Transient dynamics: the key to ecological understanding

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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.