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This article is concerned with a stochastic different equation which describes the evolution of a species in the presence of Allee effects. By utilizing the Feller boundary classification criteria, it is testified that the model has a unique dynamical bifurcation point Δ with the following properties: if Δ < 0 , then the zero solution of the equation is stable; if Δ > 0 , then the equation possesses a unique invariant measure with an explicit density form. Some previous studies are improved and extended. This article also utilizes the theoretical findings to probe the living situation of Painted Hunting Dogs in Africa. [ABSTRACT FROM AUTHOR]