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

1. Recent empirical and theoretical analyses have suggested that biomes could correspond to alterna- tive equilibrium states; one such example is the transition between forest, savanna and treeless states. 2. Fire supposes to be a key functional component of savanna ecosystems and is a powerful predic- tor of tree cover that can differentiate between forest and savanna ecosystems. Interestingly, empiri- cal 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. 3. 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. 4. 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. 5. 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. 6. 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.