Fig. 8. Population dynamics model of agricultural regime shifts.

a. Making the sustainable curve (see Figure 5), nonmonotonic. If the population density is at the dotted line that is intercepted by either point 1 or point 2, either the higher or lower equilibrium could be reached. Which equilibrium actually is attained depends on where the system is on the other axis, such that point 1 will move to the higher equilibrium, and point 2 will move to the lower equilibrium.

b. Representing the graph in a. with the axes reversed and plotting the equilibrium values. The dotted curve is superimposed illustrating that the results of the model are qualitatively the same as the previous model with alternative equilibria and a zone of hysteresis.

Fig. 8