Microbial community-level regulation explains soil carbon responses to long-term litter manipulations

Climatic, atmospheric, and land-use changes all have the potential to alter soil microbial activity, mediated by changes in plant inputs. Many microbial models of soil organic carbon (SOC) decomposition have been proposed recently to advance prediction of climate and carbon (C) feedbacks. Most of these models, however, exhibit unrealistic oscillatory behavior and SOC insensitivity to long-term changes in C inputs. Here we diagnose the source of these problems in four archetypal models and propose a density-dependent formulation of microbial turnover, motivated by community-level interactions, that limits population sizes and reduces oscillations. We compare model predictions to 24 long-term C-input field manipulations and identify key benchmarks. The proposed formulation reproduces soil C responses to long-term C-input changes and implies greater SOC storage associated with CO2-fertilization-driven increases in C inputs over the coming century compared to recent microbial models. This study provides a simple modification to improve microbial models for inclusion in Earth System Models.

, which is clearly proportional to the total C input rate; that is, . In contrast, for microbial models with density-dependent microbial turnover ( > 1), the proportionality between the steady-state MBC/SOC ratio and C input rate decreases. Consider the 2-pool microbial model with = 2, for example. In this case, the steady-state ratio of MBC/SOC can be written as This quantity has two limiting cases of sensitivity to the total C input rate, depending on the relative magnitude of the two terms in the numerator. When ( • HIJ,K ) > , which is the case for parameter sets used in the literature and given in Supplementary Table 1, then the steady-state MBC/SOC ratio is independent of the C input rate; that is, ∝ P . This decoupling of the steady-state MBC/SOC ratio from the C input rate in microbial models with densitydependence ( > 1) is corroborated by global observations showing that this ratio is confined to a narrow range around 1-2% 1,2 . First-order models, such as the 3-pool linear model in Fig. 1b, also predict a steady-state MBC/SOC ratio that is independent of the total C input rate; however, this is simply because each pool changes proportionally to the total C inputs. This proportionality of SOC stocks to the change in total C inputs was not observed in the DIRT experiments (Fig. 6).
Comparing the predicted long-term MBC/SOC ratio, in addition to individual pool sizes, to observations can be a useful metric for validating models and constraining the value of in future studies.
Supplementary Figure 1: Stability of the 2-pool microbial model for a range of densitydependent microbial turnover exponents. The damping ratio ( ; defined in equation (21)) illustrates the degree of oscillatory behavior that the system will display following a perturbation.
The system is increasingly stable with a larger density-dependent microbial turnover exponent ( ), where for ≥ 1.5, a stable node ( = 1) is achieved.  CO 2 , where > 1 corresponds to a microbial model with density-dependent microbial turnover. Here a carbon use efficiency (CUE; ε) at 20°C of 0.90 was used. Although this CUE may be unrealistically high under most soil conditions, this illustrates how the transient dynamics are dependent on the parameter values, while the steady-state behavior is largely a consequence of the model structure. Here oscillations are diminished with larger CUE (as compared to Supplementary Fig. 4). Varying the parameter H (not shown) results in a response curve that is less steep at early times, especially for larger exponents. For these datasets one-way ANOVA, using SigmaPlot version 12 (Systat Software, Inc., San Jose, CA, USA), with was utilized to compare means. A Tukey HSD post hoc test was used for comparison of means if a significant p value was found. Significance for the contrasts was set at p = 0.05.
Due to budgetary constraints we combined subsamples into one homogenous sample per experimental plot for density fractionation. Thus d 13 C and D 14 C on fractions consist of single values, so it was not possible to run statistical tests. Total C values were pooled within ecosystems by treatment (e.g., data for Noe and Wingra Woods were averaged for each experimental treatment), however, with n = 2 we were not able to run statistical tests. The numbers in bold in Table 4, then, represent where both sites comprising the mean followed the same trend of either increase or decrease in SOC relative to the Control.

Results
Bulk C response to detrital manipulation There were significant differences in soil C among detrital treatments in the forested plots, both in the most recent sampling (Table 2) and over time ( Fig. 1) After 50 years, surface soil C concentration increased by 37 % in Double Litter plots compared to Controls in both forests. Soil N followed patterns of soil C although values were more variable (data in see Table 6 in Appendix). Because bulk density decreased slightly in Double Litter plots, the increase in C content increased slightly less compared to Controls (29-33 %). Bulk C concentration decreased in all sites where litter was excluded. In the forested No Litte plots, bulk C concentration decreased by *55 % afte 50 years (Table 2). Because bulk density increased significantly in No Litter plots, the decrease in C content was 40-47 %.
In prairie exclusion plots, C losses also increased over time (1997)(1998)(1999)(2000)(2001)(2002)(2003)(2004)(2005)(2006). In 1997 in Curtis Prairie 1, soi C concentration in the top 10 cm was significantly lower than control in No Input and No Roots plots; No Litter plots did not differ from control (Table 3). By 2006 No Litter plots showed slight, but significan decreases in soil C compared to Controls for Prairie 1 but not Prairie 3; there were no differences between C content loss in No Litter versus No Root plots. No Input plots lost 69-71 % of total soil C content afte 50 years. Soil N followed patterns of soil C, although  A Tukey HSD post hoc test was used for comparison of means if a significant p value was found. Significance for the contrasts was set at p = 0.05. Due to budgetary constraints we combined subsamples into one homogenous sample per experimental plot for density fractionation. Thus d 13 C and D 14 C on fractions consist of single values, so it was not possible to run statistical tests. Total C values were pooled within ecosystems by treatment (e.g., data for Noe and Wingra Woods were averaged for each experimental treatment), however, with n = 2 we were not able to run statistical tests. The numbers in bold in Table 4, then, represent where both sites comprising the mean followed the same trend of either increase or decrease in SOC relative to the Control.

Results
Bulk C response to detrital manipulation There were significant differences in soil C among detrital treatments in the forested plots, both in the most recent sampling ( Table 2) and over time (Fig. 1). After 50 years, surface soil C concentration increased by 37 % in Double Litter plots compared to Controls in both forests. Soil N followed patterns of soil C, although values were more variable (data in see Table 6 in Appendix). Because bulk density decreased slightly in Double Litter plots, the increase in C content increased slightly less compared to Controls (29-33 %). Bulk C concentration decreased in all sites where litter was excluded. In the forested No Litter plots, bulk C concentration decreased by *55 % after 50 years (Table 2). Because bulk density increased significantly in No Litter plots, the decrease in C content was 40-47 %.
In prairie exclusion plots, C losses also increased over time (1997)(1998)(1999)(2000)(2001)(2002)(2003)(2004)(2005)(2006). In 1997 in Curtis Prairie 1, soil C concentration in the top 10 cm was significantly lower than control in No Input and No Roots plots; No Litter plots did not differ from control (Table 3). By 2006 No Litter plots showed slight, but significant decreases in soil C compared to Controls for Prairie 1 but not Prairie 3; there were no differences between C content loss in No Litter versus No Root plots. No Input plots lost 69-71 % of total soil C content after 50 years. Soil N followed patterns of soil C, although   For these datasets one-way ANOVA, using SigmaPlot version 12 (Systat Software, Inc., San Jose, CA, USA), with was utilized to compare means. A Tukey HSD post hoc test was used for comparison of means if a significant p value was found. Significance for the contrasts was set at p = 0.05.
Due to budgetary constraints we combined subsamples into one homogenous sample per experimental plot for density fractionation. Thus d 13 C and D 14 C on fractions consist of single values, so it was not possible to run statistical tests. Total C values were pooled within ecosystems by treatment (e.g., data for Noe and Wingra Woods were averaged for each experimental treatment), however, with n = 2 we were not able to run statistical tests. The numbers in bold in Table 4, then, represent where both sites comprising the mean followed the same trend of either increase or decrease

Results
Bulk C response to detrital manipulation There were significant differences in soil C among detrital treatments in the forested plots, both in the most recent sampling ( Table 2) and over time ( Fig. 1) After 50 years, surface soil C concentration increased by 37 % in Double Litter plots compared to Controls in both forests. Soil N followed patterns of soil C although values were more variable (data in see Table 6 in Appendix). Because bulk density decreased slightly in Double Litter plots, the increase in C content increased slightly less compared to Controls (29-33 %). Bulk C concentration decreased in all sites where litter was excluded. In the forested No Litter plots, bulk C concentration decreased by *55 % after 50 years (Table 2). Because bulk density increased significantly in No Litter plots, the decrease in C content was 40-47 %.
In prairie exclusion plots, C losses also increased over time (1997)(1998)(1999)(2000)(2001)(2002)(2003)(2004)(2005)(2006). In 1997 in Curtis Prairie 1, soil C concentration in the top 10 cm was significantly lower than control in No Input and No Roots plots; No Litter plots did not differ from control (Table 3). By 2006 No Litter plots showed slight, but significant decreases in soil C compared to Controls for Prairie 1 but not Prairie 3; there were no differences between C content loss in No Litter versus No Root plots. No Input plots lost 69-71 % of total soil C content after 50 years. Soil N followed patterns of soil C, although  A Tukey HSD post hoc test was used for comparison of means if a significant p value was found. Significance for the contrasts was set at p = 0.05. Due to budgetary constraints we combined subsamples into one homogenous sample per experimental plot for density fractionation. Thus d 13 C and D 14 C on fractions consist of single values, so it was not possible to run statistical tests. Total C values were pooled within ecosystems by treatment (e.g., data for Noe and Wingra Woods were averaged for each experimental treatment), however, with n = 2 we were not able to run statistical tests. The numbers in bold in Table 4,

Results
Bulk C response to detrital manipulation There were significant differences in soil C among detrital treatments in the forested plots, both in the most recent sampling ( Table 2) and over time (Fig. 1). After 50 years, surface soil C concentration increased by 37 % in Double Litter plots compared to Controls in both forests. Soil N followed patterns of soil C, although values were more variable (data in see Table 6 in Appendix). Because bulk density decreased slightly in Double Litter plots, the increase in C content increased slightly less compared to Controls (29-33 %). Bulk C concentration decreased in all sites where litter was excluded. In the forested No Litter plots, bulk C concentration decreased by *55 % after 50 years (Table 2). Because bulk density increased significantly in No Litter plots, the decrease in C content was 40-47 %.
In prairie exclusion plots, C losses also increased over time (1997)(1998)(1999)(2000)(2001)(2002)(2003)(2004)(2005)(2006). In 1997 in Curtis Prairie 1, soil C concentration in the top 10 cm was significantly lower than control in No Input and No Roots plots; No Litter plots did not differ from control (Table 3). By 2006 No Litter plots showed slight, but significant decreases in soil C compared to Controls for Prairie 1 but not Prairie 3; there were no differences between C  Due to budgetary constraints we combined subsamples into one homogenous sample per experimental plot for density fractionation. Thus d 13 C and D 14 C on fractions consist of single values, so it was not possible to run statistical tests. Total C values were pooled within ecosystems by treatment (e.g., data for Noe and Wingra Woods were averaged for each experimental treatment), however, with n = 2 we were not able to run statistical tests. The numbers in bold in Table 4, then, represent where both sites comprising the mean followed the same trend of either increase or decrease in SOC relative to the Control.

Results
Bulk C response to detrital manipulation There were significant differences in soil C among detrital treatments in the forested plots, both in the most recent sampling ( Table 2) and over time ( Fig. 1) After 50 years, surface soil C concentration increased by 37 % in Double Litter plots compared to Controls in both forests. Soil N followed patterns of soil C although values were more variable (data in see Table 6 in Appendix). Because bulk density decreased slightly in Double Litter plots, the increase in C content increased slightly less compared to Controls (29-33 %). Bulk C concentration decreased in all sites where litter was excluded. In the forested No Litter plots, bulk C concentration decreased by *55 % after 50 years (Table 2). Because bulk density increased significantly in No Litter plots, the decrease in C content was 40-47 %.
In prairie exclusion plots, C losses also increased over time (1997)(1998)(1999)(2000)(2001)(2002)(2003)(2004)(2005)(2006). In 1997 in Curtis Prairie 1, soil C concentration in the top 10 cm was significantly lower than control in No Input and No Roots plots; No Litter plots did not differ from control (Table 3). By 2006 No Litter plots showed slight, but significant decreases in soil C compared to Controls for Prairie 1 but not Prairie 3; there were no differences between C content loss in No Litter versus No Root plots. No Input plots lost 69-71 % of total soil C content after 50 years. Soil N followed patterns of soil C, although  A Tukey HSD post hoc test was used for comparison of means if a significant p value was found. Significance for the contrasts was set at p = 0.05. Due to budgetary constraints we combined subsamples into one homogenous sample per experimental plot for density fractionation. Thus d 13 C and D 14 C on fractions consist of single values, so it was not possible to run statistical tests. Total C values were pooled within ecosystems by treatment (e.g., data for Noe and Wingra Woods were averaged for each experimental treatment), however, with n = 2 we were not able to run statistical tests. The numbers in bold in Table 4, then, represent where both sites comprising the mean followed the same trend of either increase or decrease in SOC relative to the Control.

Bulk C response to detrital manipulation
There were significant differences in soil C among detrital treatments in the forested plots, both in the most recent sampling ( Table 2) and over time (Fig. 1). After 50 years, surface soil C concentration increased by 37 % in Double Litter plots compared to Controls in both forests. Soil N followed patterns of soil C, although values were more variable (data in see Table 6 in Appendix). Because bulk density decreased slightly in Double Litter plots, the increase in C content increased slightly less compared to Controls (29-33 %). Bulk C concentration decreased in all sites where litter was excluded. In the forested No Litter plots, bulk C concentration decreased by *55 % after 50 years (Table 2). Because bulk density increased significantly in No Litter plots, the decrease in C content was 40-47 %.
In prairie exclusion plots, C losses also increased over time (1997)(1998)(1999)(2000)(2001)(2002)(2003)(2004)(2005)(2006). In 1997 in Curtis Prairie 1, soil C concentration in the top 10 cm was significantly lower than control in No Input and No Roots plots; No Litter plots did not differ from control (Table 3). By 2006 No Litter plots showed slight, but significant decreases in soil C compared to Controls for Prairie 1 but not Prairie 3; there were no differences between C content loss in No Litter versus No Root plots. No Input plots lost 69-71 % of total soil C content after 50 years. Soil N followed patterns of soil C, although  Due to budgetary constraints we combined subsamples into one homogenous sample per experimental plot for density fractionation. Thus d 13 C and D 14 C on fractions consist of single values, so it was not possible to run statistical tests. Total C values were pooled within ecosystems by treatment (e.g., data for Noe and Wingra Woods were averaged for each experimental treatment), however, with n = 2 we were not able to run statistical tests. The numbers in bold in Table 4, then, represent where both sites comprising the mean followed the same trend of either increase or decrease in SOC relative to the Control.

Results
Bulk C response to detrital manipulation There were significant differences in soil C among detrital treatments in the forested plots, both in the most recent sampling ( Table 2) and over time (Fig. 1). After 50 years, surface soil C concentration increased by 37 % in Double Litter plots compared to Controls in both forests. Soil N followed patterns of soil C, although values were more variable (data in see Table 6 in Appendix). Because bulk density decreased slightly in Double Litter plots, the increase in C content increased slightly less compared to Controls (29-33 %). Bulk C concentration decreased in all sites where litter was excluded. In the forested No Litter plots, bulk C concentration decreased by *55 % after 50 years (Table 2). Because bulk density increased significantly in No Litter plots, the decrease in C content was 40-47 %.
In prairie exclusion plots, C losses also increased over time (1997)(1998)(1999)(2000)(2001)(2002)(2003)(2004)(2005)(2006). In 1997 in Curtis Prairie 1, soil C concentration in the top 10 cm was significantly lower than control in No Input and No Roots plots; No Litter plots did not differ from control (Table 3). By 2006 No Litter plots showed slight, but significant decreases in soil C compared to Controls for Prairie 1 but not Prairie 3; there were no differences between C content loss in No Litter versus No Root plots. No Input plots lost 69-71 % of total soil C content after 50 years. Soil N followed patterns of soil C, although  Table 2. When SE bars are not shown it is because the SE was smaller than the symbol For these datasets one-way ANOVA, using SigmaPlot version 12 (Systat Software, Inc., San Jose, CA, USA), with was utilized to compare means. A Tukey HSD post hoc test was used for comparison of means if a significant p value was found. Significance for the contrasts was set at p = 0.05.
Due to budgetary constraints we combined subsamples into one homogenous sample per experimental plot for density fractionation. Thus d 13 C and D 14 C on fractions consist of single values, so it was not possible to run statistical tests. Total C values were pooled within ecosystems by treatment (e.g., data for Noe and Wingra Woods were averaged for each experimental treatment), however, with n = 2 we were not able to run statistical tests. The numbers in bold in Table 4,

Results
Bulk C response to detrital manipulation There were significant differences in soil C among detrital treatments in the forested plots, both in the most recent sampling ( Table 2) and over time (Fig. 1). After 50 years, surface soil C concentration increased by 37 % in Double Litter plots compared to Controls in both forests. Soil N followed patterns of soil C, although values were more variable (data in see Table 6 in Appendix). Because bulk density decreased slightly in Double Litter plots, the increase in C content increased slightly less compared to Controls (29-33 %). Bulk C concentration decreased in all sites where litter was excluded. In the forested No Litter plots, bulk C concentration decreased by *55 % after 50 years (Table 2). Because bulk density increased significantly in No Litter plots, the decrease in C content was 40-47 %.
In prairie exclusion plots, C losses also increased over time (1997)(1998)(1999)(2000)(2001)(2002)(2003)(2004)(2005)(2006). In 1997 in Curtis Prairie 1, soil C concentration in the top 10 cm was significantly lower than control in No Input and No Roots plots; No Litter plots did not differ from control (Table 3). By 2006 No Litter plots showed slight, but significant decreases in soil C compared to Controls for Prairie 1 but not Prairie 3; there were no differences between C

Results
Bulk C response to detrital manipulation There were significant differences in soil C among detrital treatments in the forested plots, both in the most recent sampling ( Table 2) and over time (Fig. 1). After 50 years, surface soil C concentration increased by 37 % in Double Litter plots compared to Controls in both forests. Soil N followed patterns of soil C, although values were more variable (data in see Table 6 in Appendix). Because bulk density decreased slightly in Double Litter plots, the increase in C content increased slightly less compared to Controls (29-33 %). Bulk C concentration decreased in all sites where litter was excluded. In the forested No Litter plots, bulk C concentration decreased by *55 % after 50 years (Table 2). Because bulk density increased significantly in No Litter plots, the decrease in C content was 40-47 %.
In prairie exclusion plots, C losses also increased over time (1997)(1998)(1999)(2000)(2001)(2002)(2003)(2004)(2005)(2006). In 1997 in Curtis Prairie 1, soil C concentration in the top 10 cm was significantly lower than control in No Input and No Roots plots; No Litter plots did not differ from control (Table 3)  Due to budgetary constraints we combined subsamples into one homogenous sample per experimental plot for density fractionation. Thus d 13 C and D 14 C on fractions consist of single values, so it was not possible to run statistical tests. Total C values were pooled within ecosystems by treatment (e.g., data for Noe and Wingra Woods were averaged for each experimental treatment), however, with n = 2 we were not able to run statistical tests. The numbers in bold in Table 4, then, represent where both sites comprising the mean

Results
Bulk C response to detrital manipulation There were significant differences in soil C among detrital treatments in the forested plots, both in the most recent sampling ( Table 2) and over time (Fig. 1). After 50 years, surface soil C concentration increased by 37 % in Double Litter plots compared to Controls in both forests. Soil N followed patterns of soil C, although values were more variable (data in see Table 6 in Appendix). Because bulk density decreased slightly in Double Litter plots, the increase in C content increased slightly less compared to Controls (29-33 %). Bulk C concentration decreased in all sites where litter was excluded. In the forested No Litter plots, bulk C concentration decreased by *55 % after 50 years (Table 2). Because bulk density increased significantly in No Litter plots, the decrease in C content was 40-47 %.
In prairie exclusion plots, C losses also increased over time (1997)(1998)(1999)(2000)(2001)(2002)(2003)(2004)(2005)(2006). In 1997 in Curtis Prairie 1, soil C concentration in the top 10 cm was significantly lower than control in No Input and No Roots plots; No Litter plots did not differ from control (Table 3). By 2006 No Litter plots showed slight, but significant decreases in soil C compared to Controls for Prairie 1 but not Prairie 3; there were no differences between C content loss in No Litter versus No Root plots. No  Table 2. When SE bars are not shown it is because the SE was smaller than the symbol

Results
Bulk C response to detrital manipulation There were significant differences in soil C amon detrital treatments in the forested plots, both in th most recent sampling (Table 2) and over time (Fig. 1 After 50 years, surface soil C concentration increase by 37 % in Double Litter plots compared to Contro in both forests. Soil N followed patterns of soil C although values were more variable (data in se Table 6 in Appendix). Because bulk density decrease slightly in Double Litter plots, the increase in content increased slightly less compared to Contro  Table 2. When SE bars are not shown it is becau the SE was smaller than the symbol

Results
Bulk C response to detrital manipulation There were significant differences in soil C amon detrital treatments in the forested plots, both in th most recent sampling (Table 2) and over time (Fig. 1 After 50 years, surface soil C concentration increase by 37 % in Double Litter plots compared to Control in both forests. Soil N followed patterns of soil C  Table 2. When SE bars are not shown it is becaus the SE was smaller than the symbol  Table 2. When SE bars are not shown it is becaus the SE was smaller than the symbol

Results
Bulk C response to detrital manipulation There were significant differences in soil C among detrital treatments in the forested plots, both in the most recent sampling ( Table 2) and over time (Fig. 1). After 50 years, surface soil C concentration increased by 37 % in Double Litter plots compared to Controls in both forests. Soil N followed patterns of soil C, although values were more variable (data in see Table 6 in Appendix). Because bulk density decreased

Results
Bulk C response to detrital manipulation There were significant differences in soil C among detrital treatments in the forested plots, both in the most recent sampling ( Table 2) and over time (Fig. 1). After 50 years, surface soil C concentration increased  Table 2. When SE bars are not shown it is because the SE was smaller than the symbol  Table 2. When SE bars are not shown it is because the SE was smaller than the symbol