Non-linear and non-local plant-plant interactions in arid climate: Allometry, criticality and desertification

We present a model that considers the non-linear and non-local facilitative and competitive interactions in arid and semiarid climates. These two botanical processes are interconnected and operate at different spatial scales. Seed dispersal is modeled as a diffusion process. We consider landscapes populated by a dominant species to be isotropic.and homogeneous environmental conditions. We included the allometric factor in the modeling, considering the age classes. We show that allometry tends to move the critical and tipping points towards a low level of aridity. This alteration of aridity conditions can prevent desertification and thus avoid vegetation collapse. Unlike other interaction redistribution models, we show that even in the absence of allometry, critical and tipping points have a finite biomass. Consequently, a branch of low-biomass density is stabilized. Finally, we show that the allometric factor reduces the range of symmetry-breaking instability and favors the formation of homogeneous cover rather than vegetation patterns.