  Understanding the causes and effects of spatial vegetation patterns 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 up to some
maximum size. 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 wide range of parameter
values) the emergence of vegetation patches with broadly distributed cluster
sizes. Furthermore, this result is related to a percolation phenomenon that
occurs in an intermittent or fluctuating way. The model also reveals that the
power-law exponents fitting the tails of the probability distributions depend
on the overall vegetation-cover density, in agreement with empirical
observations. This supports the idea 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 phenomena occurring
under temporally-varying external conditions, that still needs further work to
be fully characterized.
