Scale dependence and patch size distribution: clarifying patch patterns in Mediterranean drylands

Abstract

In drylands, the underlying vegetation structure is associated with ecosystem functioning and ecosystem resilience. Although scale-dependent patterns are also predicted, empirical evidence often demonstrates that patch sizes are distributed according to a power-law probability distribution function or truncated power-law probability distribution function for a varied range of environmental conditions. Using satellite images and field measures, we assessed the spatial pattern of vegetation patches for a wide range of vegetation cover values in a large set of Mediterranean dryland (MDL) plots, focusing on the statistical distribution function that better fits the patch sizes. We found that power-law or truncated power-law probability distribution function does not always fit the observed patch size frequencies, while lognormal probability density function always fit well to them, implying that the vegetation structure is scale dependent for a large range of conditions. We show how the sampling approach, fit methods, and system dimensionality can affect the patch size distribution, which can explain some conflicting evidence obtained from the empirical data. Our findings question the robustness of criticality as the underlying mechanism driving vegetation patterns in MDLs. The better fit to patch size distribution provided by lognormal as compared with power-law indicates that multiplicative effects of multivariate local influences underlie pattern formation, and suggests that the role of plant–plant facilitation can be overestimated for a large range of conditions.