Resilience of Cyclic Ecosystems in the Presence of R- and P-Tipping

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Regime shifts, where a "normal" state suddenly and unexpectedly shifts to a very different one (e.g., a population that is normally abundant becomes scarce, a forest gives way to grassland), are a significant concern in the conservation of ecosystems under climate change. Mathematically, these regime shifts are caused by tipping points: A small change in a parameter causes a dynamical system to switch from one stationary base state to another. Traditionally, these tipping events are ascribed to B-tipping, i.e., the parameter crosses through a bifurcation value at which the first base state becomes unstable or disappears. Recently, however, a tipping based on rate was discovered: R-tipping between stationary base states occurs if the parameter change is fast enough, and in the absence of any classical bifurcations. Even more recently, my colleagues and I discovered P-tipping, a new type of tipping between oscillatory and stationary base states: Here it is the phase of the oscillation at the moment of parameter change that matters. These dynamic tipping behaviours typically occur before B-tipping is expected, and may thus be critically important in predicting ecosystem response to climate change. My research program is a comprehensive investigation of R- and P-tipping in predator-prey and food web models. As R- and P-tipping are only lightly explored to date, the role of these dynamic tipping processes in the survival of ecosystems is largely unknown. My students and I will therefore carry out a thorough mathematical study of R- and P-tipping in key ecosystem models. We will begin by will extending the initial work on P-tipping, which focussed on two classic predator-prey models, by examining more complex models that include other key features of ecosystems such as seasonal changes in predator behaviours, additional species (e.g., three-species food chain and food web models), and movement between habitat patches. In tackling climate change, decision-makers need to know when R- and P-tipping events will occur in ecosystems. The presence of structural sensitivity in ecological models, however, makes prediction extremely difficult, as it is unknown what mathematical functions accurately represent the species interactions and behaviours being modeled. In addition, climate change is predicted to significantly alter the mean and variability (autocorrelation, amplitude) of climate-sensitive model parameters. My research program thus includes a detailed mathematical study of structural sensitivity and temporal variation of climate-sensitive parameter values across the range of ecosystem models studied above.  This work will provide important information regarding our ability to predict when ecosystems are vulnerable to R- and P-tipping, and how likely these events are under climate change. I respectfully acknowledge that the proposed research will be done on the traditional, ancestral and unceded territory of the Syilx Okanagan Nation.