Understanding the coupling of nitrogen (

Therefore, we developed the Soil Enzyme Allocation Model (SEAM). The model explicitly represents community adaptation strategies of resource allocation to extracellular enzymes and enzyme limitations on SOM decomposition. They thus provide an abstraction from several microbial functional groups to a single holistic microbial community. Here we further simplify SEAM using a quasi-steady-state assumption for extracellular enzyme pools to derive the Soil Enzyme Steady Allocation Model (SESAM) and test whether SESAM can provide the same decadal-term predictions as SEAM.

SESAM reproduced the priming effect, the SOM banking mechanism, and the damping of fluctuations in carbon use efficiency with microbial competition as predicted by SEAM and other more detailed models. This development is an important step towards a more parsimonious representation of soil microbial effects in global land surface models.

Soil organic matter (SOM) dynamics constitutes a strong link of global nutrient cycles because the microbial decomposer community has a rather strict
homeostatic regulation of their stoichiometry

CUE is an emergent value that depends on microbial traits, such as maintenance requirements, and stoichiometric imbalances of the substrates that
microbes feed on (Sect.

In a first abstraction step models represent different microbial groups or guilds instead of single microbes

An alternative model abstraction represents a single microbial community with adapting properties by, for example, optimizing microbial growth in the
model. This concept was applied in the Soil Enzyme Allocation Model (SEAM)

In a further model abstraction, the effect of changing CUE can be modelled in conventional pool-based models without explicit microbial community by a
growth-adapted humification coefficient and stoichiometry-dependent decomposition rates as in the PRIM model

Hence, there is a need for a model abstraction with fewer details that is still able to represent effects of stoichiometry such as priming effects due
to

SESAM is intended to capture the longer-term, i.e. decadal, dynamics of SOM decomposition and abstracts from short-term dynamics,
i.e. shorter than seasonal, by applying the quasi-steady-state assumption

The aim of this paper is to present SESAM without pre-knowledge of SEAM and show that it can reproduce the predictions of SEAM at a decadal timescale and is therefore able to simulate the priming effect due to

The dynamic Soil Enzyme Steady Allocation Model (SESAM) allows exploration of the consequences of soil microbial stoichiometry for SOM cycling at the soil core
to the ecosystem scale at a decadal timescale. The modelled system consists of

State variables and model drivers. Values refer to the reference state of the sensitivity analysis and were adopted from

SESAM models several SOM pools containing

SESAM represents several SOM fractions by several pools that differ by their stoichiometry, and it represents changes in microbial community structure
by changing preferences in degrading specific SOM pools. The litter pool,

SESAM structure: microbial biomass

This paper presents model version 3, which in addition to the enzyme steady-state assumption differs from published SEAM

Decomposition of the litter and residue pools is modelled by reverse Michaelis–Menten kinetics

SESAM assumes that stoichiometry is one of the overarching controls of decadal-scale SOM changes. It assumes that microbial community and development of different SOM stocks adapt to changes in drivers without the need to explicitly model all the details of this adaptation.

There are three principle ways

SEAM and SESAM assume that a combination of options 1 and 3 is used in a way to optimize growth, and option 2 is negligible. Modelled microbial
community develops in a way so that different kinds of enzymes are produced in proportion to their revenue, i.e. the decomposition return per unit of
limiting element invested into enzyme production. This microbial enzyme allocation strategy performed better in simulation experiments

While this adaptive single microbial community was a necessary step in the direction to simplify models, SEAM required two model parameters for the dynamics of the enzyme pools. These parameters are hard to measure and added complexity to model–data integration. The presented SESAM uses only one enzyme-production-related parameter, while the enzyme turnover parameter merges with the half-saturation parameter of the SOM decomposition.

SESAM abstracts from short-term dynamics of enzyme pools in SEAM by assuming that soil extracellular enzyme pools are in a quasi-steady state

It assumes that compared to the intended decadal modelling timescale, the amount of soil extracellular enzyme mass and the composition of the microbial
community approach a steady state given the annually smoothed inputs and drivers of the modelled system and current SOM stocks. This yields the
enzyme states in Eq. (

This steady-state expression is used instead of the explicitly modelled enzyme pool in SEAM to simplify other equations. For example, decomposition of
the residue pool now depends on biomass rather than enzyme levels (Eq.

We further explored two additional potential simplifying model assumptions. First the microbial biomass can be assumed to be in a quasi-steady state
(SteadyB; Appendix

Enzyme allocation

While the original SEAM computed both the return and the investment for each element

The return of an element

When inserting the steady-state revenue into Eq. (

In order to show the ability of SESAM to reproduce the priming effects due to

We compared results of the following model variants:

SEAM – baseline model with explicit representation of extracellular enzymes,

SESAM – enzyme levels assumed in a quasi-steady state,

SESAM-NoEnzFlux – additionally neglecting the mass flux of

SESAM-SteadyB – additionally microbial biomass assumed in a quasi-steady state (Appendix

The derivatives of the model variants were implemented in the R programming language

In order to show the ability of SESAM to reproduce the damping of fluctuations in CUE with adapting microbial community, we simulated an incubation
experiment. SESAM models CUE as an emergent property instead of a model parameter. With the substrate pulse scenario we
simulated an experiment similar to the one in

In this experiment microbial community decomposes a carbon-rich chunk of initial litter whose initial

Simulations were compared between SESAM, which has dynamic enzyme allocation, and a model version where we fixed community enzyme allocation

We used the same R-based computational setup as in the increased

In order to explore which parameters most influence the steady-state and transient predictions of the increased

For each parameter we prescribed prior distributions of possible parameter values (Table

We checked robustness of the setting by repeating the analysis by sampling

While the increased

For each model run, we computed (a) the steady-state SOM stocks and (b) the change in SOM stocks after 100 years of increased

SESAM was recoded using the Julia programming language

In order to explore the possible bias in long-term predictions due to the enzyme steady-state assumption combined with the non-linearity of its effect on decomposition we simulated strong seasonal fluctuations in litter inputs causing seasonal fluctuations in elemental limitation and enzyme community allocation.

SESAM incorporates nonlinear functions. Hence, average decomposition computed with fluctuating enzyme levels will give different results compared to decomposition computed with first averaging enzyme levels. Hence, the difference between explicitly modelled enzyme levels and steady-state enzyme levels has the potential to introduce bias also in the average long-term predictions.

In order to investigate the effect of both the time-averaging and enzyme steady-state assumption we performed an experiment where we ran both SESAM and a
version of SEAM that explicitly tracks enzyme pools but otherwise uses the same formulations, with the setting of the increased

Seasonally fluctuating litter input rate was simulated by assuming 50 % of litter input by aboveground litterfall in autumn only. Physical decay of an aboveground litter pool with turnover time of 2 months then contributed to inputs to the SOM model. At year zero an increase in average annual litter input was prescribed.

The fluctuating litter scenario displayed stiff properties; hence we used the Vern7 method

SOM stocks, here approximated by the sum of litter,

The imbalance in stoichiometry with increased

Hence, the models simulated microbial

At this timescale there were no apparent differences between the enzyme explicit SEAM and the quasi-steady-state models SESAM and its SteadyB
variant. The NoEnzFlux variant lacked a refuelling of the DOM pool by the

CUE varied dynamically in the substrate pulse simulations (Fig.

Variation in carbon use efficiency (CUE) over time with the substrate pulse simulation is more dampened, i.e. is not changing as much with changing substrate stoichiometry, if microbial community can adapt enzyme allocation compared to fixed allocation. This was true both across time (

The differences in CUE across time and across initial litter

SOM stocks and their transient changes in the increased

Simulated stock change with increased

When repeating the sensitivity analysis on a subspace that included 40 % rather than 20 % of each parameter range, the results were
influenced by extreme values due to unusual parameter combinations. We observed similar total effects of SOM stocks, but first-order effects were
slightly smaller. SOM stock changes now were additionally sensitive to decomposition rate,

Simulation results differed only marginally between steady-state enzymes (SESAM) and explicit representation of enzyme level (SEAM) in the fluctuating
litter input simulations (Fig.

Small differences in transient

Fluxes based on averaging litter inputs also roughly matched the average of the fluxes based on fluctuating litter inputs at a steady state
(Fig.

The largest simulated differences due to averaging litter input were observed in transient changes in the fast pools, e.g. the inorganic

Soil organic matter (SOM) science has experienced a paradigm shift from understanding persistence of SOM formerly on chemical SOM properties towards
understanding persistence as an interactive effect of environmental conditions

Microbial processes work on pore spatial scale and hourly to daily temporal scales. In our work we pursue the hypothesis that at the pedon scale and longer
decadal-term scale, stoichiometry provides one of the most important constraints

The presented SESAM employs the simplifying assumption of enzyme levels being close to steady-state (Sect.

Because of the just-explained problems of omitting buffering capabilities of soil microbes to sudden environmental changes, we recommend driving SESAM
with annually averaged model drivers. However, averaging inputs together with nonlinear functions can cause bias

Competition between microbial groups and adaptation of the microbial community is one of the detailed processes that have been shown to exert strong
control on decadal-term SOM dynamics

Whether increased

Model–data-integration studies require observations at the modelled timescale. SESAM predicts a change in proportion of different SOM pools in
response to shifting nutrient limitations. While the relative changes in SOM pools are so small that they are very hard to directly measure, changes
can potentially be detected by observing changing

Optimal detail or complexity of models depends on the purpose of the model and on the available data to constrain the models

There are many attempts to directly implement microbial processes into global models with introducing many free parameters

SESAM aims at reducing model complexity. There are in total 14 model parameters, and long-term SOM stock changes were sensitive to only a few of them. This is a more tractable number of parameters for model inversions, although there will be more parameters for temperature and moisture dependencies and transport when integrated into larger models. Because SESAM targets the decadal-term scale, decadal-term drivers and observations should also be used in SESAM model–data-integration studies. Currently, the free air enrichment experiments are running about 20 years. Thus, obtained observations are getting long enough to calibrate and test models at a decadal timescale.

The turnover rate of microbial biomass,

The application of the quasi-steady-state assumption for extracellular enzyme pools simplified a model of microbial adaptation to substrate
stoichiometry. The simplified SESAM could reproduce important effects of microbial stoichiometry on SOM dynamics at a decadal timescale,
specifically the priming effect, microbial

For an overview of symbol definitions see Tables

Model parameters and distributions used in the sensitivity analysis.

Further symbols of quantities derived within the system.

Total enzyme production

With assuming enzyme production and turnover to be in a quasi-steady state and reverse Michaelis–Menten kinetics for substrate decomposition

We assume a quasi-steady state of the DOM pool, and hence, microbial uptake equals the sum of all influxes to the DOM pool (decomposition

With

A part of

Nitrogen fluxes are computed by dividing the respective

We assumed fixed

The inorganic

Several component fluxes sum to total mineralization flux in SESAM:

In addition to the mineralization–immobilization imbalance flux,

Potential

The

Equation (

There is a constraint on the synthesis of new biomass by each chemical element. In SESAM synthesis follows the minimum of these constraints
(Eq.

The elements in excess then are lost by imbalance fluxes (Eq.

The actual mineralization–immobilization flux

Microbes in SESAM allocate a proportion

SESAM models composition,

Community can change fast either if it is growing fast or if it is decaying fast. Hence, both terms are considered in Eq. (

SESAM3 adopts the revenue strategy where investment in enzyme synthesis is proportional to its revenue

The unnormalized weight of an element limitation,

Compared with SEAM, already a small

During microbial turnover, a part

A respective proportion of

The remainder of the microbial turnover goes to the residue pool. The current SESAM version ignores the part that enters the DOM pool and is taken up again by living microbial biomass. This corresponds to an effective uptake rate, assuming that the effects of this DOM flux on pools cancel in their parameterizations. This shortcut leads to a joint small underestimation of microbial turnover, uptake, and CUE. Investigating the effect of this simplifying assumption on isotopic tracers is an outlook.

Instead of taking the entire decomposition flux as return, one could account for the mineralization–immobilization pathway and the fact that during this path,
part of the decomposition flux is routed away from microbial biomass.

This leads to updated equations of return, revenue, and community composition (Eq.

Notice that

When one element is clearly limiting, then the returns in both the numerator
and the denominator in the computation of

We argue that the case of clear co-limitation is quite rare. Depending on fluctuations in litter input and soil heterogeneity, the microbial
community at a given time and a given spot is usually limited by one of the elements. Therefore, SESAM currently adopts the simpler version
of the return (Eq.

Results of repeated sensitivity analysis on a larger parameter subspace (Fig.

Modification of Fig.

The following figures help to understand the result of Sect.

The aboveground litter inputs in autumn caused time-lagged responses and smoothed responses in the modelled soil properties
(Fig.

Model responses to a spike of aboveground litterfall in autumn,

Due to this smoothing and lagging behaviour, the simulated steady-state enzyme levels closely tracked the explicit enzyme levels
(Fig.

Enzyme levels, here shown for residue degrading enzyme,

SESAM does not explicitly represent enzyme pools. However, the mass fluxes across the enzyme pool from biomass to DOM and to the residue pool are represented.

A model variant “NoEnzFlux” has been implemented, where the enzyme pools are still part of the revenue computation, but mass fluxes across the
enzyme pools are neglected. This has been accomplished by using

Here we derive equations for microbial biomass in a quasi-steady state.

By setting

Carbon available for biomass synthesis,

With enzymes in a quasi-steady state, the uptake from enzyme turnover equals enzyme production,

This results in a square equation. If there is no real positive solution, biomass cannot be sustained, otherwise the maximum of the two roots gives the
required steady-state biomass,

For

This results in a cubic equation. Its second root is real and gives the steady-state biomass,

While steady-state biomass can be computed and passed to other equations that involve biomass, these other equations are not simplified.

SESAM (v3.0) is available coded in R at

The model version comparison code of this study is part of the R repository in the file develop/19GMD_paper/CompareModels.Rmd. The sensitivity analysis code of this study is part of the Julia repository at inst/22paper_upscaling/sensitivity_Face.jl and the fluctuation analysis at inst/22paper_upscaling/fluctuation_analysis.jl.

TW developed the model and led the writing of the manuscript. LY implemented SESAM into a larger land model, which initiated several reformulations of model aspects. TW, LY, MS, and SZ contributed to the discussion of results and writing of the manuscript.

The contact author has declared that none of the authors has any competing interests.

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

We thank Bernhard Ahrens and Markus Reichstein for fruitful discussion. We thank the Max Planck Society for funding. Lin Yu is supported by the Swedish-government-funded Strategic Research Area Biodiversity and Ecosystems in a Changing Climate, BECC.

The article processing charges for this open-access publication were covered by the Max Planck Society.

This paper was edited by Christoph Müller and reviewed by Nadezda Vasilyeva and one anonymous referee.