Discrete state changes or shifts in equilibria over spatiotemporal gradients are common in biology and ecology. A model system for the study of dynamics underlying such spatial phenomenon is the lower boundary of mytilid mussel beds in intertidal rocky shore habitat, which is at dynamic equilibrium set by sea star predation. Using an agent-based model of mussel recruitment and growth and seastar predation, this research seeks to simulate realistic boundary sharpness/intensity as emerging from realistically parameterized individual organism behaviors and physiology, and test whether this phenomenon can arise from individual-level interactions. Observed model boundary behavior is also contrasted with the findings of other (simplified, deterministic) models; this model also shows importance of neighborhood protection against predation in setting boundaries, although any effect is small and several other factors (e.g., 3-D layering of the mussel bed) greatly influence boundary behavior. Finally, contrary to some theoretical predictions, I find no evidence for an increase in overall temporal variance as the critical transition is approached.
That is an excellent presentation of a complicated problem. I cannot claim that I understood it all. There is a lot to take in.
I do have a question. You did not mention the phenomenon of percolation. I suspect that percolation is involved in this boundary formation. You have two types of areas: those dominated by mussel growth dynamics, and those dominated by sea star predation dynamics. When there is such a clearly defined boundary between the two kinds of dynamic, there must be some variable for which the critical value determines which state any particular patch will exhibit. So, here’s my question: Is it possible to identify one variable (perhaps a calculated variable) for which there is a critical value that identifies a phase change?
Thanks for your question. If you are looking for a continuous controlling parameter with a certain critical value for which there is a switch between mussel-dominated and seastar-dominated dynamics, I think that seastar desiccation tolerance (quantified in the model as relative preference for moving downward over moving up to lower depth/higher submergence) would be what you are describing. However, increasing the number of seastars (without changing individual seastars’ physiological tolerance) is known experimentally to raise the height of the mussel bed lower boundary (Paine 1966), and increasing the number of seastars would also affect the boundary in my model, as individual seastars’ movement is stochastic and more seastars would result in more predation pressure further up (at higher submergence). So local seastar numbers have to also be taken into account.