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We study simple stochastic scenarios, based on birth-and-death Markovianprocesses, that describe populations with Allee effect, to account for the roleof demographic stochasticity. In the mean-field deterministic limit we recoverwell-known deterministic evolution equations widely employed in populationecology. The mean-time to extinction is in general obtained by theWentzel-Kramers-Brillouin (WKB) approximation for populations with strong andweak Allee effects. An exact solution for the mean time to extinction can befound via a recursive equation for special cases of the stochastic dynamics. Westudy the conditions for the validity of the WKB solution and analyze theboundary between the weak and strong Allee effect by comparing exact solutionswith numerical simulations.

Demographic stochasticity and extinction in populations with Allee effect