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.

中文翻译：

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间歇性渗流与植被簇的无标度分布

了解空间植被格局的原因和影响是生态学中的一个基本问题，特别是因为这些可以用作荒漠化过程等灾难性转变的早期预测指标。对某些地区（如旱地和半干旱地区）植被覆盖的实证研究表明，存在大小不一的植被斑块。特别是，斑块大小的概率分布可以通过幂律拟合，即植被斑块在达到某个最大尺寸时近似无标度。已经提出了不同的解释机制，例如植物 - 植物相互作用和植物 - 水反馈回路，以使这种无标度模式的出现合理化，但尚未完全理解。使用一个简单的植被动态模型，我们表明，环境时间变化——半干旱环境的一个公认的特征——以一种稳健的方式（即对于广泛的参数值）促进了具有广泛分布的集群大小的植被斑块的出现。此外，该结果与以间歇或波动方式发生的渗透现象有关。该模型还表明，拟合概率分布尾部的幂律指数取决于整体植被覆盖密度，这与经验观察一致。这支持环境可变性在无标度植被模式的形成中起着关键作用的观点。从实践的角度来看，这对于预测环境条件变化可能对真实生态系统产生的影响可能很重要。从理论上来说，