in undisturbed ecosystems relies on a fine adjustment of microbial N mineralization to plant N uptake. This adjustment can be modeled in the SYMPHONY model by considering the destruction of SOM through PE, and the interactions between two microbial functional groups: SOM decomposers and SOM builders. After estimation of parameters, SYMPHONY provided realistic predictions on forage production, soil C storage and N leaching for a permanent grassland. Consistent with recent observations, SYMPHONY predicted a CO2‐induced modification of soil microbial communities leading to an intensification of SOM mineralization and a decrease in the soil C stock. SYMPHONY also indicated that atmospheric N deposition may promote SOM accumulation via changes in the structure and metabolic activities of microbial communities. Collectively, these results suggest that the PE and functional role of microbial diversity may be incorporated in ecosystem models with a few additional parameters, improving accuracy of predictions.


Introduction
The priming effect (PE) corresponds to the acceleration of mineralization of recalcitrant soil organic matter (SOM) after addition of fresh organic matter (FOM) to soil (Bingeman et al., 1953).This acceleration enhances CO 2 emissions from SOM mineralization by 12 to 400% compared to soil without FOM addition (Wu et al., 1993;Cheng et al., 2003;Fontaine et al., 2004b).Strong and persistent increases in CO 2 emissions may lead to a negative soil C balance, reducing the soil C stock to below initial values (Fontaine et al., 2004a,b;Dijkstra & Cheng, 2007).Furthermore, the response of ecosystem C fluxes to global change has been shown to be controlled by PE intensity (Heimann & Reichstein, 2008).For example, the lack of SOM accumulation in ecosystems exposed to elevated CO 2 has been attributed to microbial priming of SOM (Hoosbeek et al., 2004;Talhelm et al., 2009;Drake et al., 2011;Iversen et al., 2012).These recent advances on PE indicate the need for a revision of current models that simulate the decomposition of SOM with first-order kinetics, considering only SOM pool size and environmental factors (Jenny, 1941;McGill, 1996).
Over the last decade, many attempts have been made to model PE and its consequences for soil C and nitrogen (N) cycles.It is remarkable that all these attempts have focused on building alternative models of SOM dynamics rather than integrating PE into existing models (Schimel & Weintraub, 2003;Fontaine & Barot, 2005;Neill & Gignoux, 2006;Blagodatskaya et al., 2010b;Guenet et al., 2010), likely because the latter approach requires changes in the core structure of current models that are relatively complex (many SOM compartments and soil processes are modeled) (McGill, 1996).Alternative models simulate the PE by considering one or several pools of microbial biomass that are linked to SOM decomposition rate using linear (Fontaine & Barot, 2005;Blagodatskaya et al., 2010b) or nonlinear saturating equations (Gignoux et al., 2001;Schimel & Weintraub, 2003).Some models also explicitly consider the stoichiometric constraints of microbial biomass (Schimel & Weintraub, 2003;Fontaine & Barot, 2005) and the interactions between distinct microbial functional groups to simulate the decrease in PE after supply of mineral nutrients to soil microbes (Fontaine et al., 2004b;Allison et al., 2008).These models have improved our understanding of the molecular, cellular, and microbial population-scale mechanisms at play and are able to predict PE in soils incubated with different C substrates and N availability (Neill & Gignoux, 2006;Blagodatskaya et al., 2010b;Neill & Guenet, 2010).However, the common missing point in all of these models is the plant compartment.The next step is to build a PE model taking into account soil/plant interactions and their feedback to C and N cycles.
Some experimental studies on PE suggest that links between plant and SOM decomposers are bidirectional.Plants stimulate SOM decomposers through deposition of energy-rich C substrates in rhizosphere (Cheng et al., 2003;Dijkstra & Cheng, 2007;Shahzad et al., 2012), whereas stimulated SOM decomposers increase gross N mineralization (Dijkstra et al., 2009(Dijkstra et al., , 2011) ) and subsequent plant N uptake.However, plant supply of C to soil decomposers can also reduce N availability for plants.Indeed, certain microbial communities immobilize N from soil solution to maintain their C/N ratio (Recous et al., 1995;Mary et al., 1996) because they are not able to mineralize SOM (Fontaine et al., 2003) or they prefer to absorb this readily available N instead of mineralizing SOM (Kuzyakov et al., 2000) which is an energy-consuming process (Fontaine et al., 2007).Part of the immobilized N is then sequestered in SOM over tens or hundreds of years (Martel & Paul, 1974) before its release by microbial mineralization (Mary et al., 1996).Consequently, the availability of N for plants depends on complex microbial mechanisms that control the N release/sequestration balance in SOM.
Recent studies report an indirect control of the N release/sequestration balance by plant uptake of mineral N (i.e., Inselsbacher et al., 2013).For example, under elevated CO 2 , plants increase their N uptake, which in turn intensifies SOM mineralization (N release) (Carney et al., 2007;Drake et al., 2011).In contrast, a reduction in plant N uptake in response to plant clipping decreases SOM mineralization leading to N sequestration (Shahzad et al., 2012).These results suggest that soils function as a bank of nutrients for plants, releasing nutrients from SOM when plant N uptake is high and sequestering mineral nutrients when plant N uptake is low.As the availability of mineral N for microorganisms drives PE intensity and N mineralization (Fontaine et al., 2004b), it has been suggested that PE could explain this bank functioning of soils (Fontaine et al., 2011).The integration of plants in PE models is, therefore, needed to better understand the 'bank mechanism' and its consequences for ecosystem function.Moreover, as this 'bank mechanism' may be sensitive both to mineral N availability and to atmospheric CO 2 that are currently increasing at a global scale (Barnola et al., 1983;Keeney & Hatfield, 2008), such a model could lead to new predictions on the ecosystem response to global change.
The objectives of this modeling work were to: (1) build a plant/soil model including the PE; (2) determine the consequences of this inclusion for plant/soil interactions and ecosystem C and N dynamics; (3) parameterize the model and test its ability to predict forage production, soil C storage and N leaching in a permanent grassland; (4) explore the role of PE and microbial diversity on ecosystem responses to rising atmospheric CO 2 and N depositions.To this end, a plant compartment was integrated in two existing models of SOM dynamics including the PE: one considers a single microbial type, the second considers two distinct microbial functional groups (Fontaine & Barot, 2005).The use of these two models allowed us to test the idea that interactions between functionally distinct microbial groups control plant/microbe coexistence and ecosystem properties as crucial as SOM accumulation.Models were analyzed mathematically at steady state, through simulations and comparison with pasture observations.We emphasize that this work is an exploration of alternative mathematical formulations that can be used to integrate the PE in existing models, and does not call into question the relevance of these models.

Plant/soil model with a single microbial type
The model consists of one plant compartment, three soil organic C pools and one pool of mineral N (Fig. 1a; Table 1).The plant compartment supplies the soil with a flux of fresh organic C m p C p where C p is the plant C and m p is the rate of plant C deposition (plant tissue turnover and root exudation).
A fraction e p of plant biomass is exported out of the ecosystem owing to herbivory or plant harvest.A fraction r p of plant C is released as CO 2 owing to respiration.Plants take up mineral nitrogen (u up ) and atmospheric CO 2 (u ph ) to form biomass with constant N : C ratio (b).At each time step, the plant N uptake (u up ) is determined by the maintenance of plant N/C ratio as follows: Plant growth can be limited by C or N.Under C limitation, plant growth is limited by the availability of atmospheric CO 2 or light.In this case, the photosynthesis flux (u ph ) is expressed by the function kC a where C a is the atmospheric CO 2 concentration and k is the fixation rate of C depending on light availability.Under N limitation, plant growth is limited by the availability of mineral N. In this case, the photosynthesis flux (u ph ) is limited by the absorption flux u up that is expressed as eN where e is N absorption rate of plant.Thus, according to Eqn (3), the photosynthesis flux u ph is calculated as follows: Liebig's law of minimum determines whether plant is C or N limited: Input of N into the ecosystem (u i , atmospheric N depositions and fertilization) is considered constant.N losses (leaching and dentrification) from ecosystem are modeled by the function lN where l is the N loss rate.
The soil C pools consist of recalcitrant organic C (C s ), fresh organic C (C f ), and decomposer C (C ds ) (Fig. 1).The N/C ratios of C s and C ds are assumed constant and equal to a.The N/C ratio of C f is assumed to be same as that of plant (b).Decomposers mineralize C s and C f together because the recalcitrant C s is not a sufficient source of energy for decomposer needs (Fontaine & Barot, 2005;Fontaine et al., 2007).A fraction (r) of decomposer biomass is released as CO 2 due to respiration and turnover.Decomposers contribute to the formation of C s by releasing recalcitrant organic compounds (s).
Uptake or release of mineral N by the decomposers (u ims ) is determined by the maintenance of decomposers N/C ratio (a): The immobilization/mineralization flux (u ims ) is positive in the case of net N mineralization and is negative in the case of net N immobilization.
In line with results of previous PE studies, the decomposition of C s is considered to be limited by decomposer biomass and activity.Accordingly, the decomposition of C s is modeled by the equation AC ds where A is the rate of SOM consumption by decomposers.The availability of SOM, C s, could also limit decomposition in soils with low SOM contents (Wutzler & Reichstein, 2008).The effect of C s limitation on model In contrast to recalcitrant soil C, the decomposition of easily degradable fresh C is limited by the amount of C when N is not limiting for decomposers (Paul & Clark, 1989).Thus, the decomposers can be either C or N limited.Under C limitation, the fresh C decomposition flux u d is expressed by the traditional function yC f where y is the decay rate of C f .Under N limitation, the decomposition flux u d is limited by the immobilization flux ÀiN where i is the immobilization rate.Thus, according to Eqn (8), the decomposition flux u d can be expressed as follows: Liebig's law of the minimum determines whether decomposers are C or N limited: Because of the strict C-N coupling in the compartments and fluxes, the differential equations for the model can be reduced to five independent variables: Plant/soil model with two microbial functional types Two microbial functional groups are distinguished in this model (called SYMPHONY hereafter in reference to the organized interactions between plant and decomposers; Fig. 1b; Table 1).As in the previous model, one group of microorganisms, called SOM decomposers (C ds ), degrades recalcitrant SOM by using fresh C as an energy source.A second group of decomposers only decomposes fresh C (Fontaine et al., 2003).This group favors SOM accumulation because it releases recalcitrant SOM compounds without mineralizing them.This group is referred to as SOM builders (C df ).Despite their contrasting roles regarding the SOM pool, SOM builders and SOM decomposers have similar characteristics: the two decomposers have the same N/C ratio (a), rate of CO 2 production (r), rate of SOM production (s) and can be limited by C or N.For C or N limitation of SOM builders, fresh C decomposition flux (u f ), and mineralization/immobilization flux (u imf ) were calculated with the same approach as in the previous model.The differential equations of the model read as follows: where u is the rate of FOM consumption by SOM builders under C limitation.The fluxes u d , u ims , u ph, and u up are expressed by the same equations as in the previous model.

Mathematical analysis of models at steady state
The two models were mathematically analyzed at steady state of all model compartments (differential equations were set to zero) except the SOM pool that does not necessarily reach equilibrium (see criteria below).The feasibility of steady states was determined by studying the conditions to obtain positive values for ecosystem compartments.Moreover, the models must be able to account for the priming effect and a number of key ecosystem properties used as criteria for model evaluation: 1 The coexistence of plant and decomposers.2 Ecosystems must be able to resist to a long-term (10 years) net nutrient output.Indeed, several long-term agro-ecological experiments (LTAE) have shown that grasslands and cultivated soils persist even when they are exposed to net nutrient outputs (biomass harvest and no fertilization) over 10 years (Kofoed & Nemming, 1976;Dyke et al., 1983;Mattsson, 1987b;Rasmussen et al., 1998).During this period, SOM serves as a reserve of nutrients for plants allowing ecosystem persistence despite the large quantity of nutrient exported (Kofoed & Nemming, 1976;Dyke et al., 1983;Mattsson, 1987b;Rasmussen et al., 1998).This soil process contributes to the stability of natural ecosystems because N inputs and N outputs are highly variable and can sometimes lead to a negative balance (Vitousek & Howarth, 1991;Rasmussen et al., 1998).In our model, ecosystem resistance to net nutrient output implies that compartment values must remain positive when u i À lN À be p C p < 0 (Fig. 1). 3 The continuous accumulation of SOM in undisturbed soils (grassland and forest soils) when there is net nutrient input to ecosystems (Syers et al., 1970;Schlesinger, 1990;Knops & Tilman, 2000), i.e., there is no theoretical limit to soil C accumulation (Reichstein et al., 2009).In our model, this property implies that dC s /dt must be > 0 when u i À lN À be p C p > 0 where u i is the N input to ecosystem, lN is the N leaching and be p C p is the N output from the ecosystem due to plant exports (herbivore consumption, plant harvest).4 Eventual steady state for SOM pool, especially in agricultural systems where N inputs balance N outputs (Johnston et al., 2009).In our model, this property implies that dC s /dt = 0 in some conditions.

Model parameterization
The model including the two microbial populations SYM-PHONY was the sole model capable of accounting for all above criteria.Therefore, SYMPHONY was parameterized to (1) study the mechanistic basis of the bank functioning of soils, (2) simulate the compartments and fluxes of study grassland, and (3) predict the grassland response to rising atmospheric CO 2 and N inputs to ecosystem (fertilization, atmospheric N depositions).Model parameters were estimated from both published studies and specific measurements made at a studied experimental site (Table 1).The site is a temperate permanent grassland located at 1040 m in France (Laqueuille, 45°38′N, 2°44′E).Mean annual precipitation and temperature are 1200 mm and 7 °C, respectively.The site is divided into two adjacent pastures grazed by heifers but at different intensities.Intensive pasture is adjusted to a mean stocking rate of 1 living stock unit (LSU) ha À1 yr À1 and is fertilized with 190 kg N ha À1 yr À1 (ammonium nitrate).Extensive pasture was adjusted to mean stocking rate of 0.5 LSU ha À1 yr À1 and was not fertilized.For more details, see Allard et al. (2007).
Decomposer consumption rate of SOM A was estimated following Fontaine et al. (2011) who quantified biomass and activity of cellulolytic fungi carrying out PE. Turnover of decomposers s + r was calculated from the decay rate of cellulolytic fungi after exhaustion of fresh C (Fontaine et al., 2007(Fontaine et al., , 2011)).Decomposer production rate of SOM s was estimated by assuming that 30% of the consumed fresh C by decomposers is humified in SOM (H enin & Dupuis, 1945;Kirkby et al., 2013).The fraction of decomposer biomass released as CO 2 r was given by the difference between s + r and s.The rate of fresh C consumption by SOM decomposers y and the rate of fresh C consumption by SOM builders u were determined by constraining SYMPHONY to compartments and fluxes of study grassland.The N/C ratio of FOM and SOM, respectively, b and a, was estimated by measuring the C/N ratio of plant roots and total soil organic matter of the studied site.Plant photosynthesis rate under C limitation k was estimated by measuring biomass accumulation in the intensive pasture where plants were considered to be limited by C due to N fertilization and more frequent grazing (Allard et al., 2007;Klumpp et al., 2011).Plant N uptake under N limitation e was estimated by measuring biomass accumulation in the extensive pasture where plants were considered to be mainly N-limited.The immobilization rate of mineral N by decomposers i was estimated by considering a ratio of 0.38 between rates of microbial immobilization i and plant N uptake e (Recous et al., 1996).Plant respiration rate r p was estimated by assuming that 40% of fixed C is released as CO 2 (Nguyen, 2003;Balesdent et al., 2011).The rate of plant C deposition m p was estimated from Picon-Cochard et al. (2012).Leaching rate l was estimated from Simon et al. (1996).Carbon dioxide (CO 2 ) concentration C a was initially fixed to ambient level (400 ppm).A matrix analysis of parameterized model was made in order to check its feasibility and stability (Appendix S3).For this analysis, the management parameters were taken from the intensive pasture.

Simulation of studied grassland functioning
To test the capacity of SYMPHONY to simulate the functioning of our study grassland, we constrained the model with the management of the intensive pasture (parameter e p and u i , Table 1) and compared predicted compartment sizes and fluxes with observations (Table 4).The deviation between modeled (MV) and observed (OV) values was minimized by fitting microbial parameters u and y using Berkeley Madonna.To give the same weight to each variable during the fitting, the relative mean deviation (RD) was calculated as follows: where n is the number of study variables.
Plant export rate e p was calculated from the stocking rate (approx. 1 LSU ha À1 yr À1 ) and by assuming an uptake of 12 kg DM day À1 LSU À1 .The total N inputs to this ecosystem (fertilization, animal excretion, biological fixation, and N depositions) were estimated by calculating a complete N balance of the intensive pasture.Given that our model does not explicitly consider animal excretion and biological fixation, we assumed that these inputs supplied the pool of mineral N through u i .The flux u i was estimated to 0.063 g N m À2 day À1 .
Mean annual compartment sizes and ecosystem fluxes were quantified in the intensive pasture over the period [2003][2004][2005][2006][2007][2008] and by considering a soil depth of 0-60 cm (Table 4).Plant C stock (C p ) was estimated from root and shoot biomass and its C content.Fresh organic C stock (C f ) was estimated by quantifying particulate organic matter (POM > 200 lm) (Loiseau & Soussana, 1999) and its C content.Soil mineral N (N) was quantified after extraction with KCl.Soil C stock (C s ) was estimated from total C and bulk density.Net carbon flux to soil (dC s /dt) was estimated by the eddy covariance technique combined with specific greenhouse gas measurements such as methane emissions (Klumpp et al., 2011).Flux of N leaching (lN) was obtained from Simon et al. (1996).Plant carbon exports (e p C p ) by heifers were estimated assuming an uptake of 12 kg DM day À1 per LSU and 42% carbon content in forage.

Study of the mechanistic basis of the bank functioning
Nitrogen inputs to the intensive pasture were drastically reduced (current inputs divided by 6) to impose a net nutrient output (u i À lN À be p C p < 0) on the ecosystem that is currently subjected to a net nutrient input (u i À lN À be p C p > 0).The response of ecosystem compartments an fluxes to these two ecosystem N balances was determined to analyze the soil capacity to release or sequester N (bank functioning).

Grassland response to rising atmospheric CO 2 and N depositions: SYMPHONY predictions
To study ecosystem responses to elevated CO 2 or N deposition, CO 2 concentration was increased by 40% (from 400 to 560 ppm), and N input to ecosystem was increased by 13% (from 0.06 to 0.07 g N m À2 day À1 ).The effect of CO 2 (C a ) and N input to ecosystem (u i ) on soil C storage (dC s /dt) was also studied mathematically at steady state to verify the generality of model predictions.

Results
Plant/soil model with a single microbial type Decomposers and plants can be limited either by N or C. Four scenarios must thus be considered.For clarity, the results are summarized into two groups of scenarios that are interpreted similarly.The equations for these scenarios at steady state are given in Table 2.
Scenarios 1 and 2: decomposers are N-limited and plants are C or N limited.All compartments have finite steady states except SOM and FOM (Table 2).The SOM and FOM compartments reach steady states under particular conditions depending on model parameters and N inputs to the ecosystem (Eqns (dC f /dt)* and (dC s /dt)*, Table 2).Decomposer biomass (Eqn C Ã ds , Table 2) and thus SOM mineralization depends on the availability of mineral N rather than fresh C, signifying these scenarios do not simulate priming effect (PE).Moreover, decomposers immobilize N (u ims = ÀiN when decomposers are N-limited) implying that whole plant N uptake (u up in Eqns N*, Table 2) must rely on N inputs to the ecosystem (u i ).However, this is not realistic because N inputs to ecosystems are commonly very low compared with plant N uptake (Mattsson, 1987a;Vitousek & Howarth, 1991;Rasmussen et al., 1998).Under these scenarios, the ecosystem is not able to resist a long-term net nutrient output (criteria 2 of model evaluation).
Scenarios 3 and 4: decomposers are C-limited and plants are C-or N-limited.All compartments have finite steady states except SOM (Table 2).Decomposer biomass (Eqn C Ã ds , Table 2) and SOM mineralization depend on fresh C availability, signifying these two scenarios allow simulating PE.Direction of SOM change (increase or decrease) only depends on microbial parameters s and A (Eqn (dC s /dt)*, Table 2).To account for the accumulation of SOM in ecosystems (criteria 3) the condition s > A is imposed in these scenarios.This SOM accumulation implies a sequestration of N leading to a continuous removal of N from the mineral pool (Eqn N*, Table 2).Decomposers can mineralize or immobilize N.This immobilization/mineralization flux is determined by Eqn (8) that can be reorganized as follows: Decomposers mineralize N if the amount of N acquired through plant litter deposition (bm p C Ã p ) is higher than the amount of N sequestered in the SOM pool (s > A to fulfill criteria 3).This equation also shows that, in the case of N mineralization, the amount of N mineralized by decomposers is always lower than the amount of N lost by the plant through litter deposition because part of litter N is sequestered in SOM.Moreover, there are several N outputs from ecosystems (plant harvest, N leaching).Under these conditions, the model predicts that the maintenance of ecosystem compartments requires that N inputs to the ecosystem always compensate plant N exports, N leaching and N sequestration in SOM (u 2).Thus, the ecosystem is not able to resist a longterm net nutrient output (criteria 2 of model evaluation).
It is worth mentioning that when the criteria 3 (SOM accumulation) is not respected (s < A), microbial N mineralization can compensate ecosystem N losses allowing ecosystem persistence (Eqn N*, Table 2).However, the model predicts a continuous decrease in SOM pool until its exhaustion, which is unrealistic.
We conclude that the plant/soil model with one microbial type cannot account for ecosystem resistance to a long-term net nutrient output and the SOM accumulation in ecosystems simultaneously (criteria 2 and 3).

Plant/soil model with two microbial functional types (SYMPHONY)
Inclusion of a second microbial type that can either be N or C limited leads to eight possible scenarios.
Scenarios 1 and 2: The two decomposers are N-limited and plants are C-or N-limited.Although the two decomposer types are taken into account, results are qualitatively similar to those of the model with one decomposer type limited by N (plant limited by C or N, scenarios 1 and 2): the two decomposers immobilize N implying that whole-plant N uptake (u up in Eqn N*, Table 3) must rely on N supply to ecosystems (u i ), which is not realistic.3).When criteria 3 (SOM accumulation) is fulfilled, the maintenance of ecosystem compartments requires that N inputs to the ecosystem always compensate plant N exports, N leaching and N sequestration in SOM (u 3), which is not realistic.
Scenarios 5 and 6: SOM decomposers are N-limited, SOM builders are C-limited and plants are C-or N-limited.Biomass of SOM decomposers (Eqn C Ã ds , Table 3) and thus SOM mineralization depend on the availability of mineral N rather than fresh C, signifying these scenarios do not simulate the PE.The immobilization/mineralization flux induced by SOM builders is determined by Eqn (23) that can be reorganized as: This equation indicates that SOM builders only release a part of plant litter N that they decompose (bu f ) the remainder being stored in SOM (asC Ã df ).Moreover, due to their N limitation, SOM decomposers immobilize mineral N (u ims = ÀiN).Under these conditions, the maintenance of ecosystem compartments requires that N inputs to the ecosystem always compensate plant N exports, N leaching and N sequestration in SOM (Eqn N*, Table 3).Thus, the ecosystem is not able to resist to a long-term net nutrient output, which is unrealistic (criteria 2 of model evaluation).
Scenarios 7 and 8: SOM decomposers are C-limited, SOM builders are N-limited and plants are C-or N-limited.All compartments have finite steady states except the SOM pool that can reach infinity or steady state (Table 3).Biomass of SOM decomposers (Eqn C Ã ds , Table 3) and SOM mineralization depends on fresh C availability, signifying that these two scenarios allow simulating the PE.As SOM decomposers compete for fresh C-with N-limited SOM builders, the intensity of PE depends  on microbial interactions as observed in recent laboratory studies (Nottingham et al., 2009;Pascault et al., 2013).Due to their N limitation, SOM builders immobilize N and sequester it in SOM.In contrast, SOM decomposers mineralize N.This mineralization flux can be expressed as: which indicates that SOM decomposers release N from plant litter they decompose (bu d ) and from the SOM pool if s < A, which is one condition of model feasibility (see paragraph on model feasibility below).
Ecosystem functioning in these two scenarios is notable because it can simultaneously account for ecosystem resistance to a long-term net N output (criteria 2) and the long-term SOM accumulation when there is net N input to ecosystem (criteria 3).These two key ecosystem properties are explained by the inclusion of PE and the interaction between SOM decomposers and SOM builders.A net N input to the ecosystem (u i À lN Ã À be p C Ã p [ 0) increases N availability and biomass of N-limited SOM builders (Fig. 3; Table 3).As the two decomposers are in competition for fresh C, an increase in biomass of SOM builders decreases the biomass of SOM decomposers (Fig. 3; Table 3).As a result, the SOM pool increases leading to N sequestration.This N sequestration is maintained as long as there is net N input to the ecosystem (Unlimited capacity of soil to accumulate SOM).When there is a net N output from an ecosystem (u i À lN Ã À be p C Ã p \0), biomass of SOM builders decreases while biomass of SOM decomposers increases resulting in destruction of SOM and release of mineral N (Fig. 3; Table 3).Thus, the soil functions as a bank of nutrients by storing mineral nutrients when they are in excess in solution and by releasing nutrients from SOM when they are in low concentration and could threaten plant persistence (Fig. 3).Finally, the model predicts that the SOM pool reaches a steady state (criteria 4) when ecosystem N inputs balance N outputs.
The model guarantees plant-decomposer coexistence (criteria 1) under some conditions of feasibility.For C Ã df [ 0 (Table 3), net N output from ecosystem must not exceed the term aðA À sÞm p C Ã p =ðs þ r À AÞ.The term m p C Ã p =ðs þ r À AÞ is the maximum biomass of SOM decomposers (all the fresh C is taken up by SOM decomposers) and a (A À s) is the rate of release of N by SOM decomposers (with A > s).Thus, the ecosystem persists if net N output from the ecosystem does not exceed the maximum capacity of SOM decomposers to release N from SOM.For C Ã ds [ 0 (Table 3), net N input to the ecosystem must not exceed the term (asm p C Ã p =s þ r) that corresponds to the maximum capacity of SOM-builders to sequester N in SOM.If this condition is not met, the mineral N pool increases, SOM builders become C-limited (the model switches to scenarios 3 and 4) and excess of N is leached (data not shown).Another condition of feasibility is that the N/C ratio of FOM must be sufficiently lower than that of decomposers (for N* > 0, as À b(s + r) must be > 0 implying that a must be ≫b, Table 3).Otherwise, SOM builders are no longer N-limited.This N limitation of SOM builders is supported by many studies showing an immobilization of N by microorganisms specialized in fresh C decomposition (Recous et al., 1995;Mary et al., 1996).Finally, C loss from SOM decomposers due to their turnover must be higher than their C uptake from SOM (For C Ã df [ 0; s þ r À A must be > 0, Table 3).This condition is supported by several studies (Fontaine et al., 2007(Fontaine et al., , 2011) ) showing that the energy required to solubilize SOM compounds (i.e., production of extracellular enzymes) is higher than the energy supplied by the respiration of these catabolites.Collectively, these results suggest that the conditions of plantdecomposer coexistence are realistic.Therefore, the model in these two scenarios meets the four evaluation criteria we chose.
Plants can be C-limited (scenario 7) or N-limited (scenario 8) depending on the relative availability of C (CO 2 + light) and N (mineral N).The conditions of switch between scenarios 7 and 8 are presented in Appendix S2.Shortly, when u i increases, mineral N also increases and plants tend to become C-limited (scenario 7).In contrast, when N leaching (l) increases, mineral N decreases and plants tend to become N-limited (scenario 8).

Simulation of studied grassland functioning
The mean annual plant biomass of the studied permanent grassland represented 525 AE 107 g C m À2 (Table 4).The continuous supply of fresh plant C led to the building of a large compartment of fresh C representing 635 AE 129 g C m À2 .The amount of N present in mineral compartment was low compared with plant and fresh organic matter compartments, which is typical of undisturbed ecosystems (e.g., grasslands and forests).Despite the high N input to this ecosystem (0.063 g N m À2 day À1 ), the N leaching was low (0.0055 AE 0.0047 g N m À2 day À1 ) representing 9% of total ecosystem N input.The low rate of N leaching is a characteristic of undisturbed grassland ecosystems compared with cultivated soils (Simon et al., 1996;Lord et al., 2002).The eddy covariance measurements showed a continuous net C storage of 0.57 AE 0.40 g C m À2 day À1 by this grassland.This result concurs with other studies (Syers et al., 1970;Schlesinger, 1990;Knops & Tilman, 2000;Sanderman et al., 2003) suggesting that permanent grasslands can continuously accumulate organic C in soil without any apparent limit of accumulation.
SYMPHONY was able to simulate plant biomass (C p ), fresh organic C (C f ), mineral N (N), forage production (e p C p ), N leaching (lN) and ecosystem C storage (dC s /dt) with only 16.4% mean deviation compared with observed values (Table 4).The model simulations of C p , C f , e p C p, and dC s /dt were particularly accurate with deviations < 6% compared to observed values.The mineral N pool and N leaching were less satisfactory with 43% deviation between observed and simulated values.However, this deviation was within the range of interannual variability observed for these variables (Table 4).Moreover, the amount of N in play in these variables was low compared to other ecosystem variables such as N in plant biomass and harvest.
Model simulations showed that the parameterized model had stable steady state (Figs 2 and 3, model compartments do not vary with time).The matrix analysis of parameterized SYMPHONY (Appendix S3) indicated that the model had only one stable steady state corresponding to scenario 7 meaning that plant is limited by C, SOM builders limited by N and SOM decomposers limited by C. The C limitation of plants is explained by the relative high N input to this intensive fertilized pasture (0.063 g N m À2 day À1 or 230 kg N ha À1 yr À1 ).

Grassland response to global change: SYMPHONY predictions
In agreement with the C limitation of plants, elevated CO 2 caused an increase in plant biomass and depositions of fresh organic C (Fig. 2).This stimulated the C-limited SOM decomposers, the degradation of SOM (PE), the release of mineral N and finally the biomass of N-limited SOM builders (data not shown) which sequester C and N in SOM.Thus, under elevated CO 2 , the bank mechanism limits (adjustment of SOM dynamics to N availability) the loss of SOM owing to PE.However, despite the bank mechanism, the compartments of mineral N and plant at steady state were higher under elevated compared with ambient CO 2 (Fig. 2).As a result, ecosystem N outputs through leaching and plant exportation increased under elevated CO 2 .Mechanically, these increased N outputs led to decrease in the SOM builders/SOM decomposers ratio (Fig. 2; Table 3 for mechanistic understanding) decelerating C and N sequestration in SOM under elevated CO 2 (Fig. 2).
The mathematical analysis of SYMPHONY indicated that the negative effect of elevated CO 2 on SOM accumulation is general to all C-limited ecosystems (scenario 7).Indeed, SOM dynamics after replacement of variables by their expressions at steady state reads as follows: where Given the conditions of feasibility of scenario 7, values of x, z, and w are strictly positive.Thus, an increase in the concentration of CO 2 (C a ) has always a negative effect on the SOM pool Eqn (27).
In agreement with the bank mechanism described in scenarios 7 and 8, SYMPHONY predicted that increased N deposition (+30 kg N ha À1 yr À1 ) increases the C df /C ds ratio and the rate of soil C storage (Fig. 3).However, increased N deposition also increased the mineral N pool (Fig. 3) and thereby N leaching (results

Discussion
Paradox of plant persistence in a nutrient-trapping environment One major outcome of our modeling analyses is that the question of plant persistence is not trivial in an environment where N is sequestered owing to SOM accumulation (Syers et al., 1970;Schlesinger, 1990) and ecosystem N inputs/outputs are large compared to plant biomass.In an environment characterized by N sequestration, plants can survive only if N sequestration stops when mineral N availability becomes critical for plants or if the external N supply compensates for N sequestration and eventual plant N exports.However, this latter condition is not realistic because N inputs to the ecosystem are not always higher than N removal by plant harvest/grazing and SOM accumulation (Vitousek & Howarth, 1991;Rasmussen et al., 1998).Moreover, it has been shown that SOM is a nutrient source for plants when there is net N output from ecosystems (Kofoed & Nemming, 1976;Dyke et al., 1983;Mattsson, 1987b;Rasmussen et al., 1998).These observations combined with our modeling results suggest the existence of a fine adjustment of soil N dynamics to plant N uptake allowing plant/microbe coexistence.

Priming effect and microbial diversity in ecosystem functioning
Among the twelve analyzed scenarios, only scenarios 7 and 8 of the SYMPHONY model were able to account for the four criteria of model evaluation: plant decomposers coexistence, ecosystem resistance to a long-term net N output from the ecosystems, the long-term SOM accumulation when there is net N input to the ecosystem and eventual steady state of SOM pool.This accounting is permitted by the fine adjustment of microbial N mineralization to plant N uptake the socalled 'bank mechanism.'Any excess of mineral nutrients is stored in SOM avoiding nutrient leaching, whereas mineral nutrients are released from SOM when they are in low concentration and could threaten plant persistence.A simple way to model this bank mechanism is to consider the destruction of SOM through PE and the interactions between two key microbial functional groups (Fontaine et al., 2003): SOM decomposers and SOM builders.These results support the idea of Fontaine and Barot (2005) that microbial diversity has key role on ecosystem persistence and properties as crucial as SOM accumulation.However, we cannot exclude the possibility of other model formulations able to simulate the bank mechanism with a single microbial type, but with more complex feedback mechanisms.
A number of laboratory studies support the model formulation presented in this study to simulate the 'bank mechanism'.Indeed, N availability drives the structure of soil microbial communities (Allison et al., 2008;Ramirez et al., 2010Ramirez et al., , 2012;;Bates et al., 2011), the activity of enzymes degrading recalcitrant SOM (Carreiro et al., 2000;Ramirez et al., 2012), the intensity of PE (Fontaine et al., 2004;Blagodatskaya et al., 2007;Fontaine et al., 2011) and thereby the direction of SOM pool change (increasing or decreasing).Now, the bank mechanism may be studied in detail in plant/soil experiments where SOM dynamics, C and N fluxes and structure of microbial communities could be determined by combining different methods such as the 13 C and 15 N labeling of plants and mineral N (Recous et al., 1995;Dijkstra & Cheng, 2007;Klumpp et al., 2009;Shahzad et al., 2012) and the pyrosequencing of microbial DNA (Wallenstein & Weintraub, 2008;Pascault et al., 2013).

Ecosystem response to global change: new predictions lessen uncertainty
The earth's future climate depends on changes in ecosystem C storage in response to rising concentrations of atmospheric CO 2 .Current models qualitatively diverge in their predictions on ecosystem response to rising atmospheric CO 2 (Amthor, 1995;Cao & Woodward, 1998a,b;Kramer et al., 2002;Krinner et al., 2005).Some models focusing on the C cycle implicitly consider that plant growth is limited by C resources (Cao & Woodward, 1998a;Krinner et al., 2005;Sokolov et al., 2008).These models consistently predict that an increase in atmospheric CO 2 will stimulate primary production, C input to soil and in fine C storage in soil (Cao & Woodward, 1998b;Krinner et al., 2005;Sokolov et al., 2008).According to these models, plants could slow down the increase in atmospheric CO 2 emissions and the subsequent global warming.In contrast, the models considering the coupling between C and nutrient cycles predict a negligible response of ecosystem to elevated CO 2 owing to limitation of plant growth by nutrient availability in soil (Kirschbaum et al., 1998;Sokolov et al., 2008;Goll et al., 2012).SYMPHONY takes account the possibility of C and N limitations of plants.It also considers changes in microbial activity and SOM mineralization induced by fresh C supply of plants grown under elevated CO 2 .The model predicts that an increase in atmospheric CO 2 will not affect primary production and soil C storage when plants are N-limited (i.e., high plant N uptake, low fertilization, high N exports and leaching).This prediction is supported by studies observing no effect of elevated CO 2 in nutrient (N or P) limited grasslands and forests (Oren et al., 2001;Menge & Field, 2007).When plants are C-limited (i.e., low plant N uptake, high fertilization, low N exports, and leaching), our model predicts an increase in primary production in response to rising atmospheric CO 2 .However, contrary to the forecasts of current models, our model indicates that a higher plant C input to soil will deplete soil C stocks and increase N leaching as a result of SOM-decomposers stimulation (PE).This prediction is supported by recent studies showing a CO 2 -induced modification of soil microbial communities (Finzi et al., 2006;Carney et al., 2007;Blagodatskaya et al., 2010a) leading to an intensification of SOM mineralization (K€ orner & Arnone, 1992;Finzi et al., 2006;Carney et al., 2007), a depletion in soil C stock (Carney et al., 2007) and an increase in N leaching (Liu et al., 2008).
Another outcome of our model was the positive effect of N inputs (i.e., fertilization, biological N fixation, and atmospheric depositions) on SOM accumulation and ecosystem C storage irrespective of plant limitation (C or N) (Fig. 3).In the model, increased N availability not only stimulates photosynthesis of N-limited plants but also shifts the soil microbial community from being dominated by SOM decomposers to SOM builders.This community change preserves the old pre-existing soil C and stimulates formation of new soil C leading to SOM accumulation.These predictions are consistent with studies showing an acceleration of SOM accumulation (Hagedorn et al., 2003;Bowden et al., 2004) by microbial communities with reduced catabolic capabilities in N-amended ecosystems (Carreiro et al., 2000;Fontaine et al., 2004b;Allison et al., 2008;Ramirez et al., 2012).Finally, by injecting N into ecosystems, legumes can also increase the SOM-builders/ SOM-decomposers ratio explaining their positive effect on soil C sequestration (Sierra & Nygren, 2005;Van Groenigen et al., 2006).

Soil modeling: the slow revolution continues
Current models of SOM dynamics are based on concepts developed seventy years ago (Jenny, 1941;H enin & Dupuis, 1945) simulating the SOM pool as a reservoir of water that flows out.This simple concept has generated models simulating C and N dynamics in a variety of ecosystem types, pedoclimatic situations, land use, and agricultural practices (Smith et al., 1997).Although this valuable legacy must be preserved and used by the scientific community, current models should also evolve to integrate new knowledge and social expectations.It is now clear that PE exerts a strong effect on SOM dynamics (Bingeman et al., 1953;Wu et al., 1993;Cheng et al., 2003;Fontaine et al., 2004a,b) with important consequences for ecosystem function and responses to global change (Hoosbeek et al., 2004;Dijkstra & Cheng, 2007;Talhelm et al., 2009;Drake et al., 2011;Iversen et al., 2012).Ecosystem models thus need to incorporate PE mechanisms if they are to accurately simulate trajectories of plant production and soil C storage under future conditions.
One of the main reasons why PE is not yet integrated in current models is the lack of an example of plant/ soil models embedding PE and providing realistic predictions for key ecosystem functions.We contribute to filling this gap by proposing the first parameterized plant-soil model embedding the PE.With five compartments and eight parameters, the soil module of SYM-PHONY is relatively simple and lies in the low range of model complexity (Smith et al., 1997).When tested on a permanent grassland, SYMPHONY provided realistic predictions for ecosystem compartments and key fluxes such as forage production, soil C storage and N leaching.SYMPHONY was also able to propose new predictions regarding the ecosystem response to elevated CO 2 and increased N depositions.In particular, SYM-PHONY may explain the stimulation of soil C mineralization (PE) induced by enhanced fresh C input in ecosystems exposed to elevated CO 2 (Carney et al., 2007;Phillips et al., 2012).This stimulation may be responsible for a positive feedback on atmospheric CO 2 concentration and climate.Collectively, these results suggest that the mathematical representation of PE proposed in SYMPHONY may be incorporated in current ecosystem models with few additional parameters, improving accuracy of predictions.
Future works could test the behavior of SYMPHONY in other ecosystems and climates in order to determine the generality of our predictions.SYMPHONY could also be used to answer further scientific questions.
Given that SYMPHONY integrates the role of two key microbial populations on SOM dynamics it can be used to model effects of an erosion of soil biodiversity on cultivated soil functioning.It may also suggest alternative agricultural practices that will optimize the fine adjustment of N mineralization to plant N uptake, minimizing N losses and fertilizer application.These new investigations will require development of SYMPHONY by including other soil processes and environmental factors (i.e.effect of temperature and water).However, a more efficient approach would be an inclusion of SYMPHONY in current models where it could benefit from the knowledge accumulated during more than 70 years of soil modeling.

Fig. 1
Fig. 1 Flow diagrams of the two study ecosystem models.Model 1 considers a single microbial type (a) whereas model 2 (SYM-PHONY) considers two distinct microbial functional types (b).Solid arrows represent flows of C and dashed arrows represent flows of N between different compartments.
Wiley & Sons Ltd, Global Change Biology, doi: 10.1111/gcb.12493P R I M I N G E F F E C T I N E C O S Y S T E M F UN C T I O N I N G 7

Scenarios 3 and 4 :
The two decomposers are C-limited and plants are C-or N-limited.Results are qualitatively similar to those of the model with one decomposer type limited by C (plants limited by C or N, scenarios 3 & 4): the SOM pool continuously increases or decreases depending only on microbial parameters s and A (Eqn (dC s /dt)*, Table

©
types can be limited by C or N leading to eight possible scenarios Decomposers Limitation Plant Limitation C SOM-decomposers: N; SOM-builders: N SOM-decomposers: C; SOM-builders: C SOM-decomposers: N; SOM-builders: C SOM-decomposers: C; SOM-builders: N 2013 John Wiley & Sons Ltd, Global Change Biology, doi: 10.1111/gcb.12493P R I M I N G E F F E C T I N E C O S Y S T E M F UN C T I O N I N G 9

Fig. 2
Fig. 2 Effects of CO 2 on plant biomass (a), fresh organic C (b), SOM-builders/SOM-decomposers ratio (C df /C ds ) (c), mineral N (d), N leaching (e) and soil C storage (f).Solid black lines represent data from the study intensive pasture at ambient CO 2 (400 ppm), while dashed red lines represent model simulations at elevated CO 2 (560 ppm).

Fig. 3
Fig.3Effects of N inputs on ecosystem N balance (a), mineral N (b), SOM-builders/SOM-decomposers ratio (C df /C ds ) (c), and soil C storage (d).Solid black lines represent data from the study-intensive pasture where N inputs to the ecosystem are 0.06 g N m À2 day À1 .Dashed red lines represent the model simulations when N input to ecosystem is reduced to 0.01 g N m À2 day À1 .These two contrasted N treatments were used to analyze the mechanistic basis of bank functioning of soil.Blue dash-dot-dot lines represent the model simulations when N input to ecosystem is increased from 0.06 to 0.07 g N m À2 day À1 to simulate enhanced atmospheric N depositions.

Table 1
Model compartments, fluxes and parameters.Parameter values were estimated both from published studies and specific measurements on the two study permanent pastures located in France (altitude 1040 m, mean annual temperature 7 °C, mean annual precipitation 1200 mm).See section 'Materials and methods' for details of estimations.The management parameters (e p and u i have been determined for the intensive pasture

Table 2
Steady states for model 1.Plants and decomposers can be limited by C or N leading to four possible scenarios

Table 3
Steady states for model 2. Plants and two microbial functional

Table 4
Observed and predicted values of plant C (C p ), fresh organic C (C f ), mineral N (N), plant harvest (e p C p ), N leaching (lN) and net soil C storage (dC s /dt).Percentage deviation for each variable was calculated as (modeled À observed)/observed.Observed variables are mean values obtained in the study intensive pasture located in France (altitude 1040 m, mean annual temperature 7 °C, mean annual precipitation 1200 mm) over the period[2003][2004][2005][2006][2007][2008].The standard deviation (SD) represents the interannual variability.See section 'Materials and methods' for details of measurements