A semi-arid grazing ecosystem simulation model with probabilistic and fuzzy parameters

Many of todayʹs grazing ecosystem management problems require a predictive understanding of the interactions between ecological processes acting across different spatiotemporal scales with complex soil, vegetation, climate, topographic and geologic characteristics. Due to complexity of ecosystems and the incomplete nature of empirical data for specific relationships involved in ecosystem dynamics, resource managers usually select management strategies without complete information or knowledge. Such vagueness in real world situations is also an obstacle to understanding and modeling ecosystem dynamics by means of conventional mathematical and computer simulation techniques. Modeling, simulating, and analyzing actual ecosystems can be significantly improved if modeling is extended to deal with imprecise and vague variables, relationships, and events. In this paper, a simulation model combining fuzzy imprecision with probabilistic uncertainty is formulated to study climate-plant-herbivore interactions in grassland ecosystems. This approach provides a unifying simulation framework to integrate numerical data, linguistic statements, and expert experience. The model includes treatment of imprecise and vague input variables as fuzzy variables, use of fuzzy arithmetic in equations when fuzzy and probability numbers are involved, and replacement of some of the relationships in the dynamic systems either with fuzzy conditional statements, or with fuzzy algorithms. The temporal patterns of herbivore population and primary production for a laissez-faire, extensive system in both Australia and China are modeled. The consistency of results obtained from the two simulations suggests the underlying mechanisms for semi-arid grassland ecosystems are those included in the model. Models combining fuzzy sets to quantify subjective parameters and traditional mechanistic techniques can be used to form a basis of long-term managerial policies for a sustainable grassland ecosystem.