The loss of utilisable rangeland in semi-arid areas results in huge economic and social costs worldwide. Only adaptive management strategies are able to cope with these systems, which are largely driven by unpredictable and stochastic rainfall. Additionally they are characterized by strong feedback mechanisms between economic and ecological factors. This study aims to contribute to the identification of basic principles for sustainable grazing management. The approach emphasizes learning from existing management systems through the use of ecological-economic modelling. Two apparently successful management systems in Namibia are used as a starting point for a broader analysis: the Gamis Karakul sheep farm and the land use system of the semi-nomadic Ova-Himba. Although the economic systems differ strongly, their management seems to have similarities: the importance of pasture resting and of adapting livestock numbers to available forage. This PhD thesis contributes substantial insights about the relevance and functioning of pasture resting for sustainable grazing management in semi-arid regions. Assessment of the two case studies leads to the hypothesis that resting in the rainy season, particularly during wet years, is fundamental for ensuring pasture productivity under low regeneration potential of the vegetation. The thesis highlights that resting during wet years acts as a risk reducing strategy. Additionally, the study reveals that access to economic risk management strategies, such as rain-index-insurance, may change farmer´s behaviour towards less conservative strategies. The used approach - learning from existing apparently successful grazing strategies by ecological-economic modelling - offers a powerful tool for tackling new questions related to global change. The scope and the limits for generalizing the key factors discovered for sustainable grazing management can be easily detected under changing ecological, climatic and economic conditions.

Cellular automata (CA) are fully discrete dynamical systems. Space is represented by a regular lattice while time proceeds in finite steps. Each cell of the lattice is assigned a state, chosen from a finite set of "values". The states of the cells are updated synchronously according to a local interaction rule, whereby each cell obeys the same rule. Formal definitions of deterministic, probabilistic and lattice-gas CA are presented. With the so-called mean-field approximation any CA model can be transformed into a deterministic model with continuous state space. CA rules, which characterise movement, single-component growth and many-component interactions are designed and explored. It is demonstrated that lattice-gas CA offer a suitable tool for modelling such processes and for analysing them by means of the corresponding mean-field approximation. In particular two types of many-component interactions in lattice-gas CA models are introduced and studied. The first CA captures in abstract form the essential ideas of activator-inhibitor interactions of biological systems. Despite of the automaton´s simplicity, self-organised formation of stationary spatial patterns emerging from a randomly perturbed uniform state is observed (Turing pattern). In the second CA, rules are designed to mimick the dynamics of excitable systems. Spatial patterns produced by this automaton are the self-organised formation of spiral waves and target patterns. Properties of both pattern formation processes can be well captured by a linear stability analysis of the corresponding nonlinear mean-field (Boltzmann) equations.