Our discussions of linear stability analysis included spatial considerations this week, opening up the floor to a diverse set of real-world examples. We first explored the interactions of activators and inhibitors and how diffusion or propagation of information can lead to pattern formation. Some spatial self-organization patterns include power-law clustering where processes occurring at one scale operate at all scales — therefore the power law always applies and spatial patterns exhibit ‘omnipresent’ self-organization. While Sole and Bascompte revealed many biotic-abiotic interactions that exhibit activator and inhibitor spatial patterns, we discussed examples of more purely abiotic patterns such as freeze-thaw cycles and wind-driven dune systems. Human societies may also fall into activator-inhibitor patterns of spatial organization where different agricultural systems (and their various scales of infrastructure) came to mind. If more than two scales of inhibition are present, the system may full under hierarchy theory where meta-patterning emerges — perhaps a ripe area for research.
In thinking about how to apply these ideas, we discussed how patterns may erase or reveal historic evolution of complex systems — with an example of how paleoecology helped unravel the mystery of ridge formation in the Everglades. In designing agricultural systems or restoration projects for resilience of landscape function, we contemplated hedgerows, windbreaks, and contour swales. Yet understanding catastrophic shifts and defining optimal length scales of restoration continue to pose challenges.
Link to detailed notes.