Stochastic resonance in climate reddening increases the risk of cyclic ecosystem extinction via phase‐tipping

Human activity is leading to changes in the mean and variability of climatic parameters in most locations around the world. The changing mean has received considerable attention from scientists and climate policy makers. However, recent work indicates that the changing variability, that is, the amplitude and the temporal autocorrelation of deviations from the mean, may have greater and more imminent impact on ecosystems. In this paper, we demonstrate that changes in climate variability alone could drive cyclic predator–prey ecosystems to extinction via so‐called phase‐tipping (P‐tipping), a new type of instability that occurs only from certain phases of the predator–prey cycle. We construct a mathematical model of a variable climate and couple it to two self‐oscillating paradigmatic predator–prey models. Most importantly, we combine realistic parameter values for the Canada lynx and snowshoe hare with actual climate data from the boreal forest. In this way, we demonstrate that critically important species in the boreal forest have increased likelihood of P‐tipping to extinction under predicted changes in climate variability, and are most vulnerable during stages of the cycle when the predator population is near its maximum. Furthermore, our analysis reveals that stochastic resonance is the underlying mechanism for the increased likelihood of P‐tipping to extinction. We demonstrate that changes in climate variability could drive cyclic ecosystems to extinction via so‐called phase‐tipping (P‐tipping), a new type of instability that occurs only from certain phases of the predator‐prey cycle. Using a mathematical model of a variable climate and realistic parameter values for the Canada lynx and snowshoe hare, we show that the likelihood of P‐tipping increases under predicted changes in climate variability due to stochastic resonance. This puts critically important species in the boreal forest (such as the Canada lynx and snowshoe hare) at increasing risk of extinction.