Skip to main content

Advertisement

Log in

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

  • Published:
The European Physical Journal Special Topics Aims and scope Submit manuscript

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, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  • A. Hastings, TREE 19, 39 (2004)

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

  • K. McCann, Nature 438, 228 (2000)

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

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

    Google Scholar 

  • S.L. Pimm, Nature 307, 322 (1984)

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

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

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

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjst/e2008-00838-0

Keywords

Navigation