A theoretical analysis of nonlinearities and feedbacks in soil carbon and nitrogen cycles

Analytical formulations of soil carbon and nitrogen cycles are used to explore the effects of model nonlinearities and feedbacks on the resulting dynamics. Two particular aspects are addressed: (i) nonlinearities in the decomposition rate of soil organic matter and (ii) nitrogen limitation feedbacks on microbial activity and plant–microbe competition. Although linear models of decomposition are more typical in the literature, nonlinear models accounting for the coupling between microbial biomass and its substrate have also been proposed. In deterministic conditions, linear models behave like exponential decay functions, while nonlinear models may also show fluctuating behavior, with dynamic bifurcations between stable-node and stable-focus equilibria as a function of the climatic parameters (e.g., soil moisture and temperature). Both data-model comparison and linear stability analysis support the conclusion that linear models are less suited to describe the soil fluctuating dynamics that arise under certain conditions. A second strong nonlinearity appears when the nitrogen-limitation feedback on decomposition is analyzed. Nitrogen limitation is often established when the substrate of the microbes is N-poor, and/or the competition with plants for mineral N is strong. Such conditions mainly occur when a large fraction of the microbial community cannot meet its nitrogen demand through organic N assimilation, so that mineral N is used. On the contrary, when the microbial community predominantly assimilates organic nitrogen, the occurrence of nitrogen-limitation is less likely and mineralization is given by microbial N surplus. The first case is traditionally modeled by the mineralization–immobilization turnover (MIT) scheme, while the second by the direct assimilation (DIR) scheme. However, since organic N assimilation and mineral N immobilization likely occur simultaneously because of soil heterogeneity and coexistence of different microbial communities, the two schemes only represent extreme cases. Thus, we combine them in a flexible model framework (parallel scheme) and explore how different efficiencies of organic nitrogen assimilation, mineral nitrogen availability and climatic factors control the outcome of plant–microbe competition. We conclude that models accounting only for the DIR pathway implicitly assume that microbes are superior competitors over plants, while models implementing only the MIT pathway might be too sensitive to N-limitation.