Dispersal-induced resilience to stochastic environmental fluctuations in populations with Allee effect

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Rodrigo Crespo-Miguel, Estructura de la Materia, Física Térmica y Electrónica, Universidad Complutense de Madrid, Madrid, Spain and Francisco J. Cao-García, IMDEA Nanoscience, Madrid, Spain

Background/Question/Methods
Many species are unsustainable at small population densities (Allee Effect), i.e., below a threshold named Allee threshold, the population decreases instead of growing. In a closed local population, environmental fluctuations always lead to extinction. Field researches have shown the impact of the Allee effect on populations of plants and animals that, for different causes, have decreased below the Allee threshold. Many of these depleted populations never recover and become extinct in some years. Some depleted populations take many years (much more than the average lifetime of the species) to get out of this situation and eventually recover. We compute the stationary population probability distributions in the mean-field limit (large dispersal distance), which elucidate the spatially extended population dynamics for finite dispersal distance, and we compare it with simulations that mimic the evolution of the population. This results clarify the conditions for sustainability in spatially extended habitats, quantifying the effects of dispersal in the resilience to stochastic environmental fluctuations.
Results/Conclusions
Here, we show how, in spatially extended habitats, dispersal can lead to a sustainable population in a region, provided the amplitude of environmental fluctuations is below an extinction threshold. We have identified two types of sustainable populations: high-density and low-density populations (through a mean-field approximation, valid in the limit of large dispersal length). Our results show that patches, where population is high, low or extinct, coexist when the population is close to global extinction (even for homogeneous habitats). The extinction threshold is maximum for characteristic dispersal distances much larger than the spatial scale of synchrony of environmental fluctuations. The extinction threshold increases proportionally to the squared root of the dispersal rate and decreases with the Allee threshold. The low-density population solution can allow understanding non-recovery events after harvesting. This theoretical framework provides a novel approach to address other factors, such as habitat fragmentation or harvesting, impacting population resilience to environmental fluctuations.