Savanna-Fire Model: Combined effects of tree-tree establishment competition and spatially explicit fire on the spatial pattern of trees in Savannas

Savannas are characterized by discontinuous tree layer superimposed on a
continuous grass layer.
They occur across a wide range of climatic, edaphic, and ecological
conditions, covering approximately one fifth of the earth\'s land area.
In some countries, these grass-dominated ecosystems are a principal
biotic resource playing important roles in both the configuration of
natural landscapes and in local economies.
Identifying the mechanisms that facilitate tree-grass coexistence in
savannas has remained a persistent challenge in ecology and is known as
the \"savanna problem.\" Recent empirical work suggests that both
tree-tree competition and fire are key factors in semi-arid to mesic
savannas. Fire is a natural feature of many savannas and is also
frequently used by humans as a management tool. Fire primarily affects
juvenile tree mortality rates, with adults being largely fire resistent.
In a previous paper a minimalistic stochastic cellular automata was
developed to study the individual and combined effects of competition
and fire on savannas. The model was implemented on a square lattice with
periodic boundary conditions. Each site on the lattice could be in one
of two states: grass-occupied or tree-occupied. The model showed the
relevance of the combined effects of nearby competing adults trees,
stochastic fire, and grazing on tree density and pattern formation in
savannas. However, fire was modeled in spatially implicit and uncorrelated way and tree development was modeled as an instantaneous
transition from seed to adult tree. In the present work, a model is
proposed to combine the previous savanna model with the Drossel-Schwabl
forest fire model, therefore representing fire in a spatially explicit
manner. We use the model to explore how the pattern of fire spread,
coupled with an explicit, fire-vulnerable tree life stage, affects tree
density and spatial pattern.