Facilitation, competition, and vegetation patchiness: from scale free distribution to patterns.

A new technique for the modeling of perennial vegetation patchiness in the arid/semiarid climatic zone is suggested. Incorporating the stochasticity that affects life history of seedlings and the deterministic dynamics of soil moisture and biomass, this model is flexible enough to yield qualitatively different forms of spatial organization. In the facilitation-dominated regime, scale free distribution of patch sizes is observed, in correspondence with recent field studies. In the competition controlled case, on the other hand, power-law statistics is valid up to a cutoff, and an intrinsic length scale appears.