Quasi-ergodic analysis of a stochastic model with two-component Allee effects

Source abstract

In this paper, we develop a stochastic diffusion model with two-component Allee effects via a continuum limit of a discrete Markov process. The boundary classification shows that zero is an exit boundary and infinity is an entrance boundary. By 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 analyzing transient dynamics and extinction in populations subject to strong Allee effects and environmental stochasticity.