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Allee effects and resilience in stochastic populations

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Abstract

Allee effects, or positive functional relationships between a population’s density (or size) and its per unit abundance growth rate, are now considered to be a widespread if not common influence on the growth of ecological populations. Here we analyze how stochasticity and Allee effects combine to impact population persistence. We compare the deterministic and stochastic properties of four models: a logistic model (without Allee effects), and three versions of the original model of Allee effects proposed by Vito Volterra representing a weak Allee effect, a strong Allee effect, and a strong Allee effect with immigration. We employ the diffusion process approach for modeling single-species populations, and we focus on the properties of stationary distributions and of the mean first passage times. We show that stochasticity amplifies the risks arising from Allee effects, mainly by prolonging the amount of time a population spends at low abundance levels. Even weak Allee effects become consequential when the ubiquitous stochastic forces affecting natural populations are accounted for in population models. Although current concepts of ecological resilience are bound up in the properties of deterministic basins of attraction, a complete understanding of alternative stable states in ecological systems must include stochasticity.

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Acknowledgments

This work was supported by a grant from King Abdul Aziz University, Saudi Arabia.

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Authors and Affiliations

  1. University of Idaho, 875 Perimeter Drive MS 1136, Moscow, ID, 83844, USA

    Brian Dennis

  2. King Abdul Aziz University, Jeddah, Saudi Arabia

    Laila Assas

  3. Trinity University, 1 Trinity Place, San Antonio, TX, 78212, USA

    Saber Elaydi & Eddy Kwessi

  4. Southwest Research Institute, San Antonio, TX, 78238, USA

    George Livadiotis

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  1. Brian Dennis
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  2. Laila Assas
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  3. Saber Elaydi
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Correspondence to Brian Dennis.

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Dennis, B., Assas, L., Elaydi, S. et al. Allee effects and resilience in stochastic populations. Theor Ecol 9, 323–335 (2016). https://doi.org/10.1007/s12080-015-0288-2

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