  The classical fold bifurcation is a paradigmatic example of a critical
transition. It has been used in a variety of contexts, including in particular
ecology and climate science, to motivate the role of slow recovery rates and
increased autocorrelations as early-warning signals of such transitions.
  We study the influence of external forcing on fold bifurcations and the
respective early-warning signals. Thereby, our prime examples are
single-species population dynamical models with Allee effect under the
influence of either quasiperiodic forcing or bounded random noise. We show that
the presence of these external factors may lead to so-called non-smooth fold
bifurcations, and thereby has a significant impact on the behaviour of the
Lyapunov exponents (and hence the recovery rates). In particular, it may lead
to the absence of critical slowing down prior to population collapse. More
precisely, unlike in the unforced case, the question whether slow recovery
rates can be observed or detected prior to the transition crucially depends on
the chosen time-scales and the size of the considered data set.
