  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.
