Population extinction in discrete-time stochastic population models with an Allee effect

Abstract

The Allee effect is often modeled as a threshold level below which there is population extinction. A minimum population size is required for population persistence. The Allee effect has been primarily studied in deterministic models. In this investigation, we develop two discrete-time stochastic population models with an Allee effect. The stochastic models are discrete-time Markov chains with demographic stochasticity. They are based on two well-known deterministic discrete-time population models. It is shown that the conditional means of the stochastic models follow the solution dynamics of the underlying deterministic models. However, near the Allee threshold value, the dynamics of the deterministic and stochastic models differ significantly. The first model is based on the well-known Ricker population model with an Allee effect. The second model is more complex. The population is subdivided according to mating status of adults and is based on a model developed for the northern spotted owl. The dynamics of the underlying deterministic models are reviewed first, then the stochastic models are formulated. The stochastic models are new formulations. Our goal is to study the probability of population extinction in the stochastic models.