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A demographic Allee effect occurs when individual fitness, at low densities,increases with population density. Coupled with environmental fluctuations indemographic rates, Allee effects can have subtle effects on populationpersistence and extinction. To understand the interplay between thesedeterministic and stochastic forces, we analyze discrete-time single speciesmodels allowing for general forms of density-dependent feedbacks and stochasticfluctuations in demographic rates. Our analysis provide criteria for stochasticpersistence, asymptotic extinction, and conditional persistence. Stochasticpersistence requires that the geometric mean of fitness at low densities isgreater than one. When this geometric mean is less than one, asymptoticextinction occurs with a high probability whenever the initial populationdensity is low. If in addition the population only experiences positivedensity-dependent feedbacks, conditional persistence occurs provided thegeometric mean of fitness at high population densities is greater than one.However, if the population experiences both positive and negativedensity-dependent feedbacks, conditional persistence is only possible iffluctuations in demographic rates are sufficiently small. Applying our resultsto stochastic models of mate-limitation, we illustrate counter-intuitively thatthe environmental fluctuations can increase the probability of persistence whenpopulations are initially at low densities, and decrease the likelihood ofpersistence when populations are initially at high densities. Alternatively,for stochastic models accounting for predator saturation and negativedensity-dependence, environmental stochasticity can result in asymptoticextinction at intermediate predation rates despite conditional persistenceoccurring at higher predation rates.

Pushed beyond the brink: Allee effects, environmental stochasticity, and extinction