Threshold dynamics of a stochastic single species model with two component Allee effects

This paper establishes a stochastic population model incorporating two component Allee effects. For the deterministic model, we rigorously prove the existence and stability of equilibria. For the stochastic model, we derive the stochastic net reproductive rate $R_0^s$, serving as a sharp threshold, that is, if $R_0^s<1$, the population is extinct almost surely, while $R_0^s>1$ results in the population being strongly stochastically permanent.