Desertification and power laws

There is an ongoing controversy on the use of the patch-size distribution as an early warning signal for abrupt shifts to a desertified state in Mediterranean arid landscapes. This controversy started with Kéfi et al.’s suggestion that, when approaching the transition point to widespread desertification, vegetation patches would switch from a power-law (PL) to a truncated power-law (TPL) distribution. Here I show that, for fundamental reasons, no untruncated power law can be found in this context, irrespective of the level of degradation. This result does not deny the importance of the findings by Kéfi et al., but means that these have to be reinterpreted by moving from the PL/TPL dichotomy to other categorizations of the patch-size distribution. Physical constraints on patch-size distributions have general interest for landscape ecology.