The coupling of biogeochemical cycles of nutrients

For any element which is incorporated into biomass, the biogeochemical cycle of that element in a given ecosystem will be coupled to that of any other element similarly incorporated. The mutual interaction of two such cycles is examined using a simple model in which each cycle is constrained into four compartments. In each cycle the assimilation rate (primary productivity) is related in a non-linear fashion to the two nutrients and to biomass. The interactions are represented by combining a hyperbolic dependence for each nutrient (involving a "Michaelis constant") with a logistic equation governing the dependence of rate on biomass (involving a "carrying capacity"). The response of the model to perturbation (e.g. mobilization of an abiotic reserve) is strongly governed by the values assigned to these constants. The coupled cycles can exhibit positive feed-back with anomalous responses of the steady state and time-dependent solutions may exhibit complex oscillatory behaviour. Both the steady-state sensitivity and the kinetic behaviour of such coupled systems are simplified if the range of atomic ratios permitted by the assimilation process is restricted. It will therefore be of importance to determine under what conditions the assimilation rates for different elements are governed by mass-action effects (Liebig's Law) or by stoichiometric constraints (Redfield ratios).