2.1 The CENTURY decomposition model

The basis of the litter decay model used in this study is the CENTURY model (Fig. 1), a first-order decay model that describes decomposition as a function of substrate availability and quality, clay content, soil moisture and soil temperature (Parton et al., 1988). Most land surface models (e.g., Kucharik et al., 2000; Sitch et al., 2003; Krinner et al., 2005) adopted a similar structure to simulate the litter and soil biogeochemical processes. Dead organic matter in CENTURY is separated into structural and metabolic litter and three SOM pools (active, slow, passive) with different turnover times. There is no explicit representation of microbial biomass in CENTURY; instead, the biomass of microbes is assumed to be in equilibrium with labile SOM and thus implicitly included in the active SOM pool. When litter is being decomposed, a fraction of the decomposed C is respired to the atmosphere and the remaining fraction (CUE_d conceptually equal to microbial CUE) enters the acceptor SOM pool. Three of such fractions are defined to characterize the transfer of C from litter to SOM: CUE_ma for transfer of the metabolic litter to the active SOM pool, and CUE_sa and CUE_ss for transfer of structural litter to active and slow SOM pools, respectively (Fig. 1). These fractions are set to be time invariant in the original version of CENTURY, so that a fixed fraction of decomposed C is retained in the acceptor pool regardless of environmental conditions and changes in the quality of the donor pool. The N flows in CENTURY follow the C flows and are equal to the product of C flow by the N : C ratio of the acceptor SOM pool. N mineralization is defined as the difference between N obtained from the donor pools and N stoichiometric demand of the acceptor pool (Parton et al., 1988; Metherell et al., 1993). In this way, net N mineralization occurs when the donor pool has a low C : N ratio, but N is immobilized (taken up by microbes) when the donor pool has a high C : N ratio.

2.2 Optimal CUE

To quantify how microbial CUE varies along gradients of nutrient availability, it can be hypothesized that microorganisms maximize their growth rate, and hence their ecological competitiveness, by adapting resource (C and nutrients) use efficiencies. This follows the growth maximization hypothesis (Mooshammer et al., 2014; Manzoni et al., 2017). Based on this hypothesis, Manzoni et al. (2017) formulated a theoretical model expressing microbial CUE as a function of the stoichiometric difference between decomposers and their substrate. The CUE for which growth rate is maximized is the optimal CUE (CUE_opt) given by

where CUE_max is the maximum microbial CUE (dimensionless) when growth is limited by C from the organic substrate. CN_D and CN_S are the C : N ratio (in mass, dimensionless) of decomposer and their substrate, respectively. Although Manzoni et al. (2017) indicated that mineral phosphorus (P) could also affect optimal CUE, we only considered N as a limiting nutrient. I_N (g N kg⁻¹ soil) is the maximum rate at which mineral N can be taken up by microbes, and U₀ (g C kg⁻¹ soil) is the C-limited uptake rate (corresponding to the decomposition rate at optimal mineral N concentration). When litter C : N is low or soil mineral N is in excess, the second term in the minimum function (Eq. 1) is higher than 1, and CUE${}_{\mathrm{opt}}={\mathrm{CUE}}_{max}$ (C-limited conditions, as in nutrient-rich litter). In contrast, when mineral N is scarce, CUE_opt decreases with increasing substrate C : N ratio (N-limited conditions, N-poor litter). Lack of N in the organic substrates can be compensated by mineral N being immobilized by microorganisms from the soil solution. Immobilization meets the nutrient demands as long as it is lower than the maximum supply rate I_N, at which point microbial CUE starts being downregulated. Thus, for any given C : N ratio in the substrate, CUE_opt increases with inorganic N concentration in the soil solution until CUE_max is reached. It should also be noted that Eq. (1) is interpreted at the microbial community scale, not for individual organisms.

2.3 Adaption of the optimal CUE model in the CENTURY model

CUE of decomposition (CUE_d) is also assumed to be equivalent to microbial CUE in this study. Then we followed the theory from Manzoni et al. (2017) (Eq. 1) to parameterize CUE_d during litter decomposition into CENTURY (Fig. 1). Due to the implicit representation of microbial growth in CENTURY, we replaced the original optimality CUE model (Eq. 1) by a simpler equation that involves the C : N ratios of the donor and acceptor pools, rather than microbial C : N ratios:

where CN_lit and CN_SOM are the C : N ratio (dimensionless) of litter (metabolic or structural) and SOM pools (active, slow or passive), respectively. The C : N ratio of SOM (around 9 : 1 on a mass basis in CENTURY) is representative of the decomposer biomass, its value being between the average C : N ratio of soil microbial communities including fungi and bacteria (7.4 : 1 in Cleveland and Liptzin, 2007) and the C : N ratio of soil fungi (13.4 : 1 in Zhang and Elser, 2017), which are probably largely responsible for fresh litter decomposition. CUE_max (dimensionless) is the maximum CUE_d achieved when nutrients are not limiting, and it is set to 0.8 based on a synthesis of observed CUE of soil microbes (Manzoni et al., 2012). The exponent a (g N kg⁻¹ soil) captures the effect of mineral N uptake by microbes on CUE_d. Because CUE_d is expected to increase with mineral N availability (Eq. 1), a is assumed to be a linear function of the mineral N concentration (N_min, g N kg⁻¹ soil):

where m₁ (kg g⁻¹ N) and n₁ (g N kg⁻¹ soil) are two coefficients that need to be calibrated. Equations (2) and (3) modulate the decrease in CUE_d with decreasing litter quality when mineral N availability changes: the exponent a increases with increasing mineral N availability, causing an increase in CUE_d at any given litter C : N ratio. Hence, increasing a mimics an increase in I_N in Eq. (1). Figure 2a illustrates how CUE_d from Eq. (2) varies as a function of mineral N concentration for different values of litter C : N.

Equations (2) and (3) were implemented in CENTURY to modify the originally fixed CUE_d (Fig. 1). With this change, the fractions of C from litter that remain in SOM are mediated by stoichiometric constraints and mineral N availability, at the expense of additional parameters to fit. The CUE_d values for C transfers between SOC pools (active, slow and passive) are not modified.

2.4 Constraint of soil nutrient availability on litter decomposition rate

CENTURY is a first-order decay model in which decomposition rates of metabolic and structural litter are modulated by scaling factors of soil temperature (f(tem)) and moisture (f(water)) (Parton et al., 1988). Here, we introduced an additional mineral N scaling factor (f(N_min), 0–1, dimensionless) to account for the limitation imposed by low mineral N availability on litter decay rate (D(C_lit)):

where C_lit is the C (g C kg⁻¹ soil) in the litter pool (metabolic or structural) and k is the potential maximum turnover rate (day⁻¹) at optimal soil temperature, moisture and nutrient conditions.

Figure 2Schematic plot of (a) the optimal carbon use efficiency (CUE_opt) as a function of soil mineral nitrogen for different litter C : N ratios (from Eq. 2) in the main text (with m₁=0.3, n₁=1.0) and (b) the N limitation function f(N_min) applied to litter decomposition rates (from Eq. 5) in the main text. CN_lit and CN_SOM are the C : N ratios of the litter and SOM pools, respectively. CUE${}_{max}=\mathrm{0.8}$ is the maximum CUE under optimal nutrient condition (C limitation only). m₁ and n₁ are the parameters of Eq. (3) and m₂ is the parameter of Eq. (5).

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In this study, we assumed that the scaling factor of mineral N increases linearly with increasing soil mineral N concentration (N_min; Eq. 5) below a threshold value of 1∕m₂ g N kg⁻¹ soil, where m₂ is a positive coefficient which needs to be calibrated (Fig. 2b). The inhibition effect of mineral N only occurs in the case of immobilization ($\mathrm{1}/{\mathrm{CN}}_{\mathrm{lit}}<{\mathrm{CUE}}_{\mathrm{opt}}/{\mathrm{CN}}_{\mathrm{SOM}}$). The specific function f(N_min) can be expressed as

Existing studies have adopted approaches that differ from our definition to explicitly represent the N inhibition effects on microbial processes (Manzoni and Porporato, 2009; Bonan et al., 2013; Fujita et al., 2014; Averill and Waring, 2018). In these previous studies, f(N_min) was assumed equal to the ratio between immobilized mineral N and the N deficit for maintaining a stable C : N of decomposer biomass or other receiver pools. Using the notation of Sect. 2, this definition of f(N_min) can be expressed as

where m₃ is a coefficient that needs to be optimized. U₀ (g C kg⁻¹ soil day⁻¹) is the C uptake rate (equivalent to the litter decomposition rate in absence of leaching) when soil mineral N is fully adequate for litter decay (i.e., $f\left({\mathrm{N}}_{min}\right)=\mathrm{1}$) and can be calculated from Eq. (7) as

In this study, we also tested this formulation in the CENTURY-based model, in addition to Eq. (5) (see model M4 in Table A3).

Table 1Optimized parameter values for the five versions of the litter decomposition model used in this study. cue_fit is the optimized value of CUE, m₁ and n₁ are the coefficients in Eq. (3), m₂ is the coefficient in Eq. (5), and m₃ is the coefficient in Eq. (6). Values in brackets following each parameter are the means (± standard deviations) of the fitted parameter values based on “leave-one-out” cross-validation (see Sect. 2.5 for more details).

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2.5 Model parameterization and validation

To determine the respective impacts of including flexible CUE_d and N availability constraining decay rates, we built four conceptual litter decay models (Table 1). Model M0 corresponds to the default CENTURY parameterization of a fixed CUE_d and no constraints of N availability on litter decay rates ($f\left({\mathrm{N}}_{min}\right)=\mathrm{1}$). Model M1 accounts for flexibility in CUE from Eq. (2) and N constraints on decay rates by Eq. (5). Model M2 has flexible CUE_d but no N constraints on decay rates ($f\left({\mathrm{N}}_{min}\right)=\mathrm{1}$). Model M3 has N constraints on decay rates but a fixed CUE_d (Table 1). All of these four models are run at a daily time step. Finally, model M4 also accounts for flexibility in CUE and N constraints on decays (Table A3), but it uses Eq. (6) to represent the N constraints on decays rate rather than Eq. (2). Results from model M4 are presented in the main text, but only shown in the Appendix. This range of models allows identifying which mechanisms are at play during decomposition: flexible CUE_d only (M3), mineral N limitation only (M2), both mechanisms (M1, M4), or none (M0).

For calibrating model parameters and evaluation of their results, we collected data of laboratory litter incubation experiments from Recous et al. (1995) (five experiments) and Guenet et al. (2010) (nine experiments; Table A2). The incubation experiments of Recous et al. (1995) and Guenet et al. (2010) continued 80 and 124 days, respectively. Recous et al. (1995) used corn residues (C : N ratio of 130) and Guenet et al. (2010) used wheat straw (C : N ration of 44) in their incubation experiments. The C : N ratios of the corn residue and wheat straw span the range of litter C : N ratios among different ecosystems (Harmon et al., 2009; Brovkin et al., 2012; Manzoni et al., 2010). In the incubation experiments, plant litter was firstly cut into fine fragments before it was mixed with mineral soil. Soil temperature and moisture condition were kept constant during the experiment. Respired C from the incubated litter and SOC as well as the soil mineral N concentrations were measured continuously across the incubation period. To distinguish the litter- and SOC-derived CO₂ flux, Guenet et al. (2010) used straw from wheat grown under ¹³C labeled CO₂, and they were therefore able to track the CO₂ coming from litter and the CO₂ coming from soil. In the experiments by Recous et al. (1995), litter-derived CO₂ flux is calculated as the difference in CO₂ flux between the incubation samples with both soil and litter, and the control samples without added litter. More detailed information about the incubation experiments of Recous et al. (1995) and Guenet et al. (2010) can be found in Table A2.

The initial C storage and C : N ratios of litter and SOM pool, as well as soil temperature and moisture conditions for decomposition in all of the five versions of the model (M0–M4), were set based on observations (Table A2). Plant litter was firstly separated into metabolic and structural litter pools based on its lignin-to-C ratio (LC_lit, dimensionless). The fraction of metabolic litter C (f_m, 0–1, dimensionless) is calculated by

where m₄ is a coefficient to be calibrated; $f_{max}=\mathrm{0.85}$ is the maximum fraction of metabolic litter (i.e., the default value in CENTURY; Parton et al., 1988). The fraction of structural litter C is thus 1−f_m. The C : N ratios of both metabolic and structural pools are assumed to be equal to the C : N ratio of litter input.

In the M1 and M3 models, the observed mineral N concentrations across the incubation period were used to calculate the daily N inhibition effect (Eq. 5). The observed cumulative respired litter C (g C kg⁻¹ soil) measured in the incubation experiments was used to calibrate the model parameter values. Moreover, to quantify the simulated CO₂ flux derived from the litter, we also performed a set of control simulations with only SOM (initial litter pools were set to 0 g kg⁻¹ soil) using the four model versions. The simulated litter-derived CO₂ flux is calculated as the difference in CO₂ flux between the simulation with both litter and SOM inputs and the simulation with only SOM input.

Parameter calibration was performed for each model with the shuffled complex evolution (SCE) algorithm developed by Duan et al. (1993). The SCE algorithm relies on a synthesis of four concepts that have proved successful for global optimization: combination of probabilistic and deterministic approaches; clustering; systematic evolution of a complex of points spanning the space in the direction of global improvement and competitive evolution (Duan et al., 1993). A more detailed description of this SCE optimization method can be found in Duan et al. (1993, 1994). In this study, the RMSE (root mean square error; Eq. 9) between simulated and measured cumulative respired litter C (%) on all observation days (Table A2) of each incubation experiment was used as the objective function, and the parameters minimizing RMSE between simulated and observed cumulative respired litter C were regarded as optimal parameter values.

where n is the number of observation days, and Sim_i and Obs_i (%) are the simulated and observed percent of cumulative litter-C flux on day i, respectively.

We used leave-one-out cross-validation (Kearns and Ron, 1997; Tramontana et al., 2016) to evaluate each of the four models (i.e., M0–M3), a cross-validation method used when data are scarce. The number of cross-validations corresponds to the number of incubation experiments (14). Each time, one of the 14 incubation experiments was left out as the validation sample, and the remaining 13 experiments were used to train model parameters. In addition to RMSE, we also adopted the Akaike information criterion (AIC; Bozdogan, 1987; Eq. 10) to determine the relative quality of the four version models on estimating cumulative respired litter C.

where n_p is the number of model parameters. The evaluation of AIC is important here because depending on the model version, different numbers of parameters have to be determined (Table 1), requiring us to weigh both model accuracy and robustness.

Note that the turnover times of SOM pools (active, slow and passive) used in this study are obtained from Organising Carbon and Hydrology In Dynamic Ecosystems – aMeliorated Interactions between Carbon and Temperature (ORCHIDEE-MICT v8.4.1; Guimberteau et al., 2018). The turnover times of litter pools (metabolic and structural), as well as the coefficient m₄ in Eq. (8), were optimized against the observed cumulative respired litter C from all of the 14 incubation experiments using the M0 and M1 models (Table A3). A previous study has shown that litter decomposability is negatively correlated to its physical size (for example, Tuomi et al., 2011). Therefore, the turnover times of the fine litter fragments used in the incubation experiments of Recous et al. (1995) and Guenet et al. (2010) are expected to be shorter than the values set in ORCHIDEE-MICT, which are representative of the turnover times of natural plant residues. In addition, the mixing of soil and litter particles in the incubation experiment likely enhances decomposition as spatial disconnection of decomposer and substrate, which can occur under natural soil conditions (Barnes et al., 2012; Hewins et al., 2013), is prevented. The calibrated turnover times of the metabolic and structural pools and the value of m₄ in Eq. (8) are 3.5 and 30 days and 0.5, respectively.

2.6 Impacts of litter stoichiometry and mineral N availability on SOM accumulation

We used model M1, with flexible CUE_d and decomposition rate function of available N to study the impacts of litter stoichiometry (C : N ratio) and soil mineral N availability on the formation and accumulation of SOM. In total, 24 idealized simulation experiments with different values of litter C : N ratios and soil mineral N availabilities were conducted (Table A4). The assumed litter C : N ratios (CN_lit) of 10, 15, 30, 60, 120 and 200 span the variation among most natural substrates and soil amendments from organic matter input in agriculture (Harmon et al., 2009; Brovkin et al., 2012; Manzoni et al., 2010). The assumed range of mineral N availability (N_min) of 0.001, 0.005, 0.01 and 0.05 g N kg⁻¹ soil spans the observed concentrations of soil mineral N in major terrestrial ecosystems (Metherall et al., 1993).

In each simulation experiment, model M1 was run for 5000 years to bring the litter and SOM pools in equilibrium with the prescribed litter input flux. The daily input rate of plant litter was set to 0.006 g C kg⁻¹ soil day⁻¹, and the initial C stock of litter and SOM pools was all set to be 0 g C kg⁻¹ soil. During the simulation, soil temperature and soil water content were assumed to be 25 ^∘C and 60 % of water holding capacity, respectively. We emphasized that our goal with this simplified scenario was to single out the effects of stoichiometric constraints, not to simulate the effects of a realistic climatic regime. Parameter values for M1 (with m₁=0.54, n₁=0.50 and m₂=296.8) used here were optimized based on all of the 14 incubation experiments from Recous et al. (1995) and Guenet et al. (2010) (see above). More detailed information about the specific settings of our simulation experiments can be found in Table A4.

3.1 Evaluation of different models

Results of leave-one-out cross-validation suggest that model M1 provides more accurate prediction of cumulative respired litter C than other models (Fig. 3). The differences between simulated and observed cumulative respired litter C from M1 are mostly less than 6 % for over 93 % of the data (Fig. A1b). The average RMSE of predicted cumulative respired litter C from M1 (3.0 %) is lower than that of model M0 (4.1 %). Models M2 and M3 have slightly lower RMSE values than M0 (3.7 % and 3.8 %, respectively) but perform worse than M1 (Fig. 4). However, the average AIC values of all the models are comparable, suggesting that models with more fitted parameters do not overfit the observations (Fig. 4).

Figure 3Comparison of the predicted cumulative respired litter C to observed values at different times during the litter decomposition process. Each dot denotes an observation of cumulative respired litter C on a certain day. In total, there are 149 points. M0–M3 are the four versions of litter decay models tested in this study (Table 1).

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Figure 4The RMSE and AIC of the simulated cumulative respired litter C from the four versions of litter decay model used in this study. Error bars denote the standard deviation of RMSE or AIC for different incubation experiments. M0–M3 denote the four models tested in this study (Table 1).

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Model M1 captures the differences in respiration rates due to different C : N ratios of substrate and varying levels of mineral N availability across the 14 incubation experiments (Fig. 5). While model M3 can reproduce the observed effect of soil mineral N availability on litter respirations rates (Fig. 5d), it underestimates the cumulative respired CO₂ from low quality litter (CN_lit=130) at high mineral N concentrations (>0.04 g N kg⁻¹ soil). Models M0 and M2 cannot represent the effects of soil mineral N on litter respiration rate (Fig. 5a, c), and their predictions are more biased from the observed values compared to M1. Model M4, which uses the alternative formulation for N constraints on litter decay (Eq. 6), reproduces the different respiration rates of substrates with contrasting C : N ratios and at different levels of mineral N availability (Fig. A2) but with a slightly higher average RMSE of cumulative respired litter C than model M1.

The predicted CUE_d and the limitation effects of soil mineral N availability on litter decay rate (f(N_min) function; Eq. 5) are different among the four tested models (Fig. A3). In models M0 and M3, which used a fixed CUE_d, the fitted values of CUE_d calculated with optimized parameters during the incubation period are about 0.57 and 0.54, respectively (Fig. A3a, d). In models M1 and M2, the CUE_d varies with the C : N ratios of plant litter and is only slightly affected by soil mineral N concentrations (Fig. A3b, c). For very low quality litter with a C : N ratio of 130, the CUE_d values in models M1 and M2 are 0.40 and 0.44, respectively, which are lower than for better-quality litter with a C : N ratio of 44 (approximately 0.55 and 0.56 in M1 and M2, respectively). Models M0 and M2 do not include the N inhibition effects on litter decay rate; thus, the f(N_min) in these two models is always 1 (Fig. A3e, g). In M1 and M3, the N inhibition effect changes with both the litter C : N ratio and the mineral N availability (Fig. A3f, h).

Figure 5Time series of the simulated (lines) and observed (dots) cumulative respired litter C (% of initial litter C) at four different levels of soil mineral N availability (N_min, g N kg⁻¹ soil). CN_lit is the C : N ratio of plant litter. M0–M3 denote the four models tested in this study (Table 1). Here, the simulation results of each model were calculated with parameters optimized based on all of the 14 samples of incubation experiments (Table A2).

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CUE_d from Eq. (2), calibrated with the data of the two incubation experiments, decreases with increasing CN_lit∕CN_SOM (Fig. 6). The average CUE_d value is larger than the average of data compiled for microbial CUE of litter decomposition in terrestrial ecosystems by Manzoni et al. (2017). This is shown by the gray circles in Fig. 6. Our optimized values of CUE_d for a given C : N ratio are more comparable with microbial CUE observed in incubations of soil mixed with litter (Gilmour and Gilmour, 1985; Devêvre and Horwáth, 2000; Thiet et al.,2006), shown as black squares in Fig. 6.

3.2 The effect of litter quality vs. quantity on equilibrium SOM stocks

Model M1 predicts that the size of the SOM pool at equilibrium is mainly determined by litter stoichiometry, with a minor effect of soil mineral N (Fig. 7). The lower the C : N ratio of litter is, the higher the equilibrium SOC stock. For litter with a specific C : N ratio, high soil mineral N concentration (e.g., above 0.05 g N kg⁻¹ soil) generally produces a slightly larger equilibrium SOC stock than a low mineral N concentration (Fig. 7). Further analysis suggests that the SOC at equilibrium increases with decreasing litter C : N because the SOC pool is positively related to the CUE_d; however, the limitation of soil mineral N on litter decomposition rate almost shows no impact on SOC (Fig. A4).

Figure 6Comparison of CUE_d (lines) predicted by Eq. (2) with parameter values (m₂=0.54, n₁=0.50) calibrated based on the incubation experiments (Table A2) of Recous et al. (1995) and Guenet et al. (2010) to observed CUE of terrestrial microorganisms along a gradient of CN_S∕CN_D. For observed CUE (dots), CN_D and CN_S are the C : N ratio of decomposers and their substrates, respectively. For simulated CUE (lines), CN_S and CN_D correspond to the C : N ratio of donor (litter pool) and acceptor (the active SOM pool of the CENTURY), respectively. Gray dots are the estimated microbial CUE of litter decomposition in natural terrestrial ecosystems from Manzoni et al. (2017). Black squares are the microbial CUE measured via laboratory incubation experiments of Gilmour and Gilmour (1985), Devêvre and Horwáth (2000) and Thiet et al. (2006). Error bars represent the standard deviations. N_min (g N kg⁻¹ soil) is the concentration of soil mineral N.

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Figure 7(a) Accumulation of soil organic carbon (SOC) for constant substrates input (plant litter) with different C : N ratios (CN_lit) at different levels of soil mineral N concentrations (N_min, g N kg⁻¹ soil), (b) change trends of equilibrium SOC stock and (c) carbon use efficiency of decomposed litter (CUE_d) with increasing litter C : N ratio.

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