Mean exit times as global measure of resilience of tropical forest systems under climatic disturbances—Analytical and numerical results

Both remotely sensed distribution of tree cover and models suggest three alternative stable vegetation states in the tropics: forest, savanna, and treeless states. Environmental fluctuation could cause critical transitions from the forest to the savanna state and quantifying the resilience of a given vegetation state is, therefore, crucial. While previous work has focused mostly on local stability concepts, we investigate here the mean exit time from a given basin of attraction, with partially absorbing and reflecting boundaries, as a global resilience measure. We provide detailed investigations using an established model for tropical tree cover with multistable precipitation regimes. We find that higher precipitation or weaker noise increases the mean exit time of the forest state and, thus, its resilience. Upon investigating the transition times from the forest state to other tree cover states, we find that in the bistable precipitation regime, the size of environmental fluctuations has a greater impact on the transition probabilities from the forest state compared to precipitation.