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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 pro- portional 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 pre- dictions 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 micro- bial community, which is required for coupled stoichiometric CNP dynamic models that are aimed to study decadal processes beyond ecosystem scale. [ABSTRACT FROM AUTHOR]

Understanding the coupling of nitrogen (N) and carbon (C) cycles of land ecosystems requires understanding microbial element use efficiencies of soil organic matter (SOM) decomposition. Whereas important controls of those efficiencies by microbial community adaptations have been shown at the scale of a soil pore, a simplified representation of those controls is needed at the ecosystem scale. However, without abstracting from the many details, models are not identifiable; i.e. they cannot be fitted without ambiguities to observations. There is a need to find, implement, and validate abstract simplified formulations of theses processes. 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. [ABSTRACT FROM AUTHOR]

Understanding the coupling of nitrogen (N) and carbon (C) cycles of land ecosystems, requires understanding microbial element use efficiencies of soil organic matter (SOM) decomposition. Whereas important controls of those efficiencies by microbial community adaptations have been shown at the scale of a soil pore, a simplified representation of those controls is needed at the ecosystem scale. However, without abstracting from the many details, models are not identifiable, i.e. can not be fitted without ambiguities to observations. There is a need to find, implement, and validate abstract simplified formulations of theses processes. Therefore, we developed the SESAM model as an abstraction of the more detailed soil enzyme allocation model (SEAM) model and tested, whether it can provide the same decadal-term predictions. SEAM explicitly models community adaptation strategies of resource allocation to extracellular enzymes and enzyme limitations on SOM decomposition. It thus provides a scaling from representing several microbial functional groups to a single holistic microbial community. Here we further abstracted the model using quasi-steady-state assumption for extracellular enzyme pools to derive the SESAM model. SESAM reproduced the priming effect, the SOM banking mechanism, and the damping of fluctuations of carbon use efficiency with microbial competition as predicted by SEAM and other more detailed models. This development is an important step towards more parsimonious representation of soil microbial effects in global land surface models. [ABSTRACT FROM AUTHOR]