Power spectra reveal the influence of stochasticity on nonlinear population dynamics

Daniel C. Reuman, Robert A. Desharnais, Robert F. Costantino, Omar S. Ahmad, Joel E. Cohen

Research output: Contribution to journalArticlepeer-review

46 Scopus citations


Stochasticity alters the nonlinear dynamics of inherently cycling populations. The power spectrum can describe and explain the impacts of stochasticity. We fitted models to short observed time series of flour beetle populations in the frequency domain, then used a well fitting stochastic mechanistic model to generate detailed predictions of population spectra. Some predicted spectral peaks represent periodic phenomena induced or modified by stochasticity and were experimentally confirmed. For one experimental treatment, linearization theory explained that these peaks represent overcompensatory decay of deviations from deterministic oscillation. In another treatment, stochasticity caused frequent directional phase shifting around a cyclic attractor. This directional phase shifting was not explained by linearization theory and modified the periodicity of the system. If field systems exhibit directional phase shifting, then changing the intensity of demographic or environmental noise while holding constant the structure of the noise can change the main frequency of population fluctuations.

Original languageEnglish (US)
Pages (from-to)18860-18865
Number of pages6
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number49
StatePublished - Dec 5 2006


  • Flour beetle
  • Fourier transform
  • Strong noise
  • Tribolium
  • Weak noise

ASJC Scopus subject areas

  • General


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