Use of recurrence analysis to measure the dynamical stability of a multi-species community model

The European Physical Journal Special Topics volume 164, pages 117–126 (2008)Cite this article

Abstract

Quantifying the effects of species richness and environmental disturbance on the stability of communities is a long-standing challenge in ecology. In this study, multivariate recurrence analysis was used to assess the dynamical stability of modelled ecological communities subject to random, correlated environmental noise. Based on an analysis of biomass time series for each species, we show that two measures computed from the joint recurrence matrix, the Kolmogorov entropy and percent determinism, capture aspects of community stability that are not detected using the coefficient of variation for the whole community. In particular, when population fluctuations are correlated in time, recurrence analysis is a superior method for detecting the stabilizing effect of species richness on a community. We conclude that recurrence analysis is an appropriate tool for the analysis of ecological data, and that it may be particularly useful for detecting the relative importance of exogenous and endogenous drivers on the dynamics of ecological communities.

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

43,34 €

Tax calculation will be finalised during checkout.

References

  1. J.W. Dippner, R. Heerkloss, J.P. Zbilut, Marine Ecol. Progr. Ser. 242, 29 (2002)

    Google Scholar 

  2. J.-P. Eckmann, S. Kamphorts, D. Ruelle, Europhys. Lett. 4, 973 (1987)

    Google Scholar 

  3. P. Faure, H. Korn, Physica D 122, 265 (1998)

    Google Scholar 

  4. H.C. Godfray, S.P. Blythe, Philos. Trans. Royal Soc. London B 330, 221 (1990)

    Google Scholar 

  5. A. Gonzalez, J.B. Descamps, Oikos 106, 105 (2004)

    Google Scholar 

  6. R.L. Habeeb, J. Trebilco, S. Wotherspoon, C.R. Johnson, Ecolog. Monogr. 75, 467 (2005)

    Google Scholar 

  7. A. Hastings, TREE 19, 39 (2004)

  8. A. Hastings, C.L. Hom, S. Ellner, P. Turchin, C.H. Godfray, An. Rev. Ecolog. System. 24, 1 (1993)

    Google Scholar 

  9. A.R. Ives, K. Gross, J.L. Klug, Science 286, 542 (1999)

    Google Scholar 

  10. A.R. Ives, J.B. Hughes, Amer. Nat. 159, 388 (2002)

    Google Scholar 

  11. C.L. Lehman, D. Tilman, Amer. Nat. 156, 534 (2000)

    Google Scholar 

  12. J. Lhomme, T. Winkel, Theor. Pop. Biol. 62, 271 (2002)

    Google Scholar 

  13. N. Marwan, M.C. Romano, M. Thiel, J. Kurths, Phys. Rep. 438, 237 (2007)

    Google Scholar 

  14. N. Marwan, N. Wessel, U. Meyerfeldt, A. Schirdewan, J. Phys. Rev. E 66, 026702 (2002)

    Google Scholar 

  15. R.M. May, Stability and Complexity in Model Ecosystems (Princeton Univ. Press, 1973)

  16. K. McCann, Nature 438, 228 (2000)

  17. J. McGrady-Steed, P.J. Morin, Ecology 438, 361 (2000)

    Google Scholar 

  18. S. Naeem, Conserv. Biol. 12, 39 (1998)

    Google Scholar 

  19. J.M. Nichols, S.T. Trickey, M. Seaver, Mech. Syst. Sign. Proc. 12, 421 (2006)

    Google Scholar 

  20. L. Parrott, Ecolog. Complex. 1, 111 (2004)

  21. M. Pascual, S. Levin, Ecology 80, 2225 (1999)

    Google Scholar 

  22. S.L. Pimm, Nature 307, 322 (1984)

  23. D. Rand, H. Wilson, Proc. R. Soc. London B 111 (1995)

  24. M.C. Romano, M. Thiel, J. Kurths, W. von Bloh, Phys. Lett. A 330, 214 (2004)

    Google Scholar 

  25. F. Royer, J.M. Fromentin, Marine Ecol. Progr. Ser. 319, 237 (2006)

    Google Scholar 

  26. C.F. Steiner, Freshwater Biol. F 50, 105 (2005)

    Google Scholar 

  27. F. Takens, Dynamical Systems and Turbulence (Springer Berlin, 1980), p. 366

  28. M. Thiel, M. Romano, P. Read, J. Kurths, Chaos 14, 234 (2004)

    Google Scholar 

  29. D. Tilman, P.B. Reich, J.M.H. Knops, Nature 14, 629 (2006)

    Google Scholar 

  30. W. von Bloh, M.C. Romano, M. Thiel, Nonlinear Proc. Geophys. 12, 471 (2005)

    Google Scholar 

  31. J.P. Zbilut, A. Giuliani, C.L. Webber Jr., Phys. Lett. A 267, 174 (2000)

    Google Scholar 

  32. J.P. Zbilut, N. Thomasson, C.L. Webber Jr., Med. Eng. Phys. 24, 53 (2002)

    Google Scholar 

Download references

Author information

Affiliations

  1. Department of Geography, University of Montreal, Complex Systems Laboratory, CP. 6128 succursale Centre-ville, Montreal, QC, H3C 3J7, Canada

    R. Proulx & L. Parrott

  2. Applied Mathematics and Industrial Engineering, École Polytechnique de Montréal, Montréal, QC, Canada

    P. Côté

Authors
  1. R. Proulx
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P. Côté
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. L. Parrott
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to R. Proulx.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Proulx, R., Côté, P. & Parrott, L. Use of recurrence analysis to measure the dynamical stability of a multi-species community model. Eur. Phys. J. Spec. Top. 164, 117–126 (2008). https://doi.org/10.1140/epjst/e2008-00838-0

Download citation

Keywords

  • Species Richness
  • European Physical Journal Special Topic
  • Dynamical Stability
  • Multivariate Time Series
  • Recurrence Plot