Fire, percolation thresholds and the savanna forest transition: a neutral model approach

Recent empirical and theoretical analyses have suggested that biomes could correspond to alternative equilibrium states; one such example is the transition between forest, savanna and treeless states. Fire supposes to be a key functional component of savanna ecosystems and is a powerful predictor of tree cover that can differentiate between forest and savanna ecosystems. Interestingly, empirical evidence suggests that fire occurrence drops at a threshold tree cover near 40%. Since savannas are ecosystems characterized by a discontinuous tree canopy cover immersed in a continuous grass layer a 40% of tree cover implies around 60% cover of grasses, which are the flammable component of this ecosystem. In this article, we hypothesize that the observed common pattern of 40% tree cover versus 60% in grass cover often reported for savanna ecosystems is the outcome of a spatial phase transition associated with the existence of a critical percolation threshold for fire spread. To test this hypothesis, we developed a spatially explicit neutral metacommunity model to explore the relationship between species cover and the emergence of percolation patterns. The model is intended to emulate savanna dynamics under neutrality assumptions. Using a statistical mechanical approach, we show that a second‐order phase transition behaviour is observed for the probability that a grass species develops a percolating cluster. Using a simple finite size scaling analysis, the percolation threshold pc for our model was estimated to be in the range of 0.53–0.62. Synthesis. Our results point out that the emergence of a spatial phase transition associated with percolation is a robust result of neutral metacommunity dynamics with a critical threshold of space occupancy close to pc ˜ 0.6, which supports our hypothesis that the empirically observed 40% tree cover (60% grass cover) is associated with a percolation threshold for C₄ grasses that in turn imply the existence of a spatially connected or spanning cluster of grass cover over which fire can spread.