Early warning signs of regime shifts in complex systems: limitations and best approaches (Invited)

Many systems at many scales, from individual populations to global climate can potentially undergo sudden large shifts in state in response to small changes in driving parameters. I will begin with a presentation of the kinds of systems, from a mathematical view, that can produce dramatic changes in state in response to small underlying parameter changes. I will then illustrate systems that can exhibit sudden changes in system state but cannot possibly exhibit early warning signs. I will discuss approaches based on model fitting that allow clear statistical approaches to prediction of regime shifts, illustrating with a variety of systems. I will finish with a discussion of open problems.