Intermittent percolation and the scale-free distribution of vegetation clusters
Paula Villa Martín, Virginia Domínguez‐García, Miguel A. Muñoz
Abstract
Understanding the causes and effects of spatial vegetation patterns is a fundamental problem in \necology, especially because these can be used as early predictors of catastrophic shifts such as \ndesertification processes. Empirical studies of the vegetation cover in some areas such as drylands \nand semiarid regions have revealed the existence of vegetation patches of broadly diverse sizes. In \nparticular, the probability distribution of patch sizes can be fitted by a power law, i.e. vegetation \npatches are approximately scale free up to some maximum size. Different explanatory \nmechanisms, such as plant–plant interactions and plant-water feedback loops have been proposed \nto rationalize the emergence of such scale-free patterns, yet a full understanding has not been \nreached. Using a simple model for vegetation dynamics, we show that environmental temporal \nvariability—a well-recognized feature of semiarid environments—promotes in a robust way (i.e. \nfor a wide range of parameter values) the emergence of vegetation patches with broadly distributed \ncluster sizes. Furthermore, this result is related to a percolation phenomenon that occurs in an \nintermittent or fluctuating way. The model also reveals that the power-law exponents fitting the \ntails of the probability distributions depend on the overall vegetation-cover density, in agreement \nwith empirical observations. This supports the idea that environmental variability plays a key role \nin the formation of scale-free vegetation patterns. From a practical viewpoint, this may be of \nimportance to predict the effects that changes in environmental conditions may have in real \necosystems. From a theoretical side, our study sheds new light on a novel type of percolation \nphenomena occurring under temporally-varying external conditions, that still needs further work \nto be fully characterized.