Pushed beyond the brink: Allee effects, environmental stochasticity, and   extinction
  A demographic Allee effect occurs when individual fitness, at low densities, increases with population density. Coupled with environmental fluctuations in demographic rates, Allee effects can have subtle effects on population persistence and extinction. To understand the interplay between these deterministic and stochastic forces, we analyze discrete-time single species models allowing for general forms of density-dependent feedbacks and stochastic fluctuations in demographic rates. Our analysis provide criteria for stochastic persistence, asymptotic extinction, and conditional persistence. Stochastic persistence requires that the geometric mean of fitness at low densities is greater than one. When this geometric mean is less than one, asymptotic extinction occurs with a high probability whenever the initial population density is low. If in addition the population only experiences positive density-dependent feedbacks, conditional persistence occurs provided the geometric mean of fitness at high population densities is greater than one. However, if the population experiences both positive and negative density-dependent feedbacks, conditional persistence is only possible if fluctuations in demographic rates are sufficiently small. Applying our results to stochastic models of mate-limitation, we illustrate counter-intuitively that the environmental fluctuations can increase the probability of persistence when populations are initially at low densities, and decrease the likelihood of persistence when populations are initially at high densities. Alternatively, for stochastic models accounting for predator saturation and negative density-dependence, environmental stochasticity can result in asymptotic extinction at intermediate predation rates despite conditional persistence occurring at higher predation rates. 
Gregory Roth and Sebastian Schreiber
math.PR