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The scarcity of water characterising drylands forces vegetation to adopt appropriate survival strategies. Some of these generate water vegetation feedback mechanisms that can lead to spatial self-organisation of vegetation, as it has been shown with models representing plants by a density of biomass, varying continuously in time and space. However, although plants are usually quite plastic they also display discrete qualities and stochastic behaviour. These features may give rise to demographic noise, which in certain cases can influence the qualitative dynamics of ecosystem models. In the present work we explore the effects of demographic noise on the resilience of a model semi-arid ecosystem. We introduce a spatial stochastic eco-hydrological hybrid model in which plants are modelled as discrete entities subject to stochastic dynamical rules, while the dynamics of surface and soil water are described by continuous variables. The model has a deterministic approximation very similar to previous continuous models of arid and semi-arid ecosystems. By means of numerical simulations we show that demographic noise can have important effects on the extinction and recovery dynamics of the system. In particular we find that the stochastic model escapes extinction under a wide range of conditions for which the corresponding deterministic approximation predicts absorption into desert states. (C) 2013 Elsevier B.V. All rights reserved.