Fig. 1. A) Illustration of a hysteresis effect for a shrub-grass savanna. Initially, grazing has little effect on grass biomass, but eventually a threshold is reached at which a slight increase in grazing (T2) causes an ecological regime shift to a situation of low grass-high shrub biomass. Decreasing the grazing only slightly will not suffice to recover the high grass biomass state; it must be decreased to a value T1 before the grassland savanna is restored. The dotted line between the upper and lower branches represents an unstable equilibrium. States of the system above this dotted line and between T1 and T2 will reach the grassy savanna or upper branch, whereas those below will result in the woody savanna or lower branch. The arrow represents a state excursion that crosses this second type of threshold (the dotted line), resulting in a switch from grassy to woody savanna. B) A transition from a grassy to woody savanna in the absence of a hysteretic effect. Changes in grazing pressure lead to a relatively smooth transition from grassy to woody savanna, with little apparent irreversibility (but see text).