A general mathematical framework for representing soil organic matter dynamics

We propose here a general mathematical framework to represent soil organic matter dynamics. This framework is expressed in the language of dynamical systems and generalizes previous modeling approaches. It is based on a set of six basic principles about the decomposition of soil organic matter: (1) mass balance, (2) substrate dependence of decomposition, (3) heterogeneity of the speed of decay, (4) internal transformations of organic matter, (5) environmental variability effects, and (6) substrate interactions. We show how the majority of models previously proposed are special cases of this general model. This approach provides tools to classify models according to the main principles or concepts they include. It also helps to identify a priori the general behavior of different models or groups of models. Another important characteristic of the proposed mathematical representation is the possibility to develop particular models at any level of detail. This characteristic is described as a modeling hierarchy, in which a general model of a high degree of abstraction can accommodate specific realizations of model structure for specific modeling objectives. This framework also allows us to study general properties of groups of models such as their qualitative behavior, timescale of application, and their dynamic stability. For instance, we find conditions under which models are asymptotically stable, i.e., converge to a stable steady state in the long term, but may approach this state with or without oscillations. We also expand the concept of dynamic stability for models that include time dependencies and do not converge to a fixed steady state, but rather to a region of stability in the state-space. As an example of the application of the concept of dynamic stability, we show how this framework helps to explain the acclimation of soil respiration fluxes in soil-warming experiments.