Spatial patterns in mesic savannas: The local facilitation limit and the role of demographic stochasticity

- Minimalistic savanna model with long-range competition and fire-induced local facilitation.
- Long-time coexistence of grass and trees. Clustering of trees may appear.
- Patterns in the system are determined by the long-range kernel competition function.
- Study the influence of demographic fluctuations in the patterns.
- Realistic patterns for mesic savannas under demographic noise and parameter constraints.

We propose a model equation for the dynamics of tree density in mesic savannas which considers long-range competition among trees and the effect of fire indirectly acting as a local facilitation mechanism. Despite the fact that we take short-range facilitation to the local-range limit, the standard full spectrum of spatial structures already obtained in self-organization models of vegetation is recovered. Nonlocal competition, in the limit of infinitesimally short facilitation, promotes the clustering of trees. The long time coexistence between trees and grass, and how fires affect the survival of trees as well as the maintenance of the patterns is studied. The influence of demographic noise is analyzed. The stochastic system, under the parameter constraints typical of mesic savannas, shows non-homogeneous patterns characteristic of realistic situations. The coexistence of trees and grass still remains at reasonable noise intensities.