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Resonant population cycles in temporally fluctuating habitats

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Abstract

Experiments with the flour beetle Tribolium have revealed that animal numbers were larger in cultures grown in a periodically fluctuating volume of medium than in cultures grown in a constant volume of the same average size. In this paper we derive and analyze a discrete stage-structured mathematical model that explains this phenomenon as a kind of resonance effect. Habitat volume is incorporated into the model by the assumption that all rates of cannibalism (larvae on eggs, adults on eggs and pupae) are inversely proportional to the volume of the culture medium. We tested this modeling assumption by conducting and statistically analyzing laboratory experiments. For parameter estimates derived from experimental data, our model indeed predicts, under certain circumstances, a larger (cycle-average) total population abundance when the habitat volume periodically fluctuates than when the habitat volume is held constant at the average volume. The model also correctly predicts certain phase relationships and transient dynamics observed in data. The analyses involve a thorough integration of mathematics, statistical methods, biological details and experimental data.

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Authors and Affiliations

  1. Department of Biological Sciences, University of Rhode Island, Kingston, 02881, USA

    R. F. Costantino

  2. Department of Mathematics, Interdisciplinary Program in Applied Mathematics, University of Arizona, Tucson, AZ, 85721, USA

    J. M. Cushing

  3. Department of Fish and Wildlife Resources and Division of Statistics, University of Idaho, Moscow, ID, 83844, USA

    Brian Dennis

  4. Department of Biology and Microbiology, California State University, Los Angeles, CA, 90032, USA

    Robert A. Desharnais

  5. Department of Mathematics, University of Arizona, Tucson, AZ, 85721, USA

    Shandelle M. Henson

Authors
  1. R. F. Costantino
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  2. J. M. Cushing
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  3. Brian Dennis
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  4. Robert A. Desharnais
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  5. Shandelle M. Henson
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Correspondence to J. M. Cushing.

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Costantino, R.F., Cushing, J.M., Dennis, B. et al. Resonant population cycles in temporally fluctuating habitats. Bull. Math. Biol. 60, 247–273 (1998). https://doi.org/10.1006/bulm.1997.0017

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  • DOI: https://doi.org/10.1006/bulm.1997.0017

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