Transient dynamics: the key to ecological understanding
Abstract: Much of classical ecological theory is focused on the long -term behavior of ecological models yet the time scales of ecological dynamics are such that a focus on asymptotic behavior is likely misguided. Ecological conclusions would likely change, but additionally much mathematical theory focuses on asymptotic behavior as well. I will begin with some of my much older work that suggests the importance of transients and some of the challenges. I will then focus on more recent work. We (now a group effort) have given a rough classification of features that produce transients similar to approaches for understanding dynamical systems, examined implications for management, and examined transients in systems where stochasticity is important. I will also explore links among non-autonomous systems, tipping points, and transients. This work opens up substantial challenges for appropriate modeling approaches.