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

Figure 3

From the merged state space (a), it is possible to draw a tentative potential-like surface (b). In the merged version (a) of the full termite state space (Figure 2), each SCC and basin has been reduced to a single node and redundant paths have been removed. Nodes representing SCCs or basins (i.e., aggregate states) are noted (s) (circles) and labeled with the components present in all their states. From this reduction of the state space, specific paths leading to the main ecosystem collapses (squares), and highlighting the sharp transitions between them, can be more easily identified. For the potential surface (b), each structural stability (SCC, e.g., B and B′) has been represented as a well with a width corresponding to its number of states and a depth corresponding to the maximum number of steps for escaping it. The deadlocks (e.g., D and D′) are bottomless wells and are connected to other topological features with a continuous surface and sometimes through tipping points (C) (red arrow). We explain in the main text why such a representation is fallacious, though.

(a)

(b)