Abstract: Ecosystems are composed of hundreds to thousands of species whose physiology and interactions are mediated by habitat structure, fluctuating environments, and individual trait distributions. We rarely have data on all of the relevant state variables and generally lack fundamental theories or first principles that can be used to constrain predictions of future states or inform management actions. As a consequence, there is a clear need for data-driven approaches for sparsely observed systems. Nonlinear forecasting based on time-delay embedding offers one possible solution. Here I will describe delay embedding and some recent developments extending these tools to non-stationary and driven systems. I will close with a re-evaluation of the frequency of chaos in natural populations.
Speaker Bio: Stephan Munch is an Adjunct Professor with the University of California in the departments of Applied Mathematics and Ecology, Evolution and Behavior. He received a Ph.D. in Oceanography from Stony Brook University in 2002, did a postdoctoral fellowship in Applied Math and Statistics at UCSC from 2002-2005, and is currently employed with NOAA Fisheries. His research interests include nonlinear dynamics, Gaussian process machine learning, and ecosystem management.