Quasi-ergodic Analysis of a Stochastic Model with Two-Component Allee Effects

We develop a stochastic diffusion model with two component Allee effects via a continu- um limit of a discrete Markov process. The boundary classification proves that zero is exit and infinity is entrance. Using intrinsic ultracontractivity of the associated semigroup, we establish the existence and uniqueness of a quasi-ergodic distribution, characterizing metastable persistence prior to extinction. Scaling laws for the mean extinction time with respect to key parameters-initial population size, mate-finding efficiency, and predation intensity-are derived. This work provides a rigorous mathematical framework for ana- lyzing transient dynamics and extinction in populations subject to strong Allee effects and environmental stochasticity.