  Critical transitions or regime shifts are sudden and unexpected changes in
the state of an ecosystem, that are usually associated with dangerous levels of
environmental change. However, recent studies show that critical transitions
can also be triggered by dangerous rates of environmental change. In contrast
to classical regime shifts, such rate-induced critical transitions do not
involve any obvious loss of stability, or a bifurcation, and thus cannot be
explained by the linear stability analysis. In this work, we demonstrate that
the well-known Rosenzweig-MacArthur predator-prey model can undergo a
rate-induced critical transition in response to a continuous decline in the
habitat quality, resulting in a collapse of the predator and prey populations.
Rather surprisingly, the collapse occurs even if the environmental change is
slower than the slowest process in the model. To explain this counterintuitive
phenomenon, we combine methods from geometric singular perturbation theory with
the concept of a moving equilibrium, and study critical rates of environmental
change with dependence on the initial state and the system parameters.
Moreover, for a fixed rate of environmental change, we determine the set of
initial states that undergo a rate-induced population collapse. Our results
suggest that ecosystems may be more sensitive to how fast environmental
conditions change than previously assumed. In particular, unexpected critical
transitions with dramatic ecological consequences can be triggered by
environmental changes that (i) do not exceed any dangerous levels, and (ii) are
slower than the natural timescales of the ecosystem. This poses an interesting
research question whether regime shifts observed in the natural world are
predominantly rate-induced or bifurcation-induced.
