title: Pushed beyond the brink: Allee effects, environmental stochasticity, and extinction.
abstract: To understand the interplay between environmental stochasticity and Allee effects, we analyse persistence, asymptotic extinction, and conditional persistence for stochastic difference equations. Our analysis reveals that 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 high probability for low initial population densities. Additionally, if 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 only occurs if environmental fluctuations are sufficiently small. We illustrate counter-intuitively that environmental fluctuations can increase the probability of persistence when populations are initially at low densities, and can cause asymptotic extinction of populations experiencing intermediate predation rates despite conditional persistence occurring at higher predation rates.
authors.affiliation: a Department of Evolution and Ecology, One Shields Avenue , University of California , Davis , CA 95616 USA.
authors.forename: Gregory
authors.initials: G
authors.lastname: Roth
authors.forename: Sebastian J
authors.initials: SJ
authors.lastname: Schreiber
mesh_terms: D000818:Animals; D004777:Environment; D053476:Extinction, Biological; D006801:Humans; D008954:Models, Biological; D011157:Population Dynamics; D013269:Stochastic Processes
keywords: demographic Allee effect; extinction; persistence; population dynamics; positive and negative density dependence; stochastic difference equations