Professor Case Western Reserve University, United States
The crossing of a tipping point is one of the reasons we may observe large and abrupt swings in population size. Tipping points have historically been understood through an equilibrium lens. For instance, tipping may refer to a once-stable state losing stability, or a large perturbation causing a population to recover to an alternative equilibrium, distinct from its pre-perturbed state. Despite these roots in equilibrium theory, transient dynamics are also central to the processes underlying tipping point crossings. For some types of tipping points, such as those that arise when an equilibrium loses stability, an understanding of transient dynamics is needed to predict how and, crucially, how quickly a population will transition to a new stable state. For other tipping points – those called “rate-dependent” – tipping occurs if an environmental change is too fast for the population to track, even if the stability properties of equilibria remain unchanged. Assessing a population’s ability to track its environment is inherently a question about transient dynamics. In this talk, I will illustrate through examples how our growing understanding of transient dynamics can be applied to the problem of tipping points to improve understanding and prediction.