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 robust coexistence of a discontinuous tree layer superimposed on a continuous grass layer. Savannas 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´´, Sarmiento(1984). Several studies have suggested that adult trees can protect vulnerable juveniles from fire, thus increasing their enhances of survival. Exactly how such protection works has not been intensively studied. However, given the frequent occurrence of fires in many savannas, it seems likely that the protection effect may be one of the most common forms of positive facilitation among savanna trees. Alternatively, many studies have documented the importance of competition among trees in diverse savannas. In a previous paper, Calabrese et al(2010), studied the interaction between competition and fire in a highly simplified savanna model. They showed that these two forces interact non-linearly with sometimes surprising consequences for tree population density and spatial pattern. However, because Calabrese et al.(2010), treated fire in a non-spatially explicit manner, they did not study the protection effect, and thus could not fully tease apart how these contrasting of local interact ions function in combination. In the present work, a model is proposed to combine the previous savanna model, with the Drossel-Schwabl(1992) 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 (tree-grass coexistence and its robustness) and spatial pattern.

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