S-system modelling approach to ecosystem: Application to a study of magnesium flow in a tropical forest

A theoretical framework suitable for modelling ecological systems is presented and applied to a previously developed material flow model for magnesium in a tropical forest in eastern Panama. An S-system representation of the system is developed within the Power Law formalism which allows not only modelling but also steady state characterization, sensitivity, steady state control and dynamic behaviour analyses of the ecological system under consideration. Results show that the system is at a stable steady state and the model is robust enough to guarantee a proper representation of the actual system. Regarding control of magnesium compartment content and fluxes, it is shown that the most controlling parameters are involved in recycling from soil to plants, magnesium input from sources other than rain or output from the ecosystem. The temporal changes in magnesium content of each trophic level after a 25% reduction in plant biomass shows that the system is stable against finite changes, returning to the previous steady state through a quasi-steady state at around 95% of the initial value. This trophic level recovers most of its initial steady state value after 100 years, but just after the first 25 years 95% of the initial value has already been reached. The remaining trophic levels, except that of soil, show a similar time profile. In this case magnesium concentration steadily decreases for 40 years and then begins to increase slowly. This result suggests a high magnesium donor capacity of the soil. Considering feasibility of ecological system management, the modelling and steady state control analysis approaches used here aid in identifying parameters in the system vital to design of manipulation strategies.