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Allee effects and stochasticity.
Dennis, Brian1, 1
ABSTRACT- An Allee effect, or positive density dependence, could seriously increase a population's risk of extinction. Theoretical studies of Allee effects have been predominantly deterministic and have featured population models that typically display a lower unstable equilibrium (critical population size) below which extinction is certain. In this presentation, I discuss the combination of stochastic forces with Allee effects, using the general stochastic models known as diffusion processes. The probability of reaching a lower population size a before reaching an upper size b, when considered as a function of initial population size, has an inflection point at the underlying deterministic unstable equilibrium. The inflection represents a threshold in the probabilistic prospects for the population and is independent of the type of stochastic fluctuations (e.g. demographic or environmental). Demographic noise alone (absent Allee effects), although considered an "extinction vortex," does not produce such threshold behavior. Formulating the problem in a stochastic framework is a key to testing for an Allee effect in species translocation or colonization data. The results provide a new understanding of the interplay of stochastic and deterministic forces in ecological populations.
KEY WORDS: Allee effect, depensation, inverse density dependence, positive density dependence