Theoretical Ecology

, Volume 7, Issue 4, pp 381–390 | Cite as

Distinguishing intrinsic limit cycles from forced oscillations in ecological time series

  • Stilianos LoucaEmail author
  • Michael Doebeli


Ecological cycles are ubiquitous in nature and have triggered ecologists’ interests for decades. Deciding whether a cyclic ecological variable, such as population density, is part of an intrinsically emerging limit cycle or simply driven by a varying environment is still an unresolved issue, particularly when the only available information is in the form of a recorded time series. We investigate the possibility of discerning intrinsic limit cycles from oscillations forced by a cyclic environment based on a single time series. We argue that such a distinction is possible because of the fundamentally different effects that perturbations have on the focal system in these two cases. Using a set of generic mathematical models, we show that random perturbations leave characteristic signatures on the power spectrum and autocovariance that differ between limit cycles and forced oscillations. We quantify these differences through two summary variables and demonstrate their predictive power using numerical simulations. Our work demonstrates that random perturbations of ecological cycles can give valuable insight into the underlying deterministic dynamics.


Ecological cycle Environmental forcing Noise Autocovariance Power spectrum Decoherence 



This work was supported by the PIMS IGTC for Mathematical Biology and NSERC (Canada).

Supplementary material

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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Institute of Applied MathematicsUniversity of British ColumbiaVancouverCanada
  2. 2.Department of ZoologyUniversity of British ColumbiaVancouverCanada

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