Recent empirical studies have shown that savanna and forest are the two alternative biome states of global vegetation distribution. This idea is well supported by current theoretical models which show that nonlinear feedbacks between fire and grass can lead to bistability in the system. However, these models cannot explain certain empirical observations of savanna-forest distribution such as spatial aggregation of savanna and forest. In other words, a savanna patch is more likely to be found near a neighboring savanna patch and a forest patch with a neighboring forest patch, with a distinct boundary (ecotone) seperating the two vegetations. This is in contrast to our current theoretical understanding of bistable models, which predict a sporadic distribution of savanna and forest patches (null expectation) in the bistable region. This suggest that there might be a neigbour dependent effects (spatial interactions) on the distribution of savanna and forest, hitherto neglected in the theoretical literature. In this work we build a spatial version of the bistable model to study the effects of saptial interactions on the distribution of savanna and forest, using theoretical concepts developed in species invasion and phase transitions in physics
Results/Conclusions
We show that local spatial interactions coupled with a large-scale spatial gradient of rainfall can lead to spatial clustering of savanna and forest, with a stable savanna-forest boundary. Furthermore, the equilibrium position of the boundary is determined by a particular rainfall value, which we refer to as Maxwell rainfall, and the geomerical shape of this rainfall contour. Our model also suggests that spatial interactions can erode the threshold point behavior of the system, resulting in reversible biome transition with no hysteresis. This may have huge ecological and management implications as there is a growing fear among scientists that rapidly changing climate, increasing draught frequencies, deforestation, land use change and other anthropogenic activities may result in abrupt and irreversible transitions between savanna and forest. Using empirical data from Africa we show that the curvature of rainfall contours may result in a non-deterministic relationship between vegetation and rainfall, which previously was thought a consequence of hysteresis.
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