  We study simple stochastic scenarios, based on birth-and-death Markovian
processes, that describe populations with Allee effect, to account for the role
of demographic stochasticity. In the mean-field deterministic limit we recover
well-known deterministic evolution equations widely employed in population
ecology. The mean-time to extinction is in general obtained by the
Wentzel-Kramers-Brillouin (WKB) approximation for populations with strong and
weak Allee effects. An exact solution for the mean time to extinction can be
found via a recursive equation for special cases of the stochastic dynamics. We
study the conditions for the validity of the WKB solution and analyze the
boundary between the weak and strong Allee effect by comparing exact solutions
with numerical simulations.
