17 May 2019
Department of Mathematics
North Carolina A & T State University
Anticipating abrupt changes in ecosystem state is key for ecosystem management and preservation. Detailed knowledge of ecological mechanisms behind a critical transition is often difficult to attain. In ecology, the theory of resilience — assessment of the ability of a system to withstand disturbances — provides a pathway to circumvent this problem. If a system is gradually approaching a tipping point, the loss of system resilience manifests as critical slowing down. Critical slowing down can be detected using summary statistics, called early warning indicators. We will illustrate the theory of early warning indicators with a series of models that represent fundamental ecological processes (e.g. density-dependence), are amenable to mathematical analysis, and are generalizable to other biological systems. The analyses provide theoretical predictions about the behavior of system state fluctuations near a tipping point. Specifically, we will elucidate the impact of intrinsic and extrinsic noise and spatial structure on early warning indicators. Finally, we discuss advantages and limitations of early warning indicators based on critical slowing down, and how a mathematical foundation is necessary to draw conclusions from summary statistics obtained from a system near a tipping point.
current theory lunch schedule