Abstract:
The dynamics of some systems are directional, meaning that the state of a system can be characterized by a function that increases in time. This includes, for example, the growth of entropy in physical systems, or the growth of fitness in certain formulations of Darwinian evolution. Yet even when directionality holds, it might be sensitive to perturbations, such as external driving of physical systems, or interactions in evolutionary dynamics.
I'll describe a model of ecosystem dynamics which features a phase-transition, from a phase where directionality is sensitive to a phase where it is robust. This has far reaching consequences: In the latter phase, the system admits many meta-stable states, that are able to expand in space, leading to selection over ecosystem states, in analogy with Darwinian selection.