An analytical solution to study substrate-microbial dynamics in soils

We provide an approximate analytical solution for the substrate-microbial dynamics of the organic carbon cycle in natural soils under hydro-climatic variable forcing conditions. The model involves mass balance in two carbon pools: substrate and biomass. The analytical solution is based on a perturbative solution of concentrations, and can properly reproduce the numerical solutions for the full non-linear problem in a system evolving towards a steady state regime governed by the amount of labile carbon supplied to the system. The substrate and the biomass pools exhibit two distinct behaviors depending on whether the amount of carbon supplied is below or above a given threshold. In the latter case, the concentration versus time curves are always monotonic. Contrarily, in the former case the C-pool concentrations present oscillations, allowing the reproduction of non-monotonic small-scale biomass concentration data in a natural soil, observed so far only in short-term experiments in the rhizosphere. Our results illustrate the theoretical dependence of oscillations from soil moisture and temperature and how they may be masked at intermediate scales due to the superposition of solutions with spatially variable parameters.