Fig. 2. Stylized trajectories through time of the fast (---) and slow (____) variables in lakes (thick blue lines) and rangelands (thin red lines) under high levels of phosphate inflow (lakes) and grazing (rangelands). In lakes, there is a very rapid change (“flip”) in water quality as the threshold is passed and an associated rapid decline in water quality and fish. The amount of phosphate in the mud (Pm) shows a short-term decline as phosphate becomes soluble and is lost from the mud to the water above. In rangelands, although the feedbacks change instantly at the threshold (as in Fig. 1c), the lag effect in shrub growth rate results in slow changes of the variables (G = grass; S = shrubs).

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