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, and the theory of resilience - assessment of the ability of a system to withstand disturbances - provides a pathway to circumvent this problem. Loss of system resilience is referred to as critical slowing down if the system is approaching a tipping point on a long time scale. Critical slowing down can be detected using summary statistics, called early warning indicators. Here, we review basic models of critical transitions and discuss advantages and limitations of early warning indicators based on critical slowing down. We introduce reactivity, which characterizes the amplification of an initial response of a system to a disturbance, as a new early warning indicator of loss of stability prior to a critical transition. We test the performance of reactivity using epidemic models approaching elimination and emergence through a simulation study.
Results/Conclusions
We show how basic stochastic models predict behavior of leading indicators of critical transitions, and describe how the form of noise can affect predictions of patterns in variance prior to a critical point. Next, we show how reactivity takes advantage of short term system behavior by changing systematically prior to elimination and emergence in infectious disease systems. The results of the simulation study indicate that predictions for reactivity patterns are robust. Finally, we discuss new theoretical directions for anticipating ecological transitions, including the use of alternative modeling approaches to stochastic differential equations, noise-induced transitions, and the inclusion of feedbacks between behavior of agents and the ecological systems they occupy.