Dynamics of Carbon and Nitrogen in the Organic Matter of the Soil: A Generic Theory

We show how it is possible, starting with the conservation of mass, to formulate a theory that, properly interpreted through a series of models, encompasses a large number of currently used formulations of soil organic matter turnover. Previously used models of turnover of soil organic matter can be derived by defining dispersion functions (D) of qualities (q,q') in the appropriate way. For example, the conventional way of dividing soil organic matter into a series of discrete state variables is obtained with D(q,q') defined by D(q,q') = ∑dijδ(q - qi)δ(q' - qj), where the summation is extended over the soil organic matter components. The qi's define the corresponding qualities, and dij is the fraction of carbon transferred from box j to box i. The theory functions in this respect as a metatheory for these other formulations. Our basic tenet is that the changes soil organic matter undergoes during decomposition should be viewed as a continuum of changes in carbon-containing compounds, described as a continuous change in the quality of soil organic matter as it is perceived by the microbial community that is feeding on it. The forces driving the system are encapsulated in three functions: a microbial production-to-assimilation ratio (e), a microbial growth rate (u), and D. These are continuous functions of the substrate quality. We demonstrate how the theory can be used at different levels of complexity, from working with the full information about the driving functions through a moment expansion that can be truncated at different orders to an adiabatic approximation, where the dispersion function is approximated with only two parameters. A major advantage of a continuous system is that qualitative aspects are more easily analyzed. This analysis shows that the qualitative effects of dispersion are to retard decomposition and increase nitrogen immobilization, although the N:C ratio will approach lower values. The retardation of the decomposition due to dispersion can even be so large that a litter cohort cannot be completelymineralized. Even where a discrete description of the soil organic matter is desirable, the theory formulated here is helpful, because it provides a way of checking the consistency of rate and transfer coefficients