Understanding Ecosystem Complexity via Application of a Process-Based State Space rather than a Potential Surface

Figure 4

Illustration of the hysteresis found in the termite ecosystem state space (a), highlighting two specific trajectories (b). The structural stability displayed is B′ (Figures 2 and 3), composed of 20 states (a) labeled with a pair n/s where n is an identifying number and s is the number of discrete steps needed to exit the B′ stability (from 0 for states defining the boundary to 3 for the maximum number of steps to reach the boundary). The edges are directed and labeled with the number of the rule that was applied to perform the transition (Table 2). One specific cycling trajectory has been chosen in the B′ stability (a) (blue and green arrows), and this hysteresis is highlighted in the plane (number of present components versus discrete steps, b left). A second trajectory is displayed in the same plane (b right) to highlight the fact that many trajectories in the state space may exhibit hysteresis.

(a)

(b)

(c)