Resonant population cycles in temporally fluctuating habitats

R. F. Costantino, J. M. Cushing, Brian Dennis, Robert A. Desharnais, Shandelle M. Henson

Research output: Contribution to journalArticlepeer-review

60 Scopus citations


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 through integration of mathematics, statistical methods, biological details and experimental data.

Original languageEnglish (US)
Pages (from-to)247-273
Number of pages27
JournalBulletin of Mathematical Biology
Issue number2
StatePublished - Mar 1998

ASJC Scopus subject areas

  • General Neuroscience
  • Immunology
  • General Mathematics
  • General Biochemistry, Genetics and Molecular Biology
  • General Environmental Science
  • Pharmacology
  • General Agricultural and Biological Sciences
  • Computational Theory and Mathematics


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