Understanding the causes and effects of spatial patterns of vegetation is a fundamental problem in ecology, especially because these can be used as early predictors of catastrophic shifts such as desertification processes. Empirical studies of the vegetation cover of drylands and semiarid regions have revealed the existence of vegetation patches of broadly diverse sizes , such that the probability distribution of their sizes can be fitted by a power law, i.e. vegetation patches are approximately scale free. Different explanatory mechanisms, such as plant-plant interactions and plant-water feedback loops have been proposed to justify such a finding , yet a full understanding has not been reached. Using a simple individual-based model for vegetation dynamics, we show that environmental  variability --a well-recognized characteristic feature of semiarid environments-- promotes the emergence of power-law vegetation patches in a robust way (i.e. for a broad range of parameter values)  . Furthermore, these are related to a percolation phenomenon that occurs in an intermittent or fluctuating way. The model also reveals that the emerging power-law exponents depend on the overall vegetation-cover density exhibiting the same trend as empirical data and, remarkably, the fitted exponents agree reasonably well with the ones measured in well-known empirical studies. We conclude that environmental variability plays a key role in the formation of such vegetation patterns. From a practical viewpoint, this may be of importance to predict the effects that changes in environmental conditions may have in real ecosystems. From a theoretical side our study shed new light on intermittent percolation phenomena occurring under fluctuating conditions.
Understanding the causes and effects of spatial patterns of vegetation is a fundamental problem in ecology, especially because these can be used as early predictors of catastrophic shifts such as desertification processes. Empirical studies of the vegetation cover in some areas such as drylands and semiarid regions have revealed the existence of vegetation patches of broadly diverse sizes . In particular, the probability distribution of patch sizes can be fitted by a power law, i.e. vegetation patches are approximately scale free. Different explanatory mechanisms, such as plant-plant interactions and plant-water feedback loops have been proposed to rationalize the emergence of such scale-free patterns , yet a full understanding has not been reached. Using a simple model for vegetation dynamics, we show that environmental temporal variability --a well-recognized feature of semiarid environments-- promotes in a robust way (i.e. for a broad range of parameter values) the emergence of scale-free vegetation patches . Furthermore, this observation is related to a percolation phenomenon that occurs in an intermittent or fluctuating way. The model also reveals that the emerging power-law exponents depend on the overall vegetation-cover density , in agreement with empirical observations, suggesting that environmental variability plays a key role in the formation of scale-free vegetation patterns. From a practical viewpoint, this may be of importance to predict the effects that changes in environmental conditions may have in real ecosystems. From a theoretical side , our study sheds new light on a novel type of percolation phenomenon occurring under temporally-varying external conditions.
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