An analytical approach to ecosystem biogeochemistry modeling

Models of terrestrial ecosystem carbon and nutrient biogeochemistry commonly utilize several compartments of organic matter (OM) to simulate the storage and turnover of OM in plant–soil systems. While much work has focused on numerical simulations of ecosystems to understand responses to perturbations, relatively little work explores the analytical properties of the mathematical systems used and their implications for the understanding of terrestrial ecosystems. We explore carbon and nutrient dynamics using a 4 × 4 transfer matrix, which is similar to the mathematical core of commonly used simulation models (e.g., Century). The C and N vectors contain one pool for photosynthesizing biomass and several pools for soil detritis. The model yields steady‐state solutions for the C pool size of each compartment dependent solely on the amount of the nutrient (nitrogen) stored within the compartment and the C:nutrient ratio. Furthermore, the C and nutrient storage in the model compartments depends on the inputs and losses of nutrients to and from the system as well as the coefficients for turnover from and transfer between compartments. When examining the transient behavior of the system, the eigenvalues for the system provide a useful tool for predicting and understanding the characteristic time scales with which plant–soil systems respond to perturbations. We use the model eigenvalues to examine ecosystem development from freshly exposed parent material as well as the response to a “catastrophic” disturbance event. Ultimately, the model's analytical tools can be extended to characterize soil organic matter (SOM) responses to several major land‐use changes occurring in agroecosystems—including the initiation of tillage, the application of industrial fertilizers, and the introduction of reduced‐tillage practices. Analysis of the eigenvalues for these cases suggests that agroecosystems tend to lose SOM more rapidly following the initiation of tillage than they can regain SOM after the initiation of conservation‐tillage practices. Additionally, the amount of N export (harvesting or loss) places an important control on the storage and future productivity of agricultural systems. Overall, we suggest that the model—with straightforward and accessible steady‐state solutions and eigenvalues—offers a complementary perspective to more complex numerical simulations. Corresponding Editor: D. S. Schimel