John Realpe-Gomez, Mara Baudena, Tobias Galla, Alan J. McKane, Max Rietkerk
The scarcity of water characterizing 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. To date these phenomena have mostly been studied with models representing plants by a density of biomass, varying continuously in time and space. Such models disregard the discrete nature of plant individuals and their intrinsically stochastic behaviour. These features give rise to demographic noise, which 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.
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http://arxiv.org/abs/1209.2588
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