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Population persistence in weakly-coupled sinks

Author

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  • Pamplona da Silva, D.J.
  • Kraenkel, R.A.

Abstract

We consider a single species population obeying a saturated growth model with spatial diffusion taken into account explicitly. Strong spatial heterogeneity is considered, represented by a position dependent reproduction rate. The geometry of the problem is that of two patches where the reproductive rate is positive, surrounded by unfavorable patches where it is negative. We focus on the particular case where the population would not persist in the single patches (sinks). We find by means of an analytical derivation, supplemented by a numerical calculation, the conditions for the persistence of the population in the compound system of weakly connected patches. We show that persistence is possible even if each individual patch is a sink where the population would go extinct. The results are of particular relevance for ecological management at the landscape level, showing that small patches may harbor populations as long as the connectivity with adjacent patches is maintained. Microcosmos experiences with bacteria could be performed for experimental verification of the predictions.

Suggested Citation

  • Pamplona da Silva, D.J. & Kraenkel, R.A., 2012. "Population persistence in weakly-coupled sinks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(1), pages 142-146.
    • Handle: RePEc:eee:phsmap:v:391:y:2012:i:1:p:142-146
    DOI: 10.1016/j.physa.2011.08.029
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    References listed on IDEAS

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    1. Kraenkel, R.A. & da Silva, D.J. Pamplona, 2010. "Stochastic Skellam model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(1), pages 60-66.
    2. Kumar, Niraj & Kenkre, V.M., 2011. "Effects of gradual spatial variation in resources on population extinction: Analytic calculations for abrupt transitions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(2), pages 257-262.
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    Cited by:

    1. Pamplona da Silva, D.J., 2018. "Crossing-effect in non-isolated and non-symmetric systems of patches," Ecological Modelling, Elsevier, vol. 384(C), pages 168-172.
    2. Pamplona da Silva, D.J. & Villar, R.P. & Ramos, L.C., 2017. "Isolation effects in a system of two mutually communicating identical patches," Applied Mathematics and Computation, Elsevier, vol. 315(C), pages 494-499.

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    1. Pamplona da Silva, D.J. & Villar, R.P. & Ramos, L.C., 2017. "Isolation effects in a system of two mutually communicating identical patches," Applied Mathematics and Computation, Elsevier, vol. 315(C), pages 494-499.
    2. Pamplona da Silva, D.J., 2018. "Crossing-effect in non-isolated and non-symmetric systems of patches," Ecological Modelling, Elsevier, vol. 384(C), pages 168-172.

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