Allee Effects, Colonization, and Extinction: The Surprising Benefits of Demographic Stochasticity

AbstractDemographic stochasticity and Allee effects are two common mechanisms that increase extinction risk in small populations. High demographic stochasticity produces population fluctuations that cause extinction in small populations. Meanwhile, strong Allee effects create low-density thresholds, where growth rates are negative below the threshold and positive above. We hypothesized that stochastic fluctuations may drive populations over these thresholds, increasing the probability that a population establishes in a habitat. To test this hypothesis, we utilized properties of discrete-time Markov processes and a Ricker model with an Allee effect to quantify colonization and extinction rates. We show that demographic stochasticity can increase colonization rates over a range of carrying capacities in populations with strong Allee effects. In contrast, while higher demographic stochasticity always increases extinction rates of established populations, waiting times to extinction due to demographic stochasticity often exceed thousands of generations, even at relatively small carrying capacities (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>K</mml:mi><mml:mo>=</mml:mo><mml:mn>50</mml:mn></mml:mrow></mml:math>). Given the frequency of catastrophic disturbances such as fires, extinction rates from demographic stochasticity are near negligible even in small populations with strong Allee effects. Thus, the net effect of demographic stochasticity is often positive. Overall, our study provides novel insights into a mechanism through which demographic stochasticity promotes species persistence.