Analysis of the production stability of mixed grasslands: II: A mathematical framework for the quantification of production stability in grassland ecosystems

The analysis of the intrinsic properties and processes of ecosystems, which regulate the production stability of mixed grasslands, has been complicated by the environmental noise caused by stochastic weather fluctuations. A mathematical framework is presented to deduct the actual, the extrinsic and the intrinsic stability of grassland ecosystems, as defined in the companion paper, from their yield patterns and the environmental patterns during a long time-course. Intrinsically stable grassland ecosystems remain stable when subjected to structured environmental fluctuations, yet are destabilised by stochastic environmental fluctuations. Contrastingly, intrinsically oscillating grassland ecosystems are on average somewhat stabilised by stochastic environmental fluctuations in temperate climates. Structured environmental fluctuations may fully stabilise these systems in continental climates. However, in these climates these ecosystems are destabilised by stochastic environmental fluctuations. As in some cases the actual stability of yields may be higher in intrinsically oscillating systems than in intrinsically stable systems, the stability of yields observed in short-term experiments is a poor reflection of the intrinsic ecosystem properties. Subsequently, this mathematical framework is applied to a number of experimental ecosystems in the Park Grass Experiment (UK) and at the Ossekampen (The Netherlands), which were subjected to various fertiliser and lime applications, and to a regime of either cutting or grazing, respectively. In the Park Grass Experiment, the yields of all plots studied appeared to be extrinsically unstable, with only small differences between fertiliser treatments. However, plots receiving lime showed a higher extrinsic stability than unlined plots. The extrinsic stability of the plot receiving farmyard manure (FYM) was lower than that of the plot receiving an equivalent of mineral nitrogen. Also at the Ossekampen, only small differences arose between the extrinsic stability of plots receiving various fertiliser treatments. Instead, the grassland management of the plots had an overriding effect on these stability levels. Whereas the extrinsic stability of all cut plots was low, all grazed plots were nearly entirely stable. It is argued that the nitrogen dynamics in grassland ecosystems have only a small impact on their extrinsic stability levels, in spite of the predictions by simulation models. Instead, pH-related soil processes and the grassland management play an overriding role in the maintenance of the production stability of mixed grassland. It is conceivable that a large number of other processes, which regulate ecosystem stability, could be identified in other plots and experiments, using the same mathematical framework.