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Describing the coupling of nitrogen (N), phosphorus (P), and carbon (C) cycles of land ecosystems requires understanding microbial element use efficiencies of soil organic matter (SOM) decomposition. These efficiencies are studied by the Soil Enzyme Steady Allocation Model (SESAM) at the decadal scale. The model assumes that the soil microbial communities and their element use efficiencies develop towards an optimum where the growth of the entire community is maximized. Specifically, SESAM approximated this growth optimization by allocating resources to several SOM-degrading enzymes proportional to the revenue of these enzymes, called the Relative approach. However, a rigorous mathematical treatment of this approximation has been lacking so far. Therefore, in this study we derive explicit formulas of enzyme allocation that maximize the total return from enzymatic processing, called the Optimal approach. Further, we derive another heuristic approach that prescribes the change of allocation without the need of deriving a formulation for the optimal allocation, called the Derivative approach. When comparing predictions across these approaches, we found that the Relative approach was a special case of the Optimal approach valid at sufficiently high microbial biomass. However, at low microbial biomass, it overestimated allocation to the enzymes having lower revenues compared to the Optimal approach. The Derivative-based allocation closely tracked the Optimal allocation. These findings increase our confidence in conclusions drawn from SESAM studies. Moreover, the new developments extend the range of conditions at which valid conclusions can be drawn. Further, based on these findings we formulated the constrained enzyme hypothesis. This hypothesis provides a complementary explanation why some substrates in soil are preserved over decades, although they are often decomposed within a few years in incubation experiments. This study shows how optimality considerations lead to simplified models, new insights, and new hypotheses. This is another step in deriving a simple representation of an adaptive microbial community, which is required for coupled stoichiometric C–N–P dynamic models that are aimed to study decadal processes beyond the ecosystem scale. [ABSTRACT FROM AUTHOR]

Describing the coupling of nitrogen (N), phosphorus (P), and carbon (C) cycles of land ecosystems requires understanding microbial element use efficiencies of soil organic matter (SOM) decomposition. These efficiencies are studied by the soil enzyme steady allocation model (SESAM) at decadal scale. The model assumes that the soil microbial communities and their element use efficiencies develop towards an optimum where the growth of the entire community is maximized. Specifically, SESAM approximated this growth optimization by allocating resources to several SOM degrading enzymes proportional to the revenue of these enzymes, called the Relative approach. However, a rigorous mathematical treatment of this approximation has been lacking so far. Therefore, in this study we derive explicit formulas of enzyme allocation that maximize total return from enzymatic processing, called the Optimal approach. Further, we derive another heuristic approach that prescribes the change of allocation without the need of deriving a formulation for the optimal allocation, called the Derivative approach. When comparing predictions across these approaches, we found that the Relative approach was a special case of the Optimal approach valid at sufficiently high microbial biomass. However, at low microbial biomass, it overestimated allocation to the enzymes having lower revenues compared to the Optimal approach. The Derivative-based allocation closely tracked the Optimal allocation. The model finding that the Relative approach was a special case of the more rigorous Optimal approach together with observing the same patterns across optimization approaches increases our confidence into conclusions drawn from SESAM studies. Moreover, the new developments extend the range of conditions at which valid conclusions can be drawn. The new model finding that a smaller set of enzyme types was expressed at low microbial biomass led us to formulate the constrained enzyme hypothesis, which provides a complementary explanation why some substrates in soil are preserved over decades although often being decomposed within a few years in incubation experiments. This study shows how optimality considerations lead to simplified models, new insights and new hypotheses. It is another step in deriving a simple representation of an adaptive microbial community, which is required for coupled stoichiometric CNP dynamic models that are aimed to study decadal processes beyond ecosystem scale. [ABSTRACT FROM AUTHOR]

The role of soil moisture for organic matter decomposition rates remains poorly understood and underrepresented in Earth System Models (ESMs). We apply the Dual Arrhenius Michaelis‐Menten (DAMM) model to a selection of ESM soil temperature and moisture outputs to investigate their effects on decomposition rates, at different soil depths, for a historical period and a future climate period. Our key finding is that the inclusion of soil moisture controls has diverging effects on both the speed and direction of projected decomposition rates (up to ±20%), compared to a temperature‐only approach. In the top soil, the majority of these changes is driven by substrate availability. In deeper soil layers, oxygen availability plays a relatively stronger role. Owing to these different moisture controls along the soil depth, our study highlights the need for depth‐resolved inclusion of soil moisture effects on decomposition rates within ESMs. This is particularly important for C‐rich soils in regions which may be subject to strong future warming and vertically opposing moisture changes, such as the peat soils at northern high latitudes. Plain Language Summary: Soils contain a lot of carbon (C). Earth System Models (ESMs) predict that the amount of C released from soils into the atmosphere as CO2 will increase in response to increased warming and microbial activity. Soil moisture also controls microbial C decomposition, but most ESMs do not yet describe this process very well. In this study we apply a simple equation to different ESMs, to see how both temperature and soil moisture change microbial decomposition under future climate. First, we show that the speed of C released into the atmosphere changes when we include soil moisture changes, compared to what is expected due to warming alone. Second, we found that the future speed at which carbon that can be decomposed in the topsoil mainly depends on how much carbon microbes have access to, but that in the deeper soil this process becomes much more affected by the absence/presence of oxygen. Including these soil moisture interactions in ESMs for different soil depths is important to predict whether soils will store more or less C in the future. Our findings are particularly relevant for high latitude soils which store large amounts of C, will warm fast, and experience frequent (re)wetting and drying. Key Points: Considering soil moisture effects can change modeled decomposition rates by up to ±20% compared to considering only temperature effectsThe majority of these changes are driven by substrate availability, in particular in the top soilIn the subsoil, oxygen availability becomes an increasingly important factor [ABSTRACT FROM AUTHOR]