Survival of the Resilient: An Exploration of Tipping Cascades with Positive Change

The most important global challenges in these uncertain times can be characterized by critical transitions – for instance, political instability, loss of biodiversity, and climate change. Critical transitions in complex systems, the sudden and abrupt changes that occur at tipping points when thresholds are passed, are at the heart of many different phenomena in ecology and evolution. How does noise-induced tipping impact the transition of a system between dynamic regimes? What are the roles of noise and network connectivity in the detection of early-warning signals? Can tipping be used to generate a positive cascade of behaviors? In this dissertation, I address all of these central questions in the context of a specific model system. First, I use a minimal, individual-based stochastic model to show how demographic stochasticity affects the dynamics of a cascade of tipping elements. Next, I develop a fast-slow stochastic model to explain the critical interplay between environmental noise and network connectivity in forecasting a tipping cascade. In the last chapter, I turn toward a useful ecological application of the work described thus far, in the context of invasive species eradication