Abstract
Population cycles that persist in time and are synchronized over space pervade ecological systems, but their underlying causes remain a long-standing enigma1,2,3,4,5,6,7,8,9,10,11. Here we examine the synchronization of complex population oscillations in networks of model communities and in natural systems, where phenomena such as unusual ‘4- and 10-year cycle’ of wildlife are often found. In the proposed spatial model, each local patch sustains a three-level trophic system composed of interacting predators, consumers and vegetation. Populations oscillate regularly and periodically in phase, but with irregular and chaotic peaks together in abundance—twin realistic features that are not found in standard ecological models. In a spatial lattice of patches, only small amounts of local migration are required to induce broad-scale ‘phase synchronization’12,13, with all populations in the lattice phase-locking to the same collective rhythm. Peak population abundances, however, remain chaotic and largely uncorrelated. Although synchronization is often perceived as being detrimental to spatially structured populations14, phase synchronization leads to the emergence of complex chaotic travelling-wave structures which may be crucial for species persistence.
This is a preview of subscription content, access via your institution
Access options
Subscribe to this journal
Receive 51 print issues and online access
$199.00 per year
only $3.90 per issue
Buy this article
- Purchase on Springer Link
- Instant access to full article PDF
Prices may be subject to local taxes which are calculated during checkout
Similar content being viewed by others
References
Elton, C. & Nicholson, M. The ten-year cycle in numbers of the lynx in Canada. J. Anim. Ecol. 11, 215–244 (1942).
May, R. M. Stability and Complexity in Model Ecosystems (Princeton University Press, Princeton, (1973).
Keith, L. B. Wildlife's 10-year cycle (University of Wisconsin Press, Madison, (1963).
Hanski, I., Turchin, P., Korpimaki, E. & Henttonen, H. Population oscillations of boreal rodents: regulation by mustelid predators leads to chaos. Nature 364, 232– 235 (1993).
Sinclair, A. R. E.et al. Can the solar cycle and climate synchronize the snowshoe hare cycle in Canada? Evidence from tree rings and ice cores. Am. Nat. 141, 173–198 ( 1993).
Royama, T. Analytical Population Dynamics (Chapman & Hall, London, ( 1992).
Moran, P. A. P. The statistical analysis of the Canadian lynx cycle. Aust. J. Zool. 1, 291–298 ( 1953).
Bulmer, M. G. Astatistical analysis of the 10-year cycle in Canada. J. Anim. Ecol. 43, 701–718 ( 1974).
Korpimaki, E. & Krebs, C. J. Predation and population cycles of small mammals. A reassessment of the predation hypothesis. BioScience 46, 754–764 ( 1996).
Ranta, E., Kaitala, V. & Lundberg, P. The spatial dimension in population fluctuations. Science 278, 1621–1623 ( 1997).
Schaffer, W. Stretching and folding in lynx fur returns: Evidence for a strange attractor in nature? Am. Nat. 124, 798– 820 (1984).
Rosenblum, M. G., Pikovsky, A. S. & Kurths, J. Phase synchronization of chaotic oscillators. Phys. Rev. Lett. 76, 1804–1807 (1996).
Schafer, C., Rosenblum, M. G., Kurths, J. & Abel, H. Heartbeat synchronized with ventilation. Nature 392 , 239–240 (1998).
Earn, D. J. D., Rohani, P. & Grenfell, B. Persistence, chaos and synchrony in ecology and epidemiology. Proc. R. Soc. Lond. B 265, 7– 10 (1998).
May, R. M. Simple mathematical models with very complicated dynamics. Nature 261, 459–467 ( 1976).
Stone, L. Period-doubling reversals and chaos in simple ecological models. Nature 365, 617–620 ( 1993).
Blasius, B., Neff, R., Beck, F. & Lüttge, U. Oscillatory model of Crassulacean acid metabolism with a dynamic hysteresis switch. Proc. R. Soc. Lond. B 266, 93–101 (1999).
Gurney, W. S. C., Crowley, P. H. & Nisbet, R. M. Locking life-cycles on to seasons: circle-map models of population dynamics and local adaptation. J. Math. Biol. 30, 251–279 (1992).
Hastings, A. & Powell, T. Chaos in a three-species food chain. Ecology 72, 896–903 (1991).
Gilpin, M. E. Spiral chaos in a predator–prey model. Am. Nat. 107, 306–308 (1979).
Vandermeer, J. Seasonal isochronic forcing of Lotka Volterra equations. Progr. Theor. Phys. 71, 13–28 ( 1996).
Gotelli, N. J. A Primer of Ecology (Sinauer, Massachusetts, (1995).
Pecora, L. M. & Carroll, T. L. Synchronization in chaotic systems. Phys. Rev. Lett. 64, 821 ( 1990).
Cohen, A. H., Holmes, P. J. & Rand, R. H. The nature of the coupling between segmental oscillators of the lamprey spinal generator for locomotion: a mathematical model. J. Math. Biol. 13, 345–369 (1982).
Ranta, E.et al. Solar activity and hare dynamics: A cross-continental comparison. Am. Nat. 149, 765–775 (1997).
Sinclair, A. R. E. & Gosline, M. Solar activity and mammal cycles in the northern hemisphere. Am. Nat. 149, 776–784 (1997).
Ranta, E. & Kaitala, V. Travelling waves in vole population dynamics. Nature 390, 456 ( 1997).
Stenseth, N. C., Falck, W., Bjornstad, O. N. & Krebs, C. J. Population regulation in snowshoe hare and Canadian lynx: Asymmetric food web configurations between hare and lynx. Proc. Natl Acad. Sci. USA 94, 5147–5152 ( 1997).
O'Donoghue, M.et al . Functional response of coyotes and lynx to the snowshoe hare cycle. Ecology 79, 1193– 1208 (1998).
Wolf, J. B., Swift, H. L. & Vastano, J. A. Determining Lyapunov exponents from a time series. Physica D 16, 285–317 (1982).
Acknowledgements
We thank MINERVA for their award of a Fellowship to B.B., and H. Bhasin for her comments on the manuscript.
Author information
Authors and Affiliations
Corresponding author
Supplementary Information
Rights and permissions
About this article
Cite this article
Blasius, B., Huppert, A. & Stone, L. Complex dynamics and phase synchronization in spatially extended ecological systems. Nature 399, 354–359 (1999). https://doi.org/10.1038/20676
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1038/20676
This article is cited by
-
Biomedical Image Encryption with a Novel Memristive Chua Oscillator Embedded in a Microcontroller
Brazilian Journal of Physics (2023)
-
Enhancing the emergence of hyperchaos using an indirect coupling and its verification based on digital implementation
Nonlinear Dynamics (2023)
-
A Robust Underactuated Synchronizer for a Five-dimensional Hyperchaotic System: Applications for Secure Communication
International Journal of Control, Automation and Systems (2023)
-
Emergent hypernetworks in weakly coupled oscillators
Nature Communications (2022)
-
Triple Compound Synchronization Among Eight Chaotic Systems with External Disturbances via Nonlinear Approach
Differential Equations and Dynamical Systems (2022)
Comments
By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.