RT Journal Article
SR Electronic
T1 Pushed beyond the brink: Allee effects, environmental stochasticity, and extinction
JF bioRxiv
FD Cold Spring Harbor Laboratory
SP 004887
DO 10.1101/004887
A1 Gregory Roth
A1 Sebastian J. Schreiber
YR 2014
UL http://biorxiv.org/content/early/2014/05/07/004887.abstract
AB 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 (the population tends to remain bounded away from extinction for all positive initial conditions), asymptotic extinction (the population tends to extinction for all initial conditions), and conditional persistence (the population persists or goes extinct with positive probability for some initial conditions). 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.