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Persistence of structured populations in random environments

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  • Benaïm, Michel
  • Schreiber, Sebastian J.

Abstract

Environmental fluctuations often have different impacts on individuals that differ in size, age, or spatial location. To understand how population structure, environmental fluctuations, and density-dependent interactions influence population dynamics, we provide a general theory for persistence for density-dependent matrix models in random environments. For populations with compensating density dependence, exhibiting “bounded†dynamics, and living in a stationary environment, we show that persistence is determined by the stochastic growth rate (alternatively, dominant Lyapunov exponent) when the population is rare. If this stochastic growth rate is negative, then the total population abundance goes to zero with probability one. If this stochastic growth rate is positive, there is a unique positive stationary distribution. Provided there are initially some individuals in the population, the population converges in distribution to this stationary distribution and the empirical measures almost surely converge to the distribution of the stationary distribution. For models with overcompensating density-dependence, weaker results are proven. Methods to estimate stochastic growth rates are presented. To illustrate the utility of these results, applications to unstructured, spatially structured, and stage-structured population models are given. For instance, we show that diffusively coupled sink populations can persist provided that within patch fitness is sufficiently variable in time but not strongly correlated across space.

Suggested Citation

  • Benaïm, Michel & Schreiber, Sebastian J., 2009. "Persistence of structured populations in random environments," Theoretical Population Biology, Elsevier, vol. 76(1), pages 19-34.
    • Handle: RePEc:eee:thpobi:v:76:y:2009:i:1:p:19-34
    DOI: 10.1016/j.tpb.2009.03.007
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    References listed on IDEAS

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    1. Dai, Jack Jie, 2000. "A result regarding convergence of random logistic maps," Statistics & Probability Letters, Elsevier, vol. 47(1), pages 11-14, March.
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    Cited by:

    1. Barraquand, Frédéric & Yoccoz, Nigel G., 2013. "When can environmental variability benefit population growth? Counterintuitive effects of nonlinearities in vital rates," Theoretical Population Biology, Elsevier, vol. 89(C), pages 1-11.
    2. Ellner, Stephen P. & Schreiber, Sebastian J., 2012. "Temporally variable dispersal and demography can accelerate the spread of invading species," Theoretical Population Biology, Elsevier, vol. 82(4), pages 283-298.
    3. Bansaye, Vincent & Lambert, Amaury, 2013. "New approaches to source–sink metapopulations decoupling demography and dispersal," Theoretical Population Biology, Elsevier, vol. 88(C), pages 31-46.
    4. Blanquart, François, 2014. "The demography of a metapopulation in an environment changing in time and space," Theoretical Population Biology, Elsevier, vol. 94(C), pages 1-9.
    5. Barraquand, Frédéric & New, Leslie F. & Redpath, Stephen & Matthiopoulos, Jason, 2015. "Indirect effects of primary prey population dynamics on alternative prey," Theoretical Population Biology, Elsevier, vol. 103(C), pages 44-59.
    6. Schreiber, Sebastian J., 2020. "When do factors promoting genetic diversity also promote population persistence? A demographic perspective on Gillespie’s SAS-CFF model," Theoretical Population Biology, Elsevier, vol. 133(C), pages 141-149.
    7. Barraquand, Frédéric & Gimenez, Olivier, 2019. "Integrating multiple data sources to fit matrix population models for interacting species," Ecological Modelling, Elsevier, vol. 411(C).

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